{
  "all_tier1_controls_passed": true,
  "evidence_tier": "tier_1_analytic_variational_numerics_not_outward_validated",
  "exact_query_engine_children": {
    "minimum_three_output_launch_A_clock_only": {
      "declared_nuisance_dimension": 1,
      "declared_nuisance_response_exact": [
        [
          "-205821/200000"
        ],
        [
          "525777/500000"
        ],
        [
          "-123019/50000"
        ]
      ],
      "declared_observation_exact": [
        [
          "-104679/1000000",
          "3127/100000"
        ],
        [
          "84503/1000000",
          "-454351/1000000"
        ],
        [
          "-63769/250000",
          "234819/1000000"
        ]
      ],
      "declared_output_metric_exact": [
        [
          "2/7",
          "0/1",
          "0/1"
        ],
        [
          "0/1",
          "2/7",
          "0/1"
        ],
        [
          "0/1",
          "0/1",
          "2/7"
        ]
      ],
      "declared_query_exact": [
        [
          "1/1",
          "0/1"
        ],
        [
          "0/1",
          "1/1"
        ]
      ],
      "declared_query_metric_exact": [
        [
          "1/1",
          "0/1"
        ],
        [
          "0/1",
          "1/1"
        ]
      ],
      "declared_source_metric_exact": [
        [
          "1/1",
          "0/1"
        ],
        [
          "0/1",
          "1/1"
        ]
      ],
      "effective_response_rank": 2,
      "factorization_and_minimax": {
        "amplification_lower_witness_exact": [
          "-100000000/1",
          "6338975/1"
        ],
        "decoder_annihilates_nuisance_exact": true,
        "decoder_exact": [
          [
            "870951254654000000/5790284233061149",
            "-164717324395000000/5790284233061149",
            "-434692792275000000/5790284233061149"
          ],
          [
            "-60316696964000000/5790284233061149",
            "-4949868960000000/5790284233061149",
            "23113161351000000/5790284233061149"
          ]
        ],
        "decoder_times_effective_response_equals_query_exact": true,
        "decoder_times_raw_observation_equals_query_exact": true,
        "descriptive_amplification_lower": 319.6156831382356,
        "descriptive_amplification_upper": 319.61568313823574,
        "factorization_exists": true,
        "interpretation": "For data-noise radius epsilon, the exact minimax query error is kappa*epsilon; the true kappa squared lies in the certified rational interval.",
        "kind": "identifiable-query-factorization",
        "minimax_amplification_exactly_zero": false,
        "minimax_amplification_squared_lower_exact": "231036845209387391926902536750000000000/2261648364358617795867283370931523",
        "minimax_amplification_squared_upper_exact": "271353552957363266708642812779285240324977831260063128781397733607/2656313622412568391830785344028483501162026017082516529217536",
        "quotient_injection_exact": [
          [
            "1/1",
            "0/1"
          ],
          [
            "0/1",
            "1/1"
          ]
        ],
        "quotient_row_coordinates_exact": [
          [
            "1/1",
            "0/1"
          ],
          [
            "0/1",
            "1/1"
          ]
        ],
        "quotient_source_metric_exact": [
          [
            "1/1",
            "0/1"
          ],
          [
            "0/1",
            "1/1"
          ]
        ],
        "reduced_data_gram_exact": [
          [
            "4196823363005538444097/28764024311193500000000000",
            "61764698372152652754781/28764024311193500000000000"
          ],
          [
            "61764698372152652754781/28764024311193500000000000",
            "487322854297530359225683/14382012155596750000000000"
          ]
        ],
        "reduced_effective_response_exact": [
          [
            "-6063089339742327/4109146330170500000",
            "-17247403101658309/164365853206820000"
          ],
          [
            "-6887514591536287/328731706413640000",
            "-518043114783954479/1643658532068200000"
          ],
          [
            "-8565024856920357/1027286582542625000",
            "-746340853514915841/8218292660341000000"
          ]
        ],
        "reduced_query_exact": [
          [
            "1/1",
            "0/1"
          ],
          [
            "0/1",
            "1/1"
          ]
        ],
        "reduced_query_form_exact": [
          [
            "1/1",
            "0/1"
          ],
          [
            "0/1",
            "1/1"
          ]
        ],
        "upper_shift_positive_by_exact_ldl": true
      },
      "identifiability": {
        "kernel_condition_exact": true,
        "kernel_counterexample_exact": null,
        "query_identifiable_exact": true
      },
      "independent_exact_verification": {
        "amplification_squared_lower_exact": "231036845209387391926902536750000000000/2261648364358617795867283370931523",
        "amplification_squared_upper_exact": "271353552957363266708642812779285240324977831260063128781397733607/2656313622412568391830785344028483501162026017082516529217536",
        "method": "exact rational reconstruction of the nuisance quotient, kernel condition, query factorization, and minimax amplification bracket",
        "passed": true,
        "query_identifiable": true
      },
      "model_kind": "shared_nuisance_protocol_mixture",
      "nuisance_elimination": {
        "effective_response_exact": [
          [
            "-6063089339742327/4109146330170500000",
            "-17247403101658309/164365853206820000"
          ],
          [
            "-6887514591536287/328731706413640000",
            "-518043114783954479/1643658532068200000"
          ],
          [
            "-8565024856920357/1027286582542625000",
            "-746340853514915841/8218292660341000000"
          ]
        ],
        "metric_orthogonal_projector_exact": [
          [
            "7159235559316/8218292660341",
            "1082159479170/8218292660341",
            "-2531989359900/8218292660341"
          ],
          [
            "1082159479170/8218292660341",
            "7112526845425/8218292660341",
            "2587222430520/8218292660341"
          ],
          [
            "-2531989359900/8218292660341",
            "2587222430520/8218292660341",
            "2164822915941/8218292660341"
          ]
        ],
        "nuisance_basis_exact": [
          [
            "1/1"
          ],
          [
            "-50074/49005"
          ],
          [
            "492076/205821"
          ]
        ],
        "profiled_information_exact": [
          [
            "4196823363005538444097/28764024311193500000000000",
            "61764698372152652754781/28764024311193500000000000"
          ],
          [
            "61764698372152652754781/28764024311193500000000000",
            "487322854297530359225683/14382012155596750000000000"
          ]
        ],
        "projector_annihilates_nuisance_exact": true,
        "projector_idempotent_exact": true,
        "projector_is_output_metric_self_adjoint_exact": true
      },
      "nuisance_rank": 1,
      "output_dimension": 3,
      "proof_boundary": "This certificate proves a finite-dimensional real rational linear theorem for the declared metrics, response, query, and one declared unrestricted nuisance shared across the active protocols. It does not prove that an external physical or continuum model is enclosed by these data.",
      "protocol_mixture": {
        "active_protocol_indices": [
          0
        ],
        "composition_rule": "stack active responses and nuisance maps; scale each output metric by budget_share/cost; profile the shared nuisance only after assembly",
        "inactive_zero_share_protocols_omitted_from_assembly": true,
        "nuisance_semantics": "one shared nuisance vector across every active protocol",
        "protocols": [
          {
            "budget_share_exact": "1/1",
            "cost_exact": "7/2",
            "name": "launch-A grouped trajectory",
            "nuisance_response_exact": [
              [
                "-205821/200000"
              ],
              [
                "525777/500000"
              ],
              [
                "-123019/50000"
              ]
            ],
            "output_metric_exact": [
              [
                "1/1",
                "0/1",
                "0/1"
              ],
              [
                "0/1",
                "1/1",
                "0/1"
              ],
              [
                "0/1",
                "0/1",
                "1/1"
              ]
            ],
            "physical_weight_exact": "2/7",
            "response_exact": [
              [
                "-104679/1000000",
                "3127/100000"
              ],
              [
                "84503/1000000",
                "-454351/1000000"
              ],
              [
                "-63769/250000",
                "234819/1000000"
              ]
            ]
          },
          {
            "budget_share_exact": "0/1",
            "cost_exact": "9/4",
            "name": "launch-B grouped trajectory",
            "nuisance_response_exact": [
              [
                "194941/500000"
              ],
              [
                "290887/500000"
              ]
            ],
            "output_metric_exact": [
              [
                "1/1",
                "0/1"
              ],
              [
                "0/1",
                "1/1"
              ]
            ],
            "physical_weight_exact": "0/1",
            "response_exact": [
              [
                "7343/500000",
                "-15557/1000000"
              ],
              [
                "93811/200000",
                "207/50000"
              ]
            ]
          },
          {
            "budget_share_exact": "0/1",
            "cost_exact": "5/2",
            "name": "launch-C grouped trajectory",
            "nuisance_response_exact": [
              [
                "290149/500000"
              ],
              [
                "-1346659/500000"
              ]
            ],
            "output_metric_exact": [
              [
                "1/1",
                "0/1"
              ],
              [
                "0/1",
                "1/1"
              ]
            ],
            "physical_weight_exact": "0/1",
            "response_exact": [
              [
                "81009/1000000",
                "-4957/20000"
              ],
              [
                "-131393/500000",
                "471277/1000000"
              ]
            ]
          }
        ],
        "schema_version": "oig-query-shared-nuisance-mixture-v1",
        "unprofiled_information_sum_exact": [
          [
            "41581107913/1750000000000",
            "-101564026127/3500000000000"
          ],
          [
            "-101564026127/3500000000000",
            "18753757633/250000000000"
          ]
        ],
        "warning": "With a shared nuisance, profiling generally does not commute with summing individually profiled protocol information forms."
      },
      "query_dimension": 2,
      "report_valid": true,
      "schema_version": "oig-query-protocol-certificate-v1",
      "source_dimension": 2,
      "status": "exact finite-linear query certificate"
    },
    "secondary_selected_clock_and_common_gain": {
      "declared_nuisance_dimension": 2,
      "declared_nuisance_response_exact": [
        [
          "-205821/200000",
          "40609/125000"
        ],
        [
          "525777/500000",
          "96047/1000000"
        ],
        [
          "-123019/50000",
          "115831/200000"
        ],
        [
          "194941/500000",
          "-420191/1000000"
        ],
        [
          "290887/500000",
          "1117927/1000000"
        ],
        [
          "290149/500000",
          "666057/1000000"
        ],
        [
          "-1346659/500000",
          "-86929/1000000"
        ]
      ],
      "declared_observation_exact": [
        [
          "-104679/1000000",
          "3127/100000"
        ],
        [
          "84503/1000000",
          "-454351/1000000"
        ],
        [
          "-63769/250000",
          "234819/1000000"
        ],
        [
          "7343/500000",
          "-15557/1000000"
        ],
        [
          "93811/200000",
          "207/50000"
        ],
        [
          "81009/1000000",
          "-4957/20000"
        ],
        [
          "-131393/500000",
          "471277/1000000"
        ]
      ],
      "declared_output_metric_exact": [
        [
          "5/42",
          "0/1",
          "0/1",
          "0/1",
          "0/1",
          "0/1",
          "0/1"
        ],
        [
          "0/1",
          "5/42",
          "0/1",
          "0/1",
          "0/1",
          "0/1",
          "0/1"
        ],
        [
          "0/1",
          "0/1",
          "5/42",
          "0/1",
          "0/1",
          "0/1",
          "0/1"
        ],
        [
          "0/1",
          "0/1",
          "0/1",
          "1/9",
          "0/1",
          "0/1",
          "0/1"
        ],
        [
          "0/1",
          "0/1",
          "0/1",
          "0/1",
          "1/9",
          "0/1",
          "0/1"
        ],
        [
          "0/1",
          "0/1",
          "0/1",
          "0/1",
          "0/1",
          "2/15",
          "0/1"
        ],
        [
          "0/1",
          "0/1",
          "0/1",
          "0/1",
          "0/1",
          "0/1",
          "2/15"
        ]
      ],
      "declared_query_exact": [
        [
          "1/1",
          "0/1"
        ],
        [
          "0/1",
          "1/1"
        ]
      ],
      "declared_query_metric_exact": [
        [
          "1/1",
          "0/1"
        ],
        [
          "0/1",
          "1/1"
        ]
      ],
      "declared_source_metric_exact": [
        [
          "1/1",
          "0/1"
        ],
        [
          "0/1",
          "1/1"
        ]
      ],
      "effective_response_rank": 2,
      "factorization_and_minimax": {
        "amplification_lower_witness_exact": [
          "-100000000/1",
          "60994978/1"
        ],
        "decoder_annihilates_nuisance_exact": true,
        "decoder_exact": [
          [
            "425227563411743670841817869797467194672123270000000/1401795535378401989538058189645006516194004982091811",
            "5204244593063242038855480164529934092313583725000000/1401795535378401989538058189645006516194004982091811",
            "-1386747201730704636961752527167349048161210665000000/1401795535378401989538058189645006516194004982091811",
            "2542043967061241674508581888561228247052111266000000/1401795535378401989538058189645006516194004982091811",
            "3986182292060813845292365394484576012983286186000000/1401795535378401989538058189645006516194004982091811",
            "-4392683708523394924469803474545175665427271756000000/1401795535378401989538058189645006516194004982091811",
            "3418814384124645859094552067391029301682510916000000/1401795535378401989538058189645006516194004982091811"
          ],
          [
            "-1212451070144836739999756810133005689697102720000000/1401795535378401989538058189645006516194004982091811",
            "-5443885415880863445141048744267765132156952325000000/1401795535378401989538058189645006516194004982091811",
            "-253293123909330862287546179624702870203929570000000/1401795535378401989538058189645006516194004982091811",
            "-1270965322437284406937896242735912707422822522000000/1401795535378401989538058189645006516194004982091811",
            "-409400384678647353672635314232130865128689221000000/1401795535378401989538058189645006516194004982091811",
            "1296142788544685414018079915786324970650449962000000/1401795535378401989538058189645006516194004982091811",
            "-1423953140029275654496353060037569362399233524000000/1401795535378401989538058189645006516194004982091811"
          ]
        ],
        "decoder_times_effective_response_equals_query_exact": true,
        "decoder_times_raw_observation_equals_query_exact": true,
        "descriptive_amplification_lower": 21.397964751609404,
        "descriptive_amplification_upper": 21.397964751609404,
        "factorization_exists": true,
        "interpretation": "For data-noise radius epsilon, the exact minimax query error is kappa*epsilon; the true kappa squared lies in the certified rational interval.",
        "kind": "identifiable-query-factorization",
        "minimax_amplification_exactly_zero": false,
        "minimax_amplification_squared_lower_exact": "2635151343073650244212891342774124224685196691000000000000/5755202740559823274230857528570480293458660835077887183",
        "minimax_amplification_squared_upper_exact": "50852135057197170529832416871813416824710960143606076357899293161818229257884513419/111061684488730216571204782315756491366704593257700653389774929875945437576298496",
        "quotient_injection_exact": [
          [
            "1/1",
            "0/1"
          ],
          [
            "0/1",
            "1/1"
          ]
        ],
        "quotient_row_coordinates_exact": [
          [
            "1/1",
            "0/1"
          ],
          [
            "0/1",
            "1/1"
          ]
        ],
        "quotient_source_metric_exact": [
          [
            "1/1",
            "0/1"
          ],
          [
            "0/1",
            "1/1"
          ]
        ],
        "reduced_data_gram_exact": [
          [
            "1615296434387604064836916696199485918897/204865068993637152056387973645600000000000",
            "66482512144640151048077872724966099049/7113370451167956668624582418250000000000"
          ],
          [
            "66482512144640151048077872724966099049/7113370451167956668624582418250000000000",
            "13449497695115185149578679896340774701423/768244008726139320211454901171000000000000"
          ]
        ],
        "reduced_effective_response_exact": [
          [
            "-583040475604094683541061386400367/12194349344859354289070712717000000",
            "-236369647013276027779451802425113/2286440502161128929200758634437500"
          ],
          [
            "-287772324646330387490888460644413/4877739737943741715628285086800000",
            "-1022987104109639315359250266533421/3658304803457806286721213815100000"
          ],
          [
            "-647975438488119673688910917218833/8129566229906236192713808478000000",
            "-317774935037280849056505794412713/3048587336214838572267678179250000"
          ],
          [
            "426147814990328436692462298091457/8129566229906236192713808478000000",
            "19673976265060511033691314123143/2032391557476559048178452119500000"
          ],
          [
            "1440751338023230646098248539340621/8129566229906236192713808478000000",
            "2355652595130460349092098228709177/12194349344859354289070712717000000"
          ],
          [
            "-587736833292798329980417506848011/4877739737943741715628285086800000",
            "-718847882734634870662502891566169/7316609606915612573442427630200000"
          ],
          [
            "118723618527860082952499313356459/1625913245981247238542761695600000",
            "3055046314001667927781358392137/81295662299062361927138084780000"
          ]
        ],
        "reduced_query_exact": [
          [
            "1/1",
            "0/1"
          ],
          [
            "0/1",
            "1/1"
          ]
        ],
        "reduced_query_form_exact": [
          [
            "1/1",
            "0/1"
          ],
          [
            "0/1",
            "1/1"
          ]
        ],
        "upper_shift_positive_by_exact_ldl": true
      },
      "identifiability": {
        "kernel_condition_exact": true,
        "kernel_counterexample_exact": null,
        "query_identifiable_exact": true
      },
      "independent_exact_verification": {
        "amplification_squared_lower_exact": "2635151343073650244212891342774124224685196691000000000000/5755202740559823274230857528570480293458660835077887183",
        "amplification_squared_upper_exact": "50852135057197170529832416871813416824710960143606076357899293161818229257884513419/111061684488730216571204782315756491366704593257700653389774929875945437576298496",
        "method": "exact rational reconstruction of the nuisance quotient, kernel condition, query factorization, and minimax amplification bracket",
        "passed": true,
        "query_identifiable": true
      },
      "model_kind": "shared_nuisance_protocol_mixture",
      "nuisance_elimination": {
        "effective_response_exact": [
          [
            "-583040475604094683541061386400367/12194349344859354289070712717000000",
            "-236369647013276027779451802425113/2286440502161128929200758634437500"
          ],
          [
            "-287772324646330387490888460644413/4877739737943741715628285086800000",
            "-1022987104109639315359250266533421/3658304803457806286721213815100000"
          ],
          [
            "-647975438488119673688910917218833/8129566229906236192713808478000000",
            "-317774935037280849056505794412713/3048587336214838572267678179250000"
          ],
          [
            "426147814990328436692462298091457/8129566229906236192713808478000000",
            "19673976265060511033691314123143/2032391557476559048178452119500000"
          ],
          [
            "1440751338023230646098248539340621/8129566229906236192713808478000000",
            "2355652595130460349092098228709177/12194349344859354289070712717000000"
          ],
          [
            "-587736833292798329980417506848011/4877739737943741715628285086800000",
            "-718847882734634870662502891566169/7316609606915612573442427630200000"
          ],
          [
            "118723618527860082952499313356459/1625913245981247238542761695600000",
            "3055046314001667927781358392137/81295662299062361927138084780000"
          ]
        ],
        "metric_orthogonal_projector_exact": [
          [
            "32932054977829495125550404926/36583048034578062867212138151",
            "1701612501633835981701060725/36583048034578062867212138151",
            "-2597425287325175607793910375/12194349344859354289070712717",
            "289509492338354146735571310/4064783114953118096356904239",
            "-3832608606755434043885857790/36583048034578062867212138151",
            "-2203307098690425827757579964/36583048034578062867212138151",
            "-636210767348611226543766036/4064783114953118096356904239"
          ],
          [
            "1701612501633835981701060725/36583048034578062867212138151",
            "67935033568257089726273228527/73166096069156125734424276302",
            "2981932158362460775888311875/24388698689718708578141425434",
            "-3734534920291412278171305/4064783114953118096356904239",
            "-3386451542137108925338300295/36583048034578062867212138151",
            "-3023169817924652820080350750/36583048034578062867212138151",
            "793111682536163783591625582/4064783114953118096356904239"
          ],
          [
            "-2597425287325175607793910375/12194349344859354289070712717",
            "2981932158362460775888311875/24388698689718708578141425434",
            "4347518544159674405361509103/8129566229906236192713808478",
            "557342733347686347548628575/4064783114953118096356904239",
            "-1930804356957562755400577125/12194349344859354289070712717",
            "-944391414947483558918083130/12194349344859354289070712717",
            "-1587062666862446391407753250/4064783114953118096356904239"
          ],
          [
            "310188741791093728645254975/4064783114953118096356904239",
            "-8002574829195883453224225/8129566229906236192713808478",
            "1194305857173613601889918375/8129566229906236192713808478",
            "3752338674949785214634272064/4064783114953118096356904239",
            "724593518607154812356649895/4064783114953118096356904239",
            "499577293174795933674027486/4064783114953118096356904239",
            "141749026179744620217281442/4064783114953118096356904239"
          ],
          [
            "-1368788788126940729959234925/12194349344859354289070712717",
            "-2418893958669363518098785925/24388698689718708578141425434",
            "-1379145969255401968143269375/8129566229906236192713808478",
            "724593518607154812356649895/4064783114953118096356904239",
            "5513995218816052534764523952/12194349344859354289070712717",
            "-4931508546500598465029348330/12194349344859354289070712717",
            "794600530551541790457467982/4064783114953118096356904239"
          ],
          [
            "-1967238480973594489069267825/36583048034578062867212138151",
            "-5398517532008308607286340625/73166096069156125734424276302",
            "-1686413240977649212353719875/24388698689718708578141425434",
            "416314410978996611395022905/4064783114953118096356904239",
            "-12328771366251496162573370825/36583048034578062867212138151",
            "27359735693301517437157514405/36583048034578062867212138151",
            "642535318329955252408392690/4064783114953118096356904239"
          ],
          [
            "-568045327989831452271219675/4064783114953118096356904239",
            "1416270861671721042127902825/8129566229906236192713808478",
            "-2834040476540082841799559375/8129566229906236192713808478",
            "118124188483120516847734535/4064783114953118096356904239",
            "662167108792951492047889985/4064783114953118096356904239",
            "642535318329955252408392690/4064783114953118096356904239",
            "2086562837546221950009705085/4064783114953118096356904239"
          ]
        ],
        "nuisance_basis_exact": [
          [
            "1/1",
            "0/1"
          ],
          [
            "0/1",
            "1/1"
          ],
          [
            "120760696390/62923271289",
            "-203297265085/440462899023"
          ],
          [
            "-68471503324/62923271289",
            "-305758913951/440462899023"
          ],
          [
            "159954708740/62923271289",
            "1339466348263/440462899023"
          ],
          [
            "92094145796/62923271289",
            "873965160841/440462899023"
          ],
          [
            "23896368040/62923271289",
            "-964442673841/440462899023"
          ]
        ],
        "profiled_information_exact": [
          [
            "1615296434387604064836916696199485918897/204865068993637152056387973645600000000000",
            "66482512144640151048077872724966099049/7113370451167956668624582418250000000000"
          ],
          [
            "66482512144640151048077872724966099049/7113370451167956668624582418250000000000",
            "13449497695115185149578679896340774701423/768244008726139320211454901171000000000000"
          ]
        ],
        "projector_annihilates_nuisance_exact": true,
        "projector_idempotent_exact": true,
        "projector_is_output_metric_self_adjoint_exact": true
      },
      "nuisance_rank": 2,
      "output_dimension": 7,
      "proof_boundary": "This certificate proves a finite-dimensional real rational linear theorem for the declared metrics, response, query, and one declared unrestricted nuisance shared across the active protocols. It does not prove that an external physical or continuum model is enclosed by these data.",
      "protocol_mixture": {
        "active_protocol_indices": [
          0,
          1,
          2
        ],
        "composition_rule": "stack active responses and nuisance maps; scale each output metric by budget_share/cost; profile the shared nuisance only after assembly",
        "inactive_zero_share_protocols_omitted_from_assembly": true,
        "nuisance_semantics": "one shared nuisance vector across every active protocol",
        "protocols": [
          {
            "budget_share_exact": "5/12",
            "cost_exact": "7/2",
            "name": "launch-A grouped trajectory",
            "nuisance_response_exact": [
              [
                "-205821/200000",
                "40609/125000"
              ],
              [
                "525777/500000",
                "96047/1000000"
              ],
              [
                "-123019/50000",
                "115831/200000"
              ]
            ],
            "output_metric_exact": [
              [
                "1/1",
                "0/1",
                "0/1"
              ],
              [
                "0/1",
                "1/1",
                "0/1"
              ],
              [
                "0/1",
                "0/1",
                "1/1"
              ]
            ],
            "physical_weight_exact": "5/42",
            "response_exact": [
              [
                "-104679/1000000",
                "3127/100000"
              ],
              [
                "84503/1000000",
                "-454351/1000000"
              ],
              [
                "-63769/250000",
                "234819/1000000"
              ]
            ]
          },
          {
            "budget_share_exact": "1/4",
            "cost_exact": "9/4",
            "name": "launch-B grouped trajectory",
            "nuisance_response_exact": [
              [
                "194941/500000",
                "-420191/1000000"
              ],
              [
                "290887/500000",
                "1117927/1000000"
              ]
            ],
            "output_metric_exact": [
              [
                "1/1",
                "0/1"
              ],
              [
                "0/1",
                "1/1"
              ]
            ],
            "physical_weight_exact": "1/9",
            "response_exact": [
              [
                "7343/500000",
                "-15557/1000000"
              ],
              [
                "93811/200000",
                "207/50000"
              ]
            ]
          },
          {
            "budget_share_exact": "1/3",
            "cost_exact": "5/2",
            "name": "launch-C grouped trajectory",
            "nuisance_response_exact": [
              [
                "290149/500000",
                "666057/1000000"
              ],
              [
                "-1346659/500000",
                "-86929/1000000"
              ]
            ],
            "output_metric_exact": [
              [
                "1/1",
                "0/1"
              ],
              [
                "0/1",
                "1/1"
              ]
            ],
            "physical_weight_exact": "2/15",
            "response_exact": [
              [
                "81009/1000000",
                "-4957/20000"
              ],
              [
                "-131393/500000",
                "471277/1000000"
              ]
            ]
          }
        ],
        "schema_version": "oig-query-shared-nuisance-mixture-v1",
        "unprofiled_information_sum_exact": [
          [
            "3500642018761/78750000000000",
            "-19586901310913/630000000000000"
          ],
          [
            "-19586901310913/630000000000000",
            "1554508710547/22500000000000"
          ]
        ],
        "warning": "With a shared nuisance, profiling generally does not commute with summing individually profiled protocol information forms."
      },
      "query_dimension": 2,
      "report_valid": true,
      "schema_version": "oig-query-protocol-certificate-v1",
      "source_dimension": 2,
      "status": "exact finite-linear query certificate"
    },
    "selected_cost_weighted_clock_only": {
      "declared_nuisance_dimension": 1,
      "declared_nuisance_response_exact": [
        [
          "-205821/200000"
        ],
        [
          "525777/500000"
        ],
        [
          "-123019/50000"
        ],
        [
          "194941/500000"
        ],
        [
          "290887/500000"
        ]
      ],
      "declared_observation_exact": [
        [
          "-104679/1000000",
          "3127/100000"
        ],
        [
          "84503/1000000",
          "-454351/1000000"
        ],
        [
          "-63769/250000",
          "234819/1000000"
        ],
        [
          "7343/500000",
          "-15557/1000000"
        ],
        [
          "93811/200000",
          "207/50000"
        ]
      ],
      "declared_output_metric_exact": [
        [
          "4/21",
          "0/1",
          "0/1",
          "0/1",
          "0/1"
        ],
        [
          "0/1",
          "4/21",
          "0/1",
          "0/1",
          "0/1"
        ],
        [
          "0/1",
          "0/1",
          "4/21",
          "0/1",
          "0/1"
        ],
        [
          "0/1",
          "0/1",
          "0/1",
          "4/27",
          "0/1"
        ],
        [
          "0/1",
          "0/1",
          "0/1",
          "0/1",
          "4/27"
        ]
      ],
      "declared_query_exact": [
        [
          "1/1",
          "0/1"
        ],
        [
          "0/1",
          "1/1"
        ]
      ],
      "declared_query_metric_exact": [
        [
          "1/1",
          "0/1"
        ],
        [
          "0/1",
          "1/1"
        ]
      ],
      "declared_source_metric_exact": [
        [
          "1/1",
          "0/1"
        ],
        [
          "0/1",
          "1/1"
        ]
      ],
      "effective_response_rank": 2,
      "factorization_and_minimax": {
        "amplification_lower_witness_exact": [
          "-93887901/1",
          "100000000/1"
        ],
        "decoder_annihilates_nuisance_exact": true,
        "decoder_exact": [
          [
            "783762021442723785149531233925600000/2087078010318407559815300403019936167",
            "678777064115682211645030331249600000/2087078010318407559815300403019936167",
            "1082169720764245387703479185871400000/2087078010318407559815300403019936167",
            "-184987061637202602448600071695000000/695692670106135853271766801006645389",
            "5108033003309453001807594554473400000/2087078010318407559815300403019936167"
          ],
          [
            "-1864008101421293190978770304652000000/2087078010318407559815300403019936167",
            "-5556062583556132891132466837485000000/2087078010318407559815300403019936167",
            "-1570440120748997951650553009752000000/2087078010318407559815300403019936167",
            "194518052700816119537099477640000000/695692670106135853271766801006645389",
            "-287322826015072028544375051655000000/2087078010318407559815300403019936167"
          ]
        ],
        "decoder_times_effective_response_equals_query_exact": true,
        "decoder_times_raw_observation_equals_query_exact": true,
        "descriptive_amplification_lower": 7.4479906096174915,
        "descriptive_amplification_upper": 7.447990609617492,
        "factorization_exists": true,
        "interpretation": "For data-noise radius epsilon, the exact minimax query error is kappa*epsilon; the true kappa squared lies in the certified rational interval.",
        "kind": "identifiable-query-factorization",
        "minimax_amplification_exactly_zero": false,
        "minimax_amplification_squared_lower_exact": "1720179956168010777290336510380256250000000/31009562716758388491553844565288974594953",
        "minimax_amplification_squared_upper_exact": "764390464694106501214925417116232161175466503411161923039119419429/13779612981787854684459904996426557359436244703963504643644850176",
        "quotient_injection_exact": [
          [
            "1/1",
            "0/1"
          ],
          [
            "0/1",
            "1/1"
          ]
        ],
        "quotient_row_coordinates_exact": [
          [
            "1/1",
            "0/1"
          ],
          [
            "0/1",
            "1/1"
          ]
        ],
        "quotient_source_metric_exact": [
          [
            "1/1",
            "0/1"
          ],
          [
            "0/1",
            "1/1"
          ]
        ],
        "reduced_data_gram_exact": [
          [
            "2237255405774073242247553/91426289066519006250000000",
            "4424900309417641148376517/731410312532152050000000000"
          ],
          [
            "4424900309417641148376517/731410312532152050000000000",
            "86697640727319906889797373/3657051562660760250000000000"
          ]
        ],
        "reduced_effective_response_exact": [
          [
            "384625758356519571/19349479167517250000",
            "-96003945282352223/967473958375862500"
          ],
          [
            "-3310380918407629691/77397916670069000000",
            "-24844937979491864063/77397916670069000000"
          ],
          [
            "206623264152286051/4837369791879312500",
            "-5973848347702680809/77397916670069000000"
          ],
          [
            "-1257833452938239/38698958335034500",
            "524513615419998023/15479583334013800000"
          ],
          [
            "30853943130322379257/77397916670069000000",
            "188452280845411153/2418684895939656250"
          ]
        ],
        "reduced_query_exact": [
          [
            "1/1",
            "0/1"
          ],
          [
            "0/1",
            "1/1"
          ]
        ],
        "reduced_query_form_exact": [
          [
            "1/1",
            "0/1"
          ],
          [
            "0/1",
            "1/1"
          ]
        ],
        "upper_shift_positive_by_exact_ldl": true
      },
      "identifiability": {
        "kernel_condition_exact": true,
        "kernel_counterexample_exact": null,
        "query_identifiable_exact": true
      },
      "independent_exact_verification": {
        "amplification_squared_lower_exact": "1720179956168010777290336510380256250000000/31009562716758388491553844565288974594953",
        "amplification_squared_upper_exact": "764390464694106501214925417116232161175466503411161923039119419429/13779612981787854684459904996426557359436244703963504643644850176",
        "method": "exact rational reconstruction of the nuisance quotient, kernel condition, query factorization, and minimax amplification bracket",
        "passed": true,
        "query_identifiable": true
      },
      "model_kind": "shared_nuisance_protocol_mixture",
      "nuisance_elimination": {
        "effective_response_exact": [
          [
            "384625758356519571/19349479167517250000",
            "-96003945282352223/967473958375862500"
          ],
          [
            "-3310380918407629691/77397916670069000000",
            "-24844937979491864063/77397916670069000000"
          ],
          [
            "206623264152286051/4837369791879312500",
            "-5973848347702680809/77397916670069000000"
          ],
          [
            "-1257833452938239/38698958335034500",
            "524513615419998023/15479583334013800000"
          ],
          [
            "30853943130322379257/77397916670069000000",
            "188452280845411153/2418684895939656250"
          ]
        ],
        "metric_orthogonal_projector_exact": [
          [
            "67866402760844/77397916670069",
            "9739435312530/77397916670069",
            "-22787904239100/77397916670069",
            "2808606609270/77397916670069",
            "4190945725890/77397916670069"
          ],
          [
            "9739435312530/77397916670069",
            "67446024335825/77397916670069",
            "23285001874680/77397916670069",
            "-2869873836396/77397916670069",
            "-4282367437572/77397916670069"
          ],
          [
            "-22787904239100/77397916670069",
            "23285001874680/77397916670069",
            "22916688970469/77397916670069",
            "6714805126120/77397916670069",
            "10019695798840/77397916670069"
          ],
          [
            "3611065640490/77397916670069",
            "-3689837789652/77397916670069",
            "8633320876440/77397916670069",
            "76333860852601/77397916670069",
            "-1587762474676/77397916670069"
          ],
          [
            "5388358790430/77397916670069",
            "-5505900991164/77397916670069",
            "12882466027080/77397916670069",
            "-1587762474676/77397916670069",
            "75028689760537/77397916670069"
          ]
        ],
        "nuisance_basis_exact": [
          [
            "1/1"
          ],
          [
            "-50074/49005"
          ],
          [
            "492076/205821"
          ],
          [
            "-389882/1029105"
          ],
          [
            "-581774/1029105"
          ]
        ],
        "profiled_information_exact": [
          [
            "2237255405774073242247553/91426289066519006250000000",
            "4424900309417641148376517/731410312532152050000000000"
          ],
          [
            "4424900309417641148376517/731410312532152050000000000",
            "86697640727319906889797373/3657051562660760250000000000"
          ]
        ],
        "projector_annihilates_nuisance_exact": true,
        "projector_idempotent_exact": true,
        "projector_is_output_metric_self_adjoint_exact": true
      },
      "nuisance_rank": 1,
      "output_dimension": 5,
      "proof_boundary": "This certificate proves a finite-dimensional real rational linear theorem for the declared metrics, response, query, and one declared unrestricted nuisance shared across the active protocols. It does not prove that an external physical or continuum model is enclosed by these data.",
      "protocol_mixture": {
        "active_protocol_indices": [
          0,
          1
        ],
        "composition_rule": "stack active responses and nuisance maps; scale each output metric by budget_share/cost; profile the shared nuisance only after assembly",
        "inactive_zero_share_protocols_omitted_from_assembly": true,
        "nuisance_semantics": "one shared nuisance vector across every active protocol",
        "protocols": [
          {
            "budget_share_exact": "2/3",
            "cost_exact": "7/2",
            "name": "launch-A grouped trajectory",
            "nuisance_response_exact": [
              [
                "-205821/200000"
              ],
              [
                "525777/500000"
              ],
              [
                "-123019/50000"
              ]
            ],
            "output_metric_exact": [
              [
                "1/1",
                "0/1",
                "0/1"
              ],
              [
                "0/1",
                "1/1",
                "0/1"
              ],
              [
                "0/1",
                "0/1",
                "1/1"
              ]
            ],
            "physical_weight_exact": "4/21",
            "response_exact": [
              [
                "-104679/1000000",
                "3127/100000"
              ],
              [
                "84503/1000000",
                "-454351/1000000"
              ],
              [
                "-63769/250000",
                "234819/1000000"
              ]
            ]
          },
          {
            "budget_share_exact": "1/3",
            "cost_exact": "9/4",
            "name": "launch-B grouped trajectory",
            "nuisance_response_exact": [
              [
                "194941/500000"
              ],
              [
                "290887/500000"
              ]
            ],
            "output_metric_exact": [
              [
                "1/1",
                "0/1"
              ],
              [
                "0/1",
                "1/1"
              ]
            ],
            "physical_weight_exact": "4/27",
            "response_exact": [
              [
                "7343/500000",
                "-15557/1000000"
              ],
              [
                "93811/200000",
                "207/50000"
              ]
            ]
          },
          {
            "budget_share_exact": "0/1",
            "cost_exact": "5/2",
            "name": "launch-C grouped trajectory",
            "nuisance_response_exact": [
              [
                "290149/500000"
              ],
              [
                "-1346659/500000"
              ]
            ],
            "output_metric_exact": [
              [
                "1/1",
                "0/1"
              ],
              [
                "0/1",
                "1/1"
              ]
            ],
            "physical_weight_exact": "0/1",
            "response_exact": [
              [
                "81009/1000000",
                "-4957/20000"
              ],
              [
                "-131393/500000",
                "471277/1000000"
              ]
            ]
          }
        ],
        "schema_version": "oig-query-shared-nuisance-mixture-v1",
        "unprofiled_information_sum_exact": [
          [
            "2290057843781/47250000000000",
            "-902082311957/47250000000000"
          ],
          [
            "-902082311957/47250000000000",
            "337826797243/6750000000000"
          ]
        ],
        "warning": "With a shared nuisance, profiling generally does not commute with summing individually profiled protocol information forms."
      },
      "query_dimension": 2,
      "report_valid": true,
      "schema_version": "oig-query-protocol-certificate-v1",
      "source_dimension": 2,
      "status": "exact finite-linear query certificate"
    }
  },
  "experimental_semantics": {
    "grouping": "Each group fixes one exact launch and collects every listed sensor/time readout as one inseparable batch. A budget share p_g and conservative additive group cost c_g give repetition weight p_g/c_g on the entire within-group output metric. One clock-dilation parameter is global across all repetitions, observations, and active group types and is profiled only after stacking.",
    "local_linearization": "all state, tangent, parameter, clock, and gain rows are evaluated locally at (u,v,epsilon,kappa)=(0,0,0,0), with kappa present only in the secondary common-gain model",
    "output_noise_metric": "the within-group metric is diagonal with each legacy scalar noise precision on its diagonal; this declares independent scalar readout noise before the common batch repetition factor p_g/c_g",
    "preparation": "launch coordinates are exact declarations; no preparation nuisance is profiled and no preparation-error bound is claimed",
    "secondary_common_gain": "Secondary optimistic control: one log multiplicative gain is shared by every dimensionless output, even across angle and scaled-velocity channels. It is not a sensor-specific calibration model.",
    "shared_clock": "one unrestricted epsilon with tau_actual=exp(epsilon)*tau_declared; epsilon is global across repetitions and group types, and its local response is tau*d(sensor output)/d tau"
  },
  "finite_library_scope": {
    "continuous_launch_time_sensor_optimization_claimed": false,
    "group_count": 3,
    "group_names": [
      "launch-A grouped trajectory",
      "launch-B grouped trajectory",
      "launch-C grouped trajectory"
    ],
    "legacy_scalar_candidate_count": 7,
    "only_declared_launches_sensors_and_times_searched": true
  },
  "grouped_protocol_library": [
    {
      "batch_repetition_semantics": "one repetition acquires every member output and scales the whole group output metric by one physical repetition weight",
      "cost_rule": "conservative sum of legacy scalar-candidate costs; no shared-run discount",
      "distinct_sensor_count": 3,
      "distinct_time_count": 2,
      "group_cost_exact": "7/2",
      "is_multi_sensor": true,
      "is_multi_time": true,
      "launch_exact": [
        "4/5",
        "-7/20",
        "0/1",
        "0/1"
      ],
      "member_names": [
        "launch-A / theta-1 / tau-1",
        "launch-A / theta-2 / tau-1",
        "launch-A / scaled-omega-2 / tau-3/2"
      ],
      "name": "launch-A grouped trajectory",
      "output_count": 3,
      "output_metric_exact": [
        [
          "1/1",
          "0/1",
          "0/1"
        ],
        [
          "0/1",
          "1/1",
          "0/1"
        ],
        [
          "0/1",
          "0/1",
          "1/1"
        ]
      ],
      "response_exact": [
        [
          "-104679/1000000",
          "3127/100000"
        ],
        [
          "84503/1000000",
          "-454351/1000000"
        ],
        [
          "-63769/250000",
          "234819/1000000"
        ]
      ],
      "shared_clock_and_common_gain_nuisance_response_exact": [
        [
          "-205821/200000",
          "40609/125000"
        ],
        [
          "525777/500000",
          "96047/1000000"
        ],
        [
          "-123019/50000",
          "115831/200000"
        ]
      ],
      "shared_clock_nuisance_response_exact": [
        [
          "-205821/200000"
        ],
        [
          "525777/500000"
        ],
        [
          "-123019/50000"
        ]
      ]
    },
    {
      "batch_repetition_semantics": "one repetition acquires every member output and scales the whole group output metric by one physical repetition weight",
      "cost_rule": "conservative sum of legacy scalar-candidate costs; no shared-run discount",
      "distinct_sensor_count": 2,
      "distinct_time_count": 2,
      "group_cost_exact": "9/4",
      "is_multi_sensor": true,
      "is_multi_time": true,
      "launch_exact": [
        "-3/5",
        "9/10",
        "0/1",
        "0/1"
      ],
      "member_names": [
        "launch-B / theta-1 / tau-3/4",
        "launch-B / scaled-omega-1 / tau-5/4"
      ],
      "name": "launch-B grouped trajectory",
      "output_count": 2,
      "output_metric_exact": [
        [
          "1/1",
          "0/1"
        ],
        [
          "0/1",
          "1/1"
        ]
      ],
      "response_exact": [
        [
          "7343/500000",
          "-15557/1000000"
        ],
        [
          "93811/200000",
          "207/50000"
        ]
      ],
      "shared_clock_and_common_gain_nuisance_response_exact": [
        [
          "194941/500000",
          "-420191/1000000"
        ],
        [
          "290887/500000",
          "1117927/1000000"
        ]
      ],
      "shared_clock_nuisance_response_exact": [
        [
          "194941/500000"
        ],
        [
          "290887/500000"
        ]
      ]
    },
    {
      "batch_repetition_semantics": "one repetition acquires every member output and scales the whole group output metric by one physical repetition weight",
      "cost_rule": "conservative sum of legacy scalar-candidate costs; no shared-run discount",
      "distinct_sensor_count": 2,
      "distinct_time_count": 2,
      "group_cost_exact": "5/2",
      "is_multi_sensor": true,
      "is_multi_time": true,
      "launch_exact": [
        "6/5",
        "2/5",
        "0/1",
        "0/1"
      ],
      "member_names": [
        "launch-C / theta-2 / tau-1",
        "launch-C / scaled-omega-2 / tau-3/2"
      ],
      "name": "launch-C grouped trajectory",
      "output_count": 2,
      "output_metric_exact": [
        [
          "1/1",
          "0/1"
        ],
        [
          "0/1",
          "1/1"
        ]
      ],
      "response_exact": [
        [
          "81009/1000000",
          "-4957/20000"
        ],
        [
          "-131393/500000",
          "471277/1000000"
        ]
      ],
      "shared_clock_and_common_gain_nuisance_response_exact": [
        [
          "290149/500000",
          "666057/1000000"
        ],
        [
          "-1346659/500000",
          "-86929/1000000"
        ]
      ],
      "shared_clock_nuisance_response_exact": [
        [
          "290149/500000"
        ],
        [
          "-1346659/500000"
        ]
      ]
    }
  ],
  "integration_and_declaration": {
    "coarse": {
      "atol": 1e-12,
      "max_step_in_tau": 0.01,
      "method": "DOP853 joint dimensionless state/parameter-sensitivity integration",
      "rtol": 1e-10,
      "sampled_scaled_energy_drift_tolerance": 1e-09
    },
    "fine": {
      "atol": 1e-14,
      "max_step_in_tau": 0.005,
      "method": "DOP853 joint dimensionless state/parameter-sensitivity integration",
      "rtol": 1e-12,
      "sampled_scaled_energy_drift_tolerance": 1e-09
    },
    "gates": {
      "clock_state_vector_relative": 1e-08,
      "parameter_sensitivity_relative": 1e-08,
      "point_rationalization_absolute": 5.1e-07,
      "state_relative": 1e-09
    },
    "point_declaration_rule": "round each fine scalar response to the nearest multiple of 1/1000000; this is not an enclosure",
    "refinement_norms": {
      "clock_state_vector_relative": "||c_c-c_f||_2/max(1,||c_f||_2)",
      "parameter_sensitivity_relative": "||S_c-S_f||_F/max(1,||S_f||_F)",
      "state_relative": "||z_c-z_f||_2/max(1,||z_f||_2)"
    }
  },
  "internal_recomputation_verification": {
    "exact_query_children_verified": true,
    "finite_rational_grid_recomputed": true,
    "outward_validation_performed": false,
    "passed": true,
    "tier1_numerics_recomputed": true
  },
  "outward_validation": {
    "clock_response_enclosed": false,
    "parameter_sensitivity_enclosed": false,
    "preparation_error_bounded": false,
    "rational_point_membership_certified": false,
    "state_enclosed": false
  },
  "proof_boundary": "The analytic inhomogeneous parameter-sensitivity solve, state solve, clock chain rule, solver refinement, and fixed-grid rationalization are Tier-1 numerical provenance. The exact query children prove finite rational linear statements only for the serialized point declarations. They do not prove that the exact double-pendulum flow or any physical response belongs to those declarations, and they do not include launch-preparation error.",
  "rank_theorem": {
    "clock_and_common_gain": "For d=2 and two independent shared nuisance columns, m>=4 is necessary and rank([B H])-rank(B)=2 is sufficient.",
    "clock_only": "For d=2 and one rank-one unrestricted shared nuisance, m-r>=d requires m>=3. Full query rank holds exactly when rank([B H])-rank(B)=2.",
    "minimum_output_condition_is_constructively_attained": true,
    "minimum_three_output_launch_A_effective_rank_exact": 2,
    "secondary_gain_effective_rank_exact": 2,
    "secondary_gain_selected_output_count": 7,
    "selected_clock_effective_rank_exact": 2,
    "selected_clock_output_count": 5
  },
  "rational_grid_search": {
    "clock_and_optimistic_common_gain": {
      "enumeration_rule": "all nonnegative three-group budget shares with integer numerators summing to the grid denominator",
      "evaluated_share_count": 91,
      "evaluations": [
        {
          "active_group_indices": [
            2
          ],
          "active_output_count": 2,
          "budget_shares_exact": [
            "0/1",
            "0/1",
            "1/1"
          ],
          "descriptive_profiled_floor_estimate": 0.0,
          "effective_response_rank_exact": 0,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "1/12",
            "11/12"
          ],
          "descriptive_profiled_floor_estimate": 2.7390146838759468e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "1/6",
            "5/6"
          ],
          "descriptive_profiled_floor_estimate": 5.2471838406648956e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "1/4",
            "3/4"
          ],
          "descriptive_profiled_floor_estimate": 7.484653023886614e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "1/3",
            "2/3"
          ],
          "descriptive_profiled_floor_estimate": 9.401989163950768e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "5/12",
            "7/12"
          ],
          "descriptive_profiled_floor_estimate": 0.00010937176728183867,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "1/2",
            "1/2"
          ],
          "descriptive_profiled_floor_estimate": 0.00012011435413075744,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "7/12",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0001252329878681864,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "2/3",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.0001234007862906378,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "3/4",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.00011285322578244423,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "5/6",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 9.120009805129771e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "11/12",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 5.513774880255256e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            1
          ],
          "active_output_count": 2,
          "budget_shares_exact": [
            "0/1",
            "1/1",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.0,
          "effective_response_rank_exact": 0,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/12",
            "0/1",
            "11/12"
          ],
          "descriptive_profiled_floor_estimate": 2.7224741281930853e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "1/12",
            "5/6"
          ],
          "descriptive_profiled_floor_estimate": 0.0006567450497298709,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "1/6",
            "3/4"
          ],
          "descriptive_profiled_floor_estimate": 0.000720953999104862,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "1/4",
            "2/3"
          ],
          "descriptive_profiled_floor_estimate": 0.0007630212351694003,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "1/3",
            "7/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0007977091683332618,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "5/12",
            "1/2"
          ],
          "descriptive_profiled_floor_estimate": 0.0008276905214266575,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "1/2",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0008533418067635033,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "7/12",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.0008740324111917788,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "2/3",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.0008880039588164303,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "3/4",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.0008907973451670905,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "5/6",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0008662875870772586,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/12",
            "11/12",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.0006374859841075651,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/6",
            "0/1",
            "5/6"
          ],
          "descriptive_profiled_floor_estimate": 4.608935489881148e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "1/12",
            "3/4"
          ],
          "descriptive_profiled_floor_estimate": 0.0011113446038980644,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "1/6",
            "2/3"
          ],
          "descriptive_profiled_floor_estimate": 0.0012478055451257712,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "1/4",
            "7/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0013150335212832364,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "1/3",
            "1/2"
          ],
          "descriptive_profiled_floor_estimate": 0.0013604637148121595,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "5/12",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0013932183794327932,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "1/2",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.0014142056737975553,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "7/12",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.0014194024967069717,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "2/3",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.0013959916499823712,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "3/4",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.00130024337487465,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/6",
            "5/6",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.000870687995451074,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/4",
            "0/1",
            "3/4"
          ],
          "descriptive_profiled_floor_estimate": 5.8304024509244226e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/4",
            "1/12",
            "2/3"
          ],
          "descriptive_profiled_floor_estimate": 0.0014365215619768276,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/4",
            "1/6",
            "7/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0016508285936519197,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/4",
            "1/4",
            "1/2"
          ],
          "descriptive_profiled_floor_estimate": 0.001738490797520654,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/4",
            "1/3",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0017820642529888118,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/4",
            "5/12",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.0017962384460094914,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/4",
            "1/2",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.0017776539669384498,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/4",
            "7/12",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.0017058331946751236,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/4",
            "2/3",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.001515865348238486,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/4",
            "3/4",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.0009341251587507983,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/3",
            "0/1",
            "2/3"
          ],
          "descriptive_profiled_floor_estimate": 6.514266510160469e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/3",
            "1/12",
            "7/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0016626181418295718,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/3",
            "1/6",
            "1/2"
          ],
          "descriptive_profiled_floor_estimate": 0.0019398551071869992,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/3",
            "1/4",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 0.002031953854178229,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/3",
            "1/3",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.002049738326721085,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/3",
            "5/12",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.0020075261810047597,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/3",
            "1/2",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.0018842995501328534,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/3",
            "7/12",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0016056485903468511,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/3",
            "2/3",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.0009159207988903932,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "5/12",
            "0/1",
            "7/12"
          ],
          "descriptive_profiled_floor_estimate": 6.757357173403444e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/12",
            "1/12",
            "1/2"
          ],
          "descriptive_profiled_floor_estimate": 0.0018071530518963795,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/12",
            "1/6",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0021166766552299875,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/12",
            "1/4",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.002184012222177317,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/12",
            "1/3",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.002135299379536326,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/12",
            "5/12",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.001970662443076712,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/12",
            "1/2",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0016192481309827659,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "5/12",
            "7/12",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.0008531769777062672,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/2",
            "0/1",
            "1/2"
          ],
          "descriptive_profiled_floor_estimate": 6.634579816578508e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/2",
            "1/12",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0018771783835289664,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/2",
            "1/6",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.0021735821529666834,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/2",
            "1/4",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.00216958742674326,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/2",
            "1/3",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.00198711133142152,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/2",
            "5/12",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0015834225698761163,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/2",
            "1/2",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.0007637061299549617,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "7/12",
            "0/1",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 6.204780713419711e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "7/12",
            "1/12",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.0018696519758433152,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "7/12",
            "1/6",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.002089419481976495,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "7/12",
            "1/4",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.001941556191721649,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "7/12",
            "1/3",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0015124765803223928,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "7/12",
            "5/12",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.0006570111979171755,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "2/3",
            "0/1",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 5.5148212354588945e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "2/3",
            "1/12",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.001768399233341956,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "2/3",
            "1/6",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.0018205419842311878,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "2/3",
            "1/4",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0014124719355677769,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "2/3",
            "1/3",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.0005385932659073363,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "3/4",
            "0/1",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 4.602457764778907e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "3/4",
            "1/12",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.0015340563588260615,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "3/4",
            "1/6",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.001279485255036294,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "3/4",
            "1/4",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.00041184687430323235,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "5/6",
            "0/1",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 3.4983703483792724e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/6",
            "1/12",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0010744275866615943,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "5/6",
            "1/6",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.00027897619205761076,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "11/12",
            "0/1",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 2.2272402911900247e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "11/12",
            "1/12",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.00014147294991076663,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0
          ],
          "active_output_count": 3,
          "budget_shares_exact": [
            "1/1",
            "0/1",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.0,
          "effective_response_rank_exact": 1,
          "nuisance_rank_exact": 2
        }
      ],
      "grid_denominator": 12,
      "leaderboard": [
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/12",
            "1/4",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.002184012222177317,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/2",
            "1/6",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.0021735821529666834,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/2",
            "1/4",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.00216958742674326,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/12",
            "1/3",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.002135299379536326,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/12",
            "1/6",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0021166766552299875,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "7/12",
            "1/6",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.002089419481976495,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/3",
            "1/3",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.002049738326721085,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/3",
            "1/4",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 0.002031953854178229,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/3",
            "5/12",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.0020075261810047597,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/2",
            "1/3",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.00198711133142152,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 2
        }
      ],
      "nuisance_model": "one shared clock dilation plus one optimistic shared common gain",
      "ordering_status": "deterministic binary64 discovery ordering; selected design receives a separate exact query-engine certificate, but grid optimality is not claimed as an exact theorem",
      "score": "smallest eigenvalue of the numerically profiled information form for the fixed rational point declarations and cost weights p_g/c_g",
      "selected": {
        "active_group_indices": [
          0,
          1,
          2
        ],
        "active_output_count": 7,
        "budget_shares_exact": [
          "5/12",
          "1/4",
          "1/3"
        ],
        "descriptive_profiled_floor_estimate": 0.002184012222177317,
        "effective_response_rank_exact": 2,
        "nuisance_rank_exact": 2
      },
      "selected_evaluation_index": 58
    },
    "clock_only": {
      "enumeration_rule": "all nonnegative three-group budget shares with integer numerators summing to the grid denominator",
      "evaluated_share_count": 91,
      "evaluations": [
        {
          "active_group_indices": [
            2
          ],
          "active_output_count": 2,
          "budget_shares_exact": [
            "0/1",
            "0/1",
            "1/1"
          ],
          "descriptive_profiled_floor_estimate": 0.0,
          "effective_response_rank_exact": 1,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "1/12",
            "11/12"
          ],
          "descriptive_profiled_floor_estimate": 0.006372611786613796,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "1/6",
            "5/6"
          ],
          "descriptive_profiled_floor_estimate": 0.007144573247083241,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "1/4",
            "3/4"
          ],
          "descriptive_profiled_floor_estimate": 0.006635013510948759,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "1/3",
            "2/3"
          ],
          "descriptive_profiled_floor_estimate": 0.006091490601952157,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "5/12",
            "7/12"
          ],
          "descriptive_profiled_floor_estimate": 0.00553871149790322,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "1/2",
            "1/2"
          ],
          "descriptive_profiled_floor_estimate": 0.004980373668503026,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "7/12",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 0.004416398749210283,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "2/3",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.00384442248505838,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "3/4",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.0032581453283721334,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "5/6",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.0026395656948298234,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            1,
            2
          ],
          "active_output_count": 4,
          "budget_shares_exact": [
            "0/1",
            "11/12",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0019140452446994036,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            1
          ],
          "active_output_count": 2,
          "budget_shares_exact": [
            "0/1",
            "1/1",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.0,
          "effective_response_rank_exact": 1,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/12",
            "0/1",
            "11/12"
          ],
          "descriptive_profiled_floor_estimate": 0.000115487126024789,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "1/12",
            "5/6"
          ],
          "descriptive_profiled_floor_estimate": 0.006356004878102612,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "1/6",
            "3/4"
          ],
          "descriptive_profiled_floor_estimate": 0.009028924528189186,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "1/4",
            "2/3"
          ],
          "descriptive_profiled_floor_estimate": 0.008792433650447335,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "1/3",
            "7/12"
          ],
          "descriptive_profiled_floor_estimate": 0.008305064725855488,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "5/12",
            "1/2"
          ],
          "descriptive_profiled_floor_estimate": 0.007764179540497253,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "1/2",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 0.007197169187859189,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "7/12",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.0066073119170287345,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "2/3",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.005986857479044804,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "3/4",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.005311168748486152,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/12",
            "5/6",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.004502439408221646,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/12",
            "11/12",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.0031738869995381995,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/6",
            "0/1",
            "5/6"
          ],
          "descriptive_profiled_floor_estimate": 0.0001701682162176842,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "1/12",
            "3/4"
          ],
          "descriptive_profiled_floor_estimate": 0.00632471011371817,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "1/6",
            "2/3"
          ],
          "descriptive_profiled_floor_estimate": 0.010256708354352795,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "1/4",
            "7/12"
          ],
          "descriptive_profiled_floor_estimate": 0.010686984201051915,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "1/3",
            "1/2"
          ],
          "descriptive_profiled_floor_estimate": 0.010336929470763003,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "5/12",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 0.009828354404802153,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "1/2",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.009250560665715923,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "7/12",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.008616169680452741,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "2/3",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.007906610680047275,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/6",
            "3/4",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.007056120960651266,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/6",
            "5/6",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.005835414928700581,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/4",
            "0/1",
            "3/4"
          ],
          "descriptive_profiled_floor_estimate": 0.00019364641776304902,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/4",
            "1/12",
            "2/3"
          ],
          "descriptive_profiled_floor_estimate": 0.006290399682340409,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/4",
            "1/6",
            "7/12"
          ],
          "descriptive_profiled_floor_estimate": 0.010896887091731047,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/4",
            "1/4",
            "1/2"
          ],
          "descriptive_profiled_floor_estimate": 0.012266443098076072,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/4",
            "1/3",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 0.012168433585663588,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/4",
            "5/12",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.011720121106417467,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/4",
            "1/2",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.011128243085943613,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/4",
            "7/12",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.010423347814767872,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/4",
            "2/3",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.009566316180291516,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/4",
            "3/4",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.008408256295570526,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/3",
            "0/1",
            "2/3"
          ],
          "descriptive_profiled_floor_estimate": 0.0001990852837105736,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/3",
            "1/12",
            "7/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0062546580902794885,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/3",
            "1/6",
            "1/2"
          ],
          "descriptive_profiled_floor_estimate": 0.011212227751980358,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/3",
            "1/4",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 0.013501447304581709,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/3",
            "1/3",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.013783456544632793,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/3",
            "5/12",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.01342937205993553,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/3",
            "1/2",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.012817023745735586,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/3",
            "7/12",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.012004621766762391,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/3",
            "2/3",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.010914901868972957,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "5/12",
            "0/1",
            "7/12"
          ],
          "descriptive_profiled_floor_estimate": 0.00019309412629476365,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/12",
            "1/12",
            "1/2"
          ],
          "descriptive_profiled_floor_estimate": 0.006217896019544471,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/12",
            "1/6",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 0.0113747120966076,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/12",
            "1/4",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.014409231342070672,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/12",
            "1/3",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.015171971007115011,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/12",
            "5/12",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.01494763872253035,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/12",
            "1/2",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.01430224550753722,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "5/12",
            "7/12",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.013328720056227214,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/2",
            "0/1",
            "1/2"
          ],
          "descriptive_profiled_floor_estimate": 0.00017930602252336572,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/2",
            "1/12",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 0.006180224499532699,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/2",
            "1/6",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.011461263120242041,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/2",
            "1/4",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.015048720457831842,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/2",
            "1/3",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.01633349714871283,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/2",
            "5/12",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.016268505516334176,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/2",
            "1/2",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.015566613432057246,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "7/12",
            "0/1",
            "5/12"
          ],
          "descriptive_profiled_floor_estimate": 0.00015985409551671692,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "7/12",
            "1/12",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.006141640661696,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "7/12",
            "1/6",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.011505988686669284,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "7/12",
            "1/4",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.015490919561475405,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "7/12",
            "1/3",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.01727857168784463,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "7/12",
            "5/12",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.01738747364213656,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "2/3",
            "0/1",
            "1/3"
          ],
          "descriptive_profiled_floor_estimate": 0.00013604884136672206,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "2/3",
            "1/12",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.006102081868578178,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "2/3",
            "1/6",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.01152529584944729,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "2/3",
            "1/4",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.01579560254966494,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "2/3",
            "1/3",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.018026929453263365,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "3/4",
            "0/1",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.00010871597339253456,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "3/4",
            "1/12",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.006061442958606325,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "3/4",
            "1/6",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.01152774531188676,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "3/4",
            "1/4",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.016005159360225816,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "5/6",
            "0/1",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 7.837610287809523e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/6",
            "1/12",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.006019579808151177,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "5/6",
            "1/6",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.011518074329934415,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            2
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "11/12",
            "0/1",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 4.534473091914089e-05,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "11/12",
            "1/12",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.005976306031772008,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0
          ],
          "active_output_count": 3,
          "budget_shares_exact": [
            "1/1",
            "0/1",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 9.789124164628073e-06,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        }
      ],
      "grid_denominator": 12,
      "leaderboard": [
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "2/3",
            "1/3",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.018026929453263365,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "7/12",
            "5/12",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.01738747364213656,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "7/12",
            "1/3",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.01727857168784463,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/2",
            "1/3",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.01633349714871283,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "1/2",
            "5/12",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.016268505516334176,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "3/4",
            "1/4",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.016005159360225816,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "2/3",
            "1/4",
            "1/12"
          ],
          "descriptive_profiled_floor_estimate": 0.01579560254966494,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1
          ],
          "active_output_count": 5,
          "budget_shares_exact": [
            "1/2",
            "1/2",
            "0/1"
          ],
          "descriptive_profiled_floor_estimate": 0.015566613432057246,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "7/12",
            "1/4",
            "1/6"
          ],
          "descriptive_profiled_floor_estimate": 0.015490919561475405,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        },
        {
          "active_group_indices": [
            0,
            1,
            2
          ],
          "active_output_count": 7,
          "budget_shares_exact": [
            "5/12",
            "1/3",
            "1/4"
          ],
          "descriptive_profiled_floor_estimate": 0.015171971007115011,
          "effective_response_rank_exact": 2,
          "nuisance_rank_exact": 1
        }
      ],
      "nuisance_model": "one shared clock dilation",
      "ordering_status": "deterministic binary64 discovery ordering; selected design receives a separate exact query-engine certificate, but grid optimality is not claimed as an exact theorem",
      "score": "smallest eigenvalue of the numerically profiled information form for the fixed rational point declarations and cost weights p_g/c_g",
      "selected": {
        "active_group_indices": [
          0,
          1
        ],
        "active_output_count": 5,
        "budget_shares_exact": [
          "2/3",
          "1/3",
          "0/1"
        ],
        "descriptive_profiled_floor_estimate": 0.018026929453263365,
        "effective_response_rank_exact": 2,
        "nuisance_rank_exact": 1
      },
      "selected_evaluation_index": 80
    }
  },
  "scalar_observation_library": [
    {
      "coarse": {
        "accepted_step_count": 100,
        "clock_log_dilation_state_response_tau_times_rhs": [
          -1.029104685801025,
          1.0515538243999436,
          -0.9793737043832088,
          1.0981739883535637
        ],
        "max_scaled_energy_drift": 2.9605947323337506e-16,
        "nfev": 1502,
        "selected_clock_response": -1.029104685801025,
        "selected_common_gain_response": 0.32487193806652953,
        "selected_parameter_response_row": [
          -0.10467857258350488,
          0.03126957565130373
        ],
        "selected_sensor_output": 0.32487193806652953,
        "terminal_parameter_sensitivity_D_state_D_uv": [
          [
            -0.10467857258350488,
            0.03126957565130373
          ],
          [
            0.08450255093508384,
            -0.45435124512936326
          ],
          [
            -0.3553480603209695,
            0.04221490924735001
          ],
          [
            0.3297600470340729,
            -0.9688160982710526
          ]
        ],
        "terminal_rhs_D_state_D_tau": [
          -1.029104685801025,
          1.0515538243999436,
          -0.9793737043832088,
          1.0981739883535637
        ],
        "terminal_state": [
          0.32487193806652953,
          0.09604744304902228,
          -1.029104685801025,
          1.0515538243999436
        ]
      },
      "declared_rational_point": {
        "absolute_errors": {
          "clock_response": 3.1419897528195406e-07,
          "common_gain_response": 6.193347024119333e-08,
          "parameter_response": [
            4.2741649508570845e-07,
            4.243486962374199e-07
          ]
        },
        "clock_response_exact": "-205821/200000",
        "common_gain_response_exact": "40609/125000",
        "fixed_denominator_before_reduction": 1000000,
        "parameter_response_exact": [
          "-104679/1000000",
          "3127/100000"
        ],
        "status": "conditional rational point; not an ODE enclosure"
      },
      "fine": {
        "accepted_step_count": 200,
        "clock_log_dilation_state_response_tau_times_rhs": [
          -1.0291046858010247,
          1.0515538243999436,
          -0.9793737043832094,
          1.0981739883535642
        ],
        "max_scaled_energy_drift": 4.440892098500626e-16,
        "nfev": 3002,
        "selected_clock_response": -1.0291046858010247,
        "selected_common_gain_response": 0.32487193806652975,
        "selected_parameter_response_row": [
          -0.10467857258350491,
          0.03126957565130376
        ],
        "selected_sensor_output": 0.32487193806652975,
        "terminal_parameter_sensitivity_D_state_D_uv": [
          [
            -0.10467857258350491,
            0.03126957565130376
          ],
          [
            0.08450255093508395,
            -0.4543512451293635
          ],
          [
            -0.35534806032096977,
            0.04221490924735028
          ],
          [
            0.3297600470340732,
            -0.9688160982710534
          ]
        ],
        "terminal_rhs_D_state_D_tau": [
          -1.0291046858010247,
          1.0515538243999436,
          -0.9793737043832094,
          1.0981739883535642
        ],
        "terminal_state": [
          0.32487193806652975,
          0.09604744304902237,
          -1.0291046858010247,
          1.0515538243999436
        ]
      },
      "launch_exact": [
        "4/5",
        "-7/20",
        "0/1",
        "0/1"
      ],
      "legacy_scalar_cost_exact": "1/1",
      "name": "launch-A / theta-1 / tau-1",
      "noise_precision_exact": "1/1",
      "observation_time_tau_exact": "1/1",
      "refinement_discrepancies": {
        "clock_state_vector_relative": 4.0281410480327055e-16,
        "parameter_sensitivity_relative": 7.992411180325297e-16,
        "state_relative": 3.334417152876837e-16
      },
      "sensor": "theta_1",
      "sensor_state_index": 0,
      "tier1_controls_passed": true
    },
    {
      "coarse": {
        "accepted_step_count": 100,
        "clock_log_dilation_state_response_tau_times_rhs": [
          -1.029104685801025,
          1.0515538243999436,
          -0.9793737043832088,
          1.0981739883535637
        ],
        "max_scaled_energy_drift": 2.9605947323337506e-16,
        "nfev": 1502,
        "selected_clock_response": 1.0515538243999436,
        "selected_common_gain_response": 0.09604744304902228,
        "selected_parameter_response_row": [
          0.08450255093508384,
          -0.45435124512936326
        ],
        "selected_sensor_output": 0.09604744304902228,
        "terminal_parameter_sensitivity_D_state_D_uv": [
          [
            -0.10467857258350488,
            0.03126957565130373
          ],
          [
            0.08450255093508384,
            -0.45435124512936326
          ],
          [
            -0.3553480603209695,
            0.04221490924735001
          ],
          [
            0.3297600470340729,
            -0.9688160982710526
          ]
        ],
        "terminal_rhs_D_state_D_tau": [
          -1.029104685801025,
          1.0515538243999436,
          -0.9793737043832088,
          1.0981739883535637
        ],
        "terminal_state": [
          0.32487193806652953,
          0.09604744304902228,
          -1.029104685801025,
          1.0515538243999436
        ]
      },
      "declared_rational_point": {
        "absolute_errors": {
          "clock_response": 1.7560005649563948e-07,
          "common_gain_response": 4.4304902237224386e-07,
          "parameter_response": [
            4.490649160443505e-07,
            2.451293634742058e-07
          ]
        },
        "clock_response_exact": "525777/500000",
        "common_gain_response_exact": "96047/1000000",
        "fixed_denominator_before_reduction": 1000000,
        "parameter_response_exact": [
          "84503/1000000",
          "-454351/1000000"
        ],
        "status": "conditional rational point; not an ODE enclosure"
      },
      "fine": {
        "accepted_step_count": 200,
        "clock_log_dilation_state_response_tau_times_rhs": [
          -1.0291046858010247,
          1.0515538243999436,
          -0.9793737043832094,
          1.0981739883535642
        ],
        "max_scaled_energy_drift": 4.440892098500626e-16,
        "nfev": 3002,
        "selected_clock_response": 1.0515538243999436,
        "selected_common_gain_response": 0.09604744304902237,
        "selected_parameter_response_row": [
          0.08450255093508395,
          -0.4543512451293635
        ],
        "selected_sensor_output": 0.09604744304902237,
        "terminal_parameter_sensitivity_D_state_D_uv": [
          [
            -0.10467857258350491,
            0.03126957565130376
          ],
          [
            0.08450255093508395,
            -0.4543512451293635
          ],
          [
            -0.35534806032096977,
            0.04221490924735028
          ],
          [
            0.3297600470340732,
            -0.9688160982710534
          ]
        ],
        "terminal_rhs_D_state_D_tau": [
          -1.0291046858010247,
          1.0515538243999436,
          -0.9793737043832094,
          1.0981739883535642
        ],
        "terminal_state": [
          0.32487193806652975,
          0.09604744304902237,
          -1.0291046858010247,
          1.0515538243999436
        ]
      },
      "launch_exact": [
        "4/5",
        "-7/20",
        "0/1",
        "0/1"
      ],
      "legacy_scalar_cost_exact": "1/1",
      "name": "launch-A / theta-2 / tau-1",
      "noise_precision_exact": "1/1",
      "observation_time_tau_exact": "1/1",
      "refinement_discrepancies": {
        "clock_state_vector_relative": 4.0281410480327055e-16,
        "parameter_sensitivity_relative": 7.992411180325297e-16,
        "state_relative": 3.334417152876837e-16
      },
      "sensor": "theta_2",
      "sensor_state_index": 1,
      "tier1_controls_passed": true
    },
    {
      "coarse": {
        "accepted_step_count": 150,
        "clock_log_dilation_state_response_tau_times_rhs": [
          -1.2187562839522024,
          0.8687322701015355,
          1.3411545393127948,
          -2.460379665903023
        ],
        "max_scaled_energy_drift": 4.440892098500626e-16,
        "nfev": 2252,
        "selected_clock_response": -2.460379665903023,
        "selected_common_gain_response": 0.579154846734357,
        "selected_parameter_response_row": [
          -0.2550760943638317,
          0.2348187582489396
        ],
        "selected_sensor_output": 0.579154846734357,
        "terminal_parameter_sensitivity_D_state_D_uv": [
          [
            -0.1637662243320772,
            -0.10100156705243023
          ],
          [
            0.09324582533813075,
            -0.6115465985122622
          ],
          [
            0.12683252751862692,
            -0.3136203963731859
          ],
          [
            -0.2550760943638317,
            0.2348187582489396
          ]
        ],
        "terminal_rhs_D_state_D_tau": [
          -0.8125041893014683,
          0.579154846734357,
          0.8941030262085299,
          -1.6402531106020155
        ],
        "terminal_state": [
          -0.17692510902831923,
          0.5645250795095645,
          -0.8125041893014683,
          0.579154846734357
        ]
      },
      "declared_rational_point": {
        "absolute_errors": {
          "clock_response": 3.340969776388647e-07,
          "common_gain_response": 1.5326564362094786e-07,
          "parameter_response": [
            9.436383147098937e-08,
            2.4175106050350337e-07
          ]
        },
        "clock_response_exact": "-123019/50000",
        "common_gain_response_exact": "115831/200000",
        "fixed_denominator_before_reduction": 1000000,
        "parameter_response_exact": [
          "-63769/250000",
          "234819/1000000"
        ],
        "status": "conditional rational point; not an ODE enclosure"
      },
      "fine": {
        "accepted_step_count": 301,
        "clock_log_dilation_state_response_tau_times_rhs": [
          -1.2187562839522024,
          0.8687322701015345,
          1.3411545393127937,
          -2.460379665903022
        ],
        "max_scaled_energy_drift": 5.921189464667501e-16,
        "nfev": 4517,
        "selected_clock_response": -2.460379665903022,
        "selected_common_gain_response": 0.5791548467343564,
        "selected_parameter_response_row": [
          -0.2550760943638315,
          0.2348187582489395
        ],
        "selected_sensor_output": 0.5791548467343564,
        "terminal_parameter_sensitivity_D_state_D_uv": [
          [
            -0.16376622433207744,
            -0.1010015670524301
          ],
          [
            0.09324582533813099,
            -0.6115465985122627
          ],
          [
            0.12683252751862673,
            -0.31362039637318617
          ],
          [
            -0.2550760943638315,
            0.2348187582489395
          ]
        ],
        "terminal_rhs_D_state_D_tau": [
          -0.8125041893014683,
          0.5791548467343564,
          0.8941030262085291,
          -1.6402531106020148
        ],
        "terminal_state": [
          -0.1769251090283187,
          0.5645250795095644,
          -0.8125041893014683,
          0.5791548467343564
        ]
      },
      "launch_exact": [
        "4/5",
        "-7/20",
        "0/1",
        "0/1"
      ],
      "legacy_scalar_cost_exact": "3/2",
      "name": "launch-A / scaled-omega-2 / tau-3/2",
      "noise_precision_exact": "1/1",
      "observation_time_tau_exact": "3/2",
      "refinement_discrepancies": {
        "clock_state_vector_relative": 5.470156899064814e-16,
        "parameter_sensitivity_relative": 7.122428991233243e-16,
        "state_relative": 7.386570073456718e-16
      },
      "sensor": "scaled_omega_2",
      "sensor_state_index": 3,
      "tier1_controls_passed": true
    },
    {
      "coarse": {
        "accepted_step_count": 75,
        "clock_log_dilation_state_response_tau_times_rhs": [
          0.38988229494542537,
          -0.5388671805334858,
          0.7087596425232121,
          -0.9719282678247139
        ],
        "max_scaled_energy_drift": 2.9605947323337506e-16,
        "nfev": 1127,
        "selected_clock_response": 0.38988229494542537,
        "selected_common_gain_response": -0.42019112762997535,
        "selected_parameter_response_row": [
          0.01468629982830584,
          -0.015556885676873041
        ],
        "selected_sensor_output": -0.42019112762997535,
        "terminal_parameter_sensitivity_D_state_D_uv": [
          [
            0.01468629982830584,
            -0.015556885676873041
          ],
          [
            -0.004806478090718757,
            0.2541308902208739
          ],
          [
            0.0748399968260444,
            -0.08996921626346899
          ],
          [
            -0.03555481021717647,
            0.7579104877985554
          ]
        ],
        "terminal_rhs_D_state_D_tau": [
          0.5198430599272338,
          -0.7184895740446477,
          0.9450128566976161,
          -1.2959043570996185
        ],
        "terminal_state": [
          -0.42019112762997535,
          0.6507916348378678,
          0.5198430599272338,
          -0.7184895740446477
        ]
      },
      "declared_rational_point": {
        "absolute_errors": {
          "clock_response": 2.9494542558294867e-07,
          "common_gain_response": 1.2762997531057252e-07,
          "parameter_response": [
            2.9982830583065445e-07,
            1.1432312697901015e-07
          ]
        },
        "clock_response_exact": "194941/500000",
        "common_gain_response_exact": "-420191/1000000",
        "fixed_denominator_before_reduction": 1000000,
        "parameter_response_exact": [
          "7343/500000",
          "-15557/1000000"
        ],
        "status": "conditional rational point; not an ODE enclosure"
      },
      "fine": {
        "accepted_step_count": 150,
        "clock_log_dilation_state_response_tau_times_rhs": [
          0.3898822949454256,
          -0.5388671805334861,
          0.7087596425232123,
          -0.9719282678247142
        ],
        "max_scaled_energy_drift": 1.4802973661668753e-16,
        "nfev": 2252,
        "selected_clock_response": 0.3898822949454256,
        "selected_common_gain_response": -0.4201911276299753,
        "selected_parameter_response_row": [
          0.01468629982830583,
          -0.01555688567687302
        ],
        "selected_sensor_output": -0.4201911276299753,
        "terminal_parameter_sensitivity_D_state_D_uv": [
          [
            0.01468629982830583,
            -0.01555688567687302
          ],
          [
            -0.004806478090718739,
            0.2541308902208738
          ],
          [
            0.07483999682604439,
            -0.08996921626346888
          ],
          [
            -0.0355548102171764,
            0.7579104877985547
          ]
        ],
        "terminal_rhs_D_state_D_tau": [
          0.5198430599272341,
          -0.7184895740446482,
          0.9450128566976164,
          -1.295904357099619
        ],
        "terminal_state": [
          -0.4201911276299753,
          0.6507916348378678,
          0.5198430599272341,
          -0.7184895740446482
        ]
      },
      "launch_exact": [
        "-3/5",
        "9/10",
        "0/1",
        "0/1"
      ],
      "legacy_scalar_cost_exact": "1/1",
      "name": "launch-B / theta-1 / tau-3/4",
      "noise_precision_exact": "1/1",
      "observation_time_tau_exact": "3/4",
      "refinement_discrepancies": {
        "clock_state_vector_relative": 4.1184927015440223e-16,
        "parameter_sensitivity_relative": 6.819030069943916e-16,
        "state_relative": 4.737753517202695e-16
      },
      "sensor": "theta_1",
      "sensor_state_index": 0,
      "tier1_controls_passed": true
    },
    {
      "coarse": {
        "accepted_step_count": 125,
        "clock_log_dilation_state_response_tau_times_rhs": [
          1.397408678273901,
          -1.9288127284131382,
          0.5817741920153442,
          -0.8431539720635917
        ],
        "max_scaled_energy_drift": 2.9605947323337506e-16,
        "nfev": 1877,
        "selected_clock_response": 0.5817741920153442,
        "selected_common_gain_response": 1.1179269426191207,
        "selected_parameter_response_row": [
          0.46905473801960634,
          0.004140122027466567
        ],
        "selected_sensor_output": 1.1179269426191207,
        "terminal_parameter_sensitivity_D_state_D_uv": [
          [
            0.14519389780583336,
            -0.11348828558373852
          ],
          [
            -0.11013111104591304,
            0.8607493710377603
          ],
          [
            0.46905473801960634,
            0.004140122027466567
          ],
          [
            -0.41445726915744574,
            1.248028363506962
          ]
        ],
        "terminal_rhs_D_state_D_tau": [
          1.1179269426191207,
          -1.5430501827305105,
          0.4654193536122753,
          -0.6745231776508733
        ],
        "terminal_state": [
          -0.011759710472838678,
          0.08757250244486336,
          1.1179269426191207,
          -1.5430501827305105
        ]
      },
      "declared_rational_point": {
        "absolute_errors": {
          "clock_response": 1.920153386292256e-07,
          "common_gain_response": 5.738087915929668e-08,
          "parameter_response": [
            2.6198039415614716e-07,
            1.2202746886742777e-07
          ]
        },
        "clock_response_exact": "290887/500000",
        "common_gain_response_exact": "1117927/1000000",
        "fixed_denominator_before_reduction": 1000000,
        "parameter_response_exact": [
          "93811/200000",
          "207/50000"
        ],
        "status": "conditional rational point; not an ODE enclosure"
      },
      "fine": {
        "accepted_step_count": 251,
        "clock_log_dilation_state_response_tau_times_rhs": [
          1.397408678273901,
          -1.9288127284131398,
          0.5817741920153386,
          -0.843153972063584
        ],
        "max_scaled_energy_drift": 2.9605947323337506e-16,
        "nfev": 3767,
        "selected_clock_response": 0.5817741920153386,
        "selected_common_gain_response": 1.1179269426191207,
        "selected_parameter_response_row": [
          0.46905473801960584,
          0.004140122027468867
        ],
        "selected_sensor_output": 1.1179269426191207,
        "terminal_parameter_sensitivity_D_state_D_uv": [
          [
            0.14519389780583333,
            -0.1134882855837382
          ],
          [
            -0.11013111104591304,
            0.8607493710377595
          ],
          [
            0.46905473801960584,
            0.004140122027468867
          ],
          [
            -0.41445726915744524,
            1.2480283635069578
          ]
        ],
        "terminal_rhs_D_state_D_tau": [
          1.1179269426191207,
          -1.5430501827305119,
          0.4654193536122709,
          -0.6745231776508672
        ],
        "terminal_state": [
          -0.011759710472838239,
          0.08757250244486285,
          1.1179269426191207,
          -1.5430501827305119
        ]
      },
      "launch_exact": [
        "-3/5",
        "9/10",
        "0/1",
        "0/1"
      ],
      "legacy_scalar_cost_exact": "5/4",
      "name": "launch-B / scaled-omega-1 / tau-5/4",
      "noise_precision_exact": "1/1",
      "observation_time_tau_exact": "5/4",
      "refinement_discrepancies": {
        "clock_state_vector_relative": 3.697675994458229e-15,
        "parameter_sensitivity_relative": 2.9797339907384054e-15,
        "state_relative": 7.830787268968204e-16
      },
      "sensor": "scaled_omega_1",
      "sensor_state_index": 2,
      "tier1_controls_passed": true
    },
    {
      "coarse": {
        "accepted_step_count": 100,
        "clock_log_dilation_state_response_tau_times_rhs": [
          -1.0996598246560352,
          0.5802981313706875,
          -0.5493350564965217,
          -0.09511378751595966
        ],
        "max_scaled_energy_drift": 4.440892098500626e-16,
        "nfev": 1502,
        "selected_clock_response": 0.5802981313706875,
        "selected_common_gain_response": 0.6660572261645687,
        "selected_parameter_response_row": [
          0.08100880454212712,
          -0.24785046457454626
        ],
        "selected_sensor_output": 0.6660572261645687,
        "terminal_parameter_sensitivity_D_state_D_uv": [
          [
            -0.08897486601649039,
            -0.002705996727448154
          ],
          [
            0.08100880454212712,
            -0.24785046457454626
          ],
          [
            -0.18733042993622093,
            -0.06909002597405553
          ],
          [
            0.15694398760829192,
            -0.41298633581223104
          ]
        ],
        "terminal_rhs_D_state_D_tau": [
          -1.0996598246560352,
          0.5802981313706875,
          -0.5493350564965217,
          -0.09511378751595966
        ],
        "terminal_state": [
          0.6442015486075852,
          0.6660572261645687,
          -1.0996598246560352,
          0.5802981313706875
        ]
      },
      "declared_rational_point": {
        "absolute_errors": {
          "clock_response": 1.3137068644031302e-07,
          "common_gain_response": 2.2616456940571794e-07,
          "parameter_response": [
            1.9545787280361715e-07,
            4.6457454627724104e-07
          ]
        },
        "clock_response_exact": "290149/500000",
        "common_gain_response_exact": "666057/1000000",
        "fixed_denominator_before_reduction": 1000000,
        "parameter_response_exact": [
          "81009/1000000",
          "-4957/20000"
        ],
        "status": "conditional rational point; not an ODE enclosure"
      },
      "fine": {
        "accepted_step_count": 200,
        "clock_log_dilation_state_response_tau_times_rhs": [
          -1.099659824656034,
          0.5802981313706864,
          -0.5493350564965185,
          -0.09511378751596475
        ],
        "max_scaled_energy_drift": 5.921189464667501e-16,
        "nfev": 3002,
        "selected_clock_response": 0.5802981313706864,
        "selected_common_gain_response": 0.6660572261645694,
        "selected_parameter_response_row": [
          0.0810088045421272,
          -0.24785046457454626
        ],
        "selected_sensor_output": 0.6660572261645694,
        "terminal_parameter_sensitivity_D_state_D_uv": [
          [
            -0.08897486601649052,
            -0.002705996727448175
          ],
          [
            0.0810088045421272,
            -0.24785046457454626
          ],
          [
            -0.18733042993622048,
            -0.0690900259740557
          ],
          [
            0.15694398760829126,
            -0.41298633581223
          ]
        ],
        "terminal_rhs_D_state_D_tau": [
          -1.099659824656034,
          0.5802981313706864,
          -0.5493350564965185,
          -0.09511378751596475
        ],
        "terminal_state": [
          0.6442015486075846,
          0.6660572261645694,
          -1.099659824656034,
          0.5802981313706864
        ]
      },
      "launch_exact": [
        "6/5",
        "2/5",
        "0/1",
        "0/1"
      ],
      "legacy_scalar_cost_exact": "1/1",
      "name": "launch-C / theta-2 / tau-1",
      "noise_precision_exact": "1/1",
      "observation_time_tau_exact": "1/1",
      "refinement_discrepancies": {
        "clock_state_vector_relative": 4.569535288123972e-15,
        "parameter_sensitivity_relative": 1.342373438313509e-15,
        "state_relative": 1.1566627726381805e-15
      },
      "sensor": "theta_2",
      "sensor_state_index": 1,
      "tier1_controls_passed": true
    },
    {
      "coarse": {
        "accepted_step_count": 150,
        "clock_log_dilation_state_response_tau_times_rhs": [
          -1.466408002234337,
          -0.13039302312028433,
          0.8615674968548457,
          -2.693317660166115
        ],
        "max_scaled_energy_drift": 4.440892098500626e-16,
        "nfev": 2252,
        "selected_clock_response": -2.693317660166115,
        "selected_common_gain_response": -0.08692868208018956,
        "selected_parameter_response_row": [
          -0.2627857193301506,
          0.471276722080529
        ],
        "selected_sensor_output": -0.08692868208018956,
        "terminal_parameter_sensitivity_D_state_D_uv": [
          [
            -0.07976354302457699,
            -0.07189853776920785
          ],
          [
            0.029367343214650857,
            -0.23674167795883466
          ],
          [
            0.18283172077856283,
            -0.12556194650109845
          ],
          [
            -0.2627857193301506,
            0.471276722080529
          ]
        ],
        "terminal_rhs_D_state_D_tau": [
          -0.9776053348228914,
          -0.08692868208018956,
          0.5743783312365638,
          -1.79554510677741
        ],
        "terminal_state": [
          0.10306906954767595,
          0.8233692720774803,
          -0.9776053348228914,
          -0.08692868208018956
        ]
      },
      "declared_rational_point": {
        "absolute_errors": {
          "clock_response": 3.398338876969831e-07,
          "common_gain_response": 3.17919808826006e-07,
          "parameter_response": [
            2.8066984925079197e-07,
            2.77919470603738e-07
          ]
        },
        "clock_response_exact": "-1346659/500000",
        "common_gain_response_exact": "-86929/1000000",
        "fixed_denominator_before_reduction": 1000000,
        "parameter_response_exact": [
          "-131393/500000",
          "471277/1000000"
        ],
        "status": "conditional rational point; not an ODE enclosure"
      },
      "fine": {
        "accepted_step_count": 301,
        "clock_log_dilation_state_response_tau_times_rhs": [
          -1.4664080022343353,
          -0.13039302312028678,
          0.8615674968548452,
          -2.6933176601661124
        ],
        "max_scaled_energy_drift": 5.921189464667501e-16,
        "nfev": 4517,
        "selected_clock_response": -2.6933176601661124,
        "selected_common_gain_response": -0.08692868208019118,
        "selected_parameter_response_row": [
          -0.26278571933015077,
          0.4712767220805294
        ],
        "selected_sensor_output": -0.08692868208019118,
        "terminal_parameter_sensitivity_D_state_D_uv": [
          [
            -0.07976354302457693,
            -0.07189853776920763
          ],
          [
            0.029367343214650638,
            -0.2367416779588342
          ],
          [
            0.18283172077856297,
            -0.12556194650109812
          ],
          [
            -0.26278571933015077,
            0.4712767220805294
          ]
        ],
        "terminal_rhs_D_state_D_tau": [
          -0.9776053348228901,
          -0.08692868208019118,
          0.5743783312365635,
          -1.7955451067774084
        ],
        "terminal_state": [
          0.1030690695476757,
          0.8233692720774805,
          -0.9776053348228901,
          -0.08692868208019118
        ]
      },
      "launch_exact": [
        "6/5",
        "2/5",
        "0/1",
        "0/1"
      ],
      "legacy_scalar_cost_exact": "3/2",
      "name": "launch-C / scaled-omega-2 / tau-3/2",
      "noise_precision_exact": "1/1",
      "observation_time_tau_exact": "3/2",
      "refinement_discrepancies": {
        "clock_state_vector_relative": 1.2709787074699707e-15,
        "parameter_sensitivity_relative": 7.9480630270599e-16,
        "state_relative": 1.5950526654686568e-15
      },
      "sensor": "scaled_omega_2",
      "sensor_state_index": 3,
      "tier1_controls_passed": true
    }
  ],
  "schema_version": "oig-double-pendulum-grouped-protocol-v1",
  "selected_designs": {
    "cost_weighted_clock_only": {
      "budget_shares_exact": [
        "2/3",
        "1/3",
        "0/1"
      ],
      "positive_floor": {
        "descriptive_profiled_floor_lower": 0.018026929453263358,
        "identity_query_relation": "profiled floor = 1/(minimax identity-query amplification squared)",
        "profiled_floor_lower_exact": "13779612981787854684459904996426557359436244703963504643644850176/764390464694106501214925417116232161175466503411161923039119419429",
        "profiled_floor_upper_exact": "31009562716758388491553844565288974594953/1720179956168010777290336510380256250000000",
        "strictly_positive_exact": true
      }
    },
    "minimum_clock_only": {
      "budget_shares_exact": [
        "1/1",
        "0/1",
        "0/1"
      ],
      "positive_floor": {
        "descriptive_profiled_floor_lower": 9.789124164627926e-06,
        "identity_query_relation": "profiled floor = 1/(minimax identity-query amplification squared)",
        "profiled_floor_lower_exact": "2656313622412568391830785344028483501162026017082516529217536/271353552957363266708642812779285240324977831260063128781397733607",
        "profiled_floor_upper_exact": "2261648364358617795867283370931523/231036845209387391926902536750000000000",
        "strictly_positive_exact": true
      }
    },
    "secondary_clock_and_common_gain": {
      "budget_shares_exact": [
        "5/12",
        "1/4",
        "1/3"
      ],
      "positive_floor": {
        "descriptive_profiled_floor_lower": 0.0021840122221773164,
        "identity_query_relation": "profiled floor = 1/(minimax identity-query amplification squared)",
        "profiled_floor_lower_exact": "111061684488730216571204782315756491366704593257700653389774929875945437576298496/50852135057197170529832416871813416824710960143606076357899293161818229257884513419",
        "profiled_floor_upper_exact": "5755202740559823274230857528570480293458660835077887183/2635151343073650244212891342774124224685196691000000000000",
        "strictly_positive_exact": true
      },
      "scope": "Secondary optimistic control: one log multiplicative gain is shared by every dimensionless output, even across angle and scaled-velocity channels. It is not a sensor-specific calibration model."
    }
  },
  "source_model": {
    "base_point_exact": [
      "0/1",
      "0/1"
    ],
    "coordinates": [
      "u=log(m2/m1)",
      "v=log(l2/l1)"
    ],
    "dimensionless_convention": "m1=l1=g=1, m2=exp(u), l2=exp(v), tau=t*sqrt(g/l1), nu=dtheta/dtau",
    "query": "the full two-dimensional identity query in (u,v)"
  },
  "status": "constructive positive grouped-protocol floor"
}