{
  "schema": "ggii.calibration-artifact/1",
  "baseCoreVersion": "0.1.0",
  "globalGeometryIICoreVersion": "0.2.0-alpha.5",
  "scientificScope": {
    "spectralResult": "finite computational calibration of a profile-equivalence candidate",
    "metricResult": "proved-here nonuniversality for the declared one-skeleton graph metrics",
    "diffusionResult": "proved-here common Gaussian finite-dimensional limit for the declared square and equilateral-triangular walks",
    "robustDiffusionResult": "proved-here uniform finite-dimensional Gaussian limit over bounded centered nondegenerate iid laws after covariance whitening",
    "notEstablished": [
      "a common metric-measure-operator limit",
      "bounded-disk or disordered universality",
      "path-space functional convergence in this artifact",
      "semigroup or operator convergence",
      "boundary or disordered-conductance invariance principles",
      "physical material validation"
    ]
  },
  "elementaryTheoremLedger": [
    {
      "artifacts": [
        "GLOBAL_GEOMETRY_II_FOUNDATIONS.md"
      ],
      "assumptions": [
        "fixed adjacency",
        "synchronous writes",
        "bounded read radius",
        "equivariant local kernel"
      ],
      "basis": "proved-here",
      "claim": "A synchronous radius-R local rule on fixed adjacency has an exact radius-RT causal cone after T steps.",
      "dependencies": [],
      "digest": "837f47f2",
      "digestAlgorithm": "fnv1a32-canonical-json",
      "falsifier": "Two matched initial states agreeing on the radius-RT neighborhood produce different root states within T updates without an adjacency rewrite or differing broadcast.",
      "id": "ggii.theorem.p3.1.causal-cone",
      "limitations": [
        "not valid across undeclared structural rewrites",
        "requires a fixed combinatorial bound for metric-defined neighborhoods"
      ],
      "method": "Induct on the number of synchronous updates and the nested neighborhoods each update can read.",
      "proofAnchor": "GLOBAL_GEOMETRY_II_FOUNDATIONS.md Proposition 3.1",
      "result": {
        "conclusion": "proved in declared finite scope",
        "theoremId": "3.1"
      },
      "schemaVersion": 2,
      "scope": "Deterministic synchronous L0 rules on a fixed declared adjacency, with identical broadcasts when L1 data are present.",
      "sourceUrls": [],
      "status": "proved",
      "tests": [
        "release-1 L0 causal-cone fixture"
      ]
    },
    {
      "artifacts": [
        "GLOBAL_GEOMETRY_II_FOUNDATIONS.md"
      ],
      "assumptions": [
        "rooted-neighborhood isomorphism invariance",
        "equivariant commit"
      ],
      "basis": "proved-here",
      "claim": "Neighborhood-isomorphism local kernels with equivariant synchronous commit commute with every carrier relabeling.",
      "dependencies": [],
      "digest": "10eeadcc",
      "digestAlgorithm": "fnv1a32-canonical-json",
      "falsifier": "A carrier permutation changes an intrinsic output while all neighborhood data and conflict resolution are transported equivariantly.",
      "id": "ggii.theorem.p3.2.relabeling",
      "limitations": [],
      "method": "Transport every rooted decorated neighborhood and corresponding write through the carrier isomorphism.",
      "proofAnchor": "GLOBAL_GEOMETRY_II_FOUNDATIONS.md Proposition 3.2",
      "result": {
        "conclusion": "proved in declared finite scope",
        "theoremId": "3.2"
      },
      "schemaVersion": 2,
      "scope": "Finite decorated carriers and rules that exclude absolute IDs and serialization order from their read semantics.",
      "sourceUrls": [],
      "status": "proved",
      "tests": [
        "release-1 relabeling invariance fixtures"
      ]
    },
    {
      "artifacts": [
        "GLOBAL_GEOMETRY_II_FOUNDATIONS.md"
      ],
      "assumptions": [
        "no carrier rewrite"
      ],
      "basis": "proved-here",
      "claim": "State-only updates on a fixed finite carrier preserve its homology and Euler characteristic.",
      "dependencies": [],
      "digest": "190afc9a",
      "digestAlgorithm": "fnv1a32-canonical-json",
      "falsifier": "A combinatorial invariant changes while every cell and boundary matrix remains byte-identical.",
      "id": "ggii.theorem.p3.3.fixed-topology",
      "limitations": [
        "scale-dependent inferred topology may change even when exact carrier topology does not"
      ],
      "method": "The chain groups and boundary matrices are identical at every time, so their ranks, kernels, images, and alternating cell count are identical.",
      "proofAnchor": "GLOBAL_GEOMETRY_II_FOUNDATIONS.md Proposition 3.3",
      "result": {
        "conclusion": "proved in declared finite scope",
        "theoremId": "3.3"
      },
      "schemaVersion": 2,
      "scope": "Any trajectory whose cell sets and boundary operators remain unchanged.",
      "sourceUrls": [],
      "status": "proved",
      "tests": [
        "topology remains constant under release-1 diffusion and curvature steps"
      ]
    },
    {
      "artifacts": [
        "GLOBAL_GEOMETRY_II_FOUNDATIONS.md"
      ],
      "assumptions": [
        "deterministic observer",
        "equivariant local rule",
        "matched broadcasts"
      ],
      "basis": "proved-here",
      "claim": "No deterministic equivariant radius-R observer running for T rounds distinguishes roots with isomorphic radius-RT decorated neighborhoods and matched broadcasts.",
      "dependencies": [
        "ggii.theorem.p3.1.causal-cone",
        "ggii.theorem.p3.2.relabeling"
      ],
      "digest": "84155205",
      "digestAlgorithm": "fnv1a32-canonical-json",
      "falsifier": "A bounded observer returns different root histories for two coupled radius-RT-identical inputs.",
      "id": "ggii.theorem.p3.4.local-indistinguishability",
      "limitations": [
        "does not restrict observers with growing radius or trusted global data"
      ],
      "method": "Couple the two executions through the rooted isomorphism and apply the causal-cone and equivariance propositions.",
      "proofAnchor": "GLOBAL_GEOMETRY_II_FOUNDATIONS.md Proposition 3.4",
      "result": {
        "conclusion": "proved in declared finite scope",
        "theoremId": "3.4"
      },
      "schemaVersion": 2,
      "scope": "Bounded-round deterministic distributed recognition on declared rooted decorated carriers.",
      "sourceUrls": [],
      "status": "proved",
      "tests": []
    },
    {
      "artifacts": [
        "GLOBAL_GEOMETRY_II_FOUNDATIONS.md"
      ],
      "assumptions": [
        "strict face inequalities",
        "shared-edge length consistency",
        "valid links for the surface conclusion"
      ],
      "basis": "proved-here",
      "claim": "Positive shared edge lengths satisfying strict triangle inequalities define a piecewise-Euclidean triangular length space; valid vertex links make it a surface with boundary.",
      "dependencies": [],
      "digest": "71f8442e",
      "digestAlgorithm": "fnv1a32-canonical-json",
      "falsifier": "A face satisfying all strict inequalities lacks a Euclidean SSS realization, or equal shared edges cannot be glued isometrically.",
      "id": "ggii.theorem.p4.1.triangle-gluing",
      "limitations": [
        "intrinsic construction does not prove an embedding in three-space"
      ],
      "method": "Apply side-side-side realization facewise, glue equal edge copies isometrically, and use the path/cycle link criterion.",
      "proofAnchor": "GLOBAL_GEOMETRY_II_FOUNDATIONS.md Proposition 4.1",
      "result": {
        "conclusion": "proved in declared finite scope",
        "theoremId": "4.1"
      },
      "schemaVersion": 2,
      "scope": "Finite triangular complexes with one authoritative length per abstract edge.",
      "sourceUrls": [],
      "status": "proved",
      "tests": [
        "release-1 surface-validity and intrinsic-curvature fixtures"
      ]
    },
    {
      "artifacts": [
        "GLOBAL_GEOMETRY_II_FOUNDATIONS.md"
      ],
      "assumptions": [
        "strictly positive radii",
        "tangency length law"
      ],
      "basis": "proved-here",
      "claim": "Positive tangency-circle radii with edge lengths l_ij=r_i+r_j satisfy every strict triangular face inequality.",
      "dependencies": [],
      "digest": "d6e49b63",
      "digestAlgorithm": "fnv1a32-canonical-json",
      "falsifier": "Positive radii yield a nonpositive triangle slack under l_ij=r_i+r_j.",
      "id": "ggii.theorem.p4.2.circle-face-compatibility",
      "limitations": [
        "does not establish prescribed-curvature realizability"
      ],
      "method": "Each triangle slack reduces exactly to twice the radius at the intervening vertex.",
      "proofAnchor": "GLOBAL_GEOMETRY_II_FOUNDATIONS.md Proposition 4.2",
      "result": {
        "conclusion": "proved in declared finite scope",
        "theoremId": "4.2"
      },
      "schemaVersion": 2,
      "scope": "Triangular faces in the positive tangency circle-packing metric.",
      "sourceUrls": [],
      "status": "proved",
      "tests": [
        "circle-packing length property fixtures"
      ]
    },
    {
      "artifacts": [
        "GLOBAL_GEOMETRY_II_FOUNDATIONS.md"
      ],
      "assumptions": [
        "valid surface links",
        "nondegenerate Euclidean triangles",
        "declared boundary convention"
      ],
      "basis": "proved-here",
      "claim": "Angle defects on a finite nondegenerate triangulated surface, using interior target angle 2pi and boundary target angle pi, sum to 2pi times Euler characteristic.",
      "dependencies": [],
      "digest": "0d9d5ce7",
      "digestAlgorithm": "fnv1a32-canonical-json",
      "falsifier": "An exact valid triangulation violates the symbolic angle-count identity under the stated boundary convention.",
      "id": "ggii.theorem.p4.3.gauss-bonnet",
      "limitations": [
        "floating residuals are computational audits",
        "the total condition is not sufficient for a target metric"
      ],
      "method": "Sum face angles, use 3F=2E_i+E_b and E_b=V_b, then identify the Euler alternating count.",
      "proofAnchor": "GLOBAL_GEOMETRY_II_FOUNDATIONS.md Proposition 4.3",
      "result": {
        "conclusion": "proved in declared finite scope",
        "theoremId": "4.3"
      },
      "schemaVersion": 2,
      "scope": "Compact finite triangular two-manifolds with boundary and nondegenerate Euclidean faces.",
      "sourceUrls": [],
      "status": "proved",
      "tests": [
        "release-1 disk, sphere, puncture, and invalid-surface fixtures"
      ]
    },
    {
      "artifacts": [
        "GLOBAL_GEOMETRY_II_FOUNDATIONS.md"
      ],
      "assumptions": [
        "undirected graph",
        "positive edge weights",
        "declared isolated-vertex convention"
      ],
      "basis": "proved-here",
      "claim": "The zero-eigenvalue multiplicity of the symmetric normalized Laplacian equals the number of connected components.",
      "dependencies": [],
      "digest": "d78ec840",
      "digestAlgorithm": "fnv1a32-canonical-json",
      "falsifier": "An eligible graph has normalized-Laplacian nullity different from its component count.",
      "id": "ggii.theorem.p4.4.laplacian-nullity",
      "limitations": [],
      "method": "Characterize the kernel from the nonnegative Dirichlet quadratic form component by component.",
      "proofAnchor": "GLOBAL_GEOMETRY_II_FOUNDATIONS.md Proposition 4.4",
      "result": {
        "conclusion": "proved in declared finite scope",
        "theoremId": "4.4"
      },
      "schemaVersion": 2,
      "scope": "Finite undirected graphs with positive edge weights and the declared zero-block isolated-vertex convention.",
      "sourceUrls": [],
      "status": "proved",
      "tests": [
        "release-1 connected and disconnected spectral fixtures"
      ]
    },
    {
      "artifacts": [
        "GLOBAL_GEOMETRY_II_FOUNDATIONS.md"
      ],
      "assumptions": [
        "symmetric conductance",
        "same edge flux used at both endpoints"
      ],
      "basis": "proved-here",
      "claim": "A symmetric edge-flux update conserves the declared measure-weighted total exactly in algebra.",
      "dependencies": [],
      "digest": "ad9353cf",
      "digestAlgorithm": "fnv1a32-canonical-json",
      "falsifier": "The symbolic weighted sum changes under a finite symmetric flux update.",
      "id": "ggii.theorem.p4.5.flux-conservation",
      "limitations": [
        "conservation alone does not ensure positivity or time-step stability"
      ],
      "method": "Pair and cancel the two oriented contributions of every undirected edge.",
      "proofAnchor": "GLOBAL_GEOMETRY_II_FOUNDATIONS.md Proposition 4.5",
      "result": {
        "conclusion": "proved in declared finite scope",
        "theoremId": "4.5"
      },
      "schemaVersion": 2,
      "scope": "Finite graphs with symmetric nonnegative conductance and the stated antisymmetric neighbor-difference update.",
      "sourceUrls": [],
      "status": "proved",
      "tests": []
    },
    {
      "artifacts": [
        "GLOBAL_GEOMETRY_II_FOUNDATIONS.md"
      ],
      "assumptions": [
        "connected carrier",
        "edge-sum system is solvable"
      ],
      "basis": "proved-here",
      "claim": "When circle-radius edge-sum equations are solvable on a connected graph, radii are unique exactly when the graph is nonbipartite; a bipartite graph retains a one-dimensional alternating gauge.",
      "dependencies": [],
      "digest": "b65c4c93",
      "digestAlgorithm": "fnv1a32-canonical-json",
      "falsifier": "A solvable connected nonbipartite instance has two radius solutions, or a connected bipartite instance has a homogeneous solution outside the alternating line.",
      "id": "ggii.theorem.p5.1.radius-identifiability",
      "limitations": [
        "positivity bounds restrict but do not generally remove the bipartite gauge"
      ],
      "method": "Differences of two solutions alternate sign along paths; an odd cycle forces the root difference to zero.",
      "proofAnchor": "GLOBAL_GEOMETRY_II_FOUNDATIONS.md Proposition 5.1",
      "result": {
        "conclusion": "proved in declared finite scope",
        "theoremId": "5.1"
      },
      "schemaVersion": 2,
      "scope": "Connected finite graphs and real solutions of r_i+r_j=l_ij on every edge.",
      "sourceUrls": [],
      "status": "proved",
      "tests": []
    },
    {
      "artifacts": [
        "GLOBAL_GEOMETRY_II_FOUNDATIONS.md"
      ],
      "assumptions": [
        "fixed graph",
        "positive lengths",
        "connectedness"
      ],
      "basis": "proved-here",
      "claim": "Changing every edge length of a fixed connected N-vertex graph by at most epsilon changes every shortest-path distance by at most (N-1)epsilon.",
      "dependencies": [],
      "digest": "acf9ae0c",
      "digestAlgorithm": "fnv1a32-canonical-json",
      "falsifier": "A pairwise distance changes by more than (N-1) times the maximum edge perturbation.",
      "id": "ggii.theorem.p5.2.metric-stability",
      "limitations": [
        "a useful refinement bound additionally requires the rescaled factor to vanish"
      ],
      "method": "Evaluate each old shortest simple path in the perturbed metric and reverse the argument.",
      "proofAnchor": "GLOBAL_GEOMETRY_II_FOUNDATIONS.md Proposition 5.2",
      "result": {
        "conclusion": "proved in declared finite scope",
        "theoremId": "5.2"
      },
      "schemaVersion": 2,
      "scope": "Fixed finite connected graphs with positive edge lengths.",
      "sourceUrls": [],
      "status": "proved",
      "tests": []
    },
    {
      "artifacts": [
        "GLOBAL_GEOMETRY_II_FOUNDATIONS.md"
      ],
      "assumptions": [
        "deterministic generator",
        "canonical serialization",
        "fixed seed",
        "deterministic updates"
      ],
      "basis": "proved-here",
      "claim": "A closed deterministic generator, seed, parameter record, broadcast sequence, and synchronous update determine one finite trajectory.",
      "dependencies": [],
      "digest": "ea357d85",
      "digestAlgorithm": "fnv1a32-canonical-json",
      "falsifier": "Two executions with the identical closed record produce different exact finite states before environment-only metadata.",
      "id": "ggii.theorem.p5.3.deterministic-replay",
      "limitations": [
        "floating libraries may require schema-aware tolerance rather than byte equality"
      ],
      "method": "The initial state is fixed by the closed record; induction fixes each subsequent deterministic update.",
      "proofAnchor": "GLOBAL_GEOMETRY_II_FOUNDATIONS.md Proposition 5.3",
      "result": {
        "conclusion": "proved in declared finite scope",
        "theoremId": "5.3"
      },
      "schemaVersion": 2,
      "scope": "Finite computations without undeclared nondeterministic inputs.",
      "sourceUrls": [],
      "status": "proved",
      "tests": [
        "release-1 replay fixtures",
        "Global Geometry II checksum and manifest fixtures"
      ]
    },
    {
      "artifacts": [
        "GLOBAL_GEOMETRY_II_FOUNDATIONS.md"
      ],
      "assumptions": [
        "same face metrics",
        "consistent edge subdivisions",
        "piecewise-Euclidean path metric"
      ],
      "basis": "proved-here",
      "claim": "Straight inherited subdivision of a piecewise-Euclidean complex is isometric to the original piecewise-Euclidean realization.",
      "dependencies": [],
      "digest": "f8effbea",
      "digestAlgorithm": "fnv1a32-canonical-json",
      "falsifier": "A path changes intrinsic piecewise-Euclidean length under a purely inherited straight subdivision.",
      "id": "ggii.theorem.p6.1.metric-null-subdivision",
      "limitations": [
        "a changed graph one-skeleton distance is not the same metric"
      ],
      "method": "The identity on every old face preserves every rectifiable path length before and after partition.",
      "proofAnchor": "GLOBAL_GEOMETRY_II_FOUNDATIONS.md Proposition 6.1",
      "result": {
        "conclusion": "proved in declared finite scope",
        "theoremId": "6.1"
      },
      "schemaVersion": 2,
      "scope": "Facewise straight subdivisions with consistent shared-edge subdivisions and inherited Euclidean lengths.",
      "sourceUrls": [],
      "status": "proved",
      "tests": []
    },
    {
      "artifacts": [
        "formula:square-word-distance",
        "formula:triangular-word-distance"
      ],
      "assumptions": [
        "uniform positive edge length",
        "declared square and triangular generator sets",
        "one-skeleton shortest-path metric"
      ],
      "basis": "proved-here",
      "claim": "Unit-edge square and triangular one-skeleton refinements have different normed-plane metric limits: the square unit ball has four extreme points and the triangular unit ball has six.",
      "dependencies": [],
      "digest": "47b91141",
      "digestAlgorithm": "fnv1a32-canonical-json",
      "falsifier": "An integer coordinate contradicting either word-distance formula, or a surjective normed-space isometry preserving neither extreme-point count, would refute the stated proof fixture.",
      "id": "ggii.graph-metric.square-triangular.p8.1",
      "limitations": [
        "does not obstruct a shared covariance-normalized diffusion limit",
        "does not apply when both meshes are given a common facewise piecewise-Euclidean metric"
      ],
      "method": "Use the exact word-distance formula |m|+|n| for square generators and max(|m|,|n|,|m+n|) for triangular generators, then count the extreme points of their polyhedral unit balls.",
      "proofAnchor": "GLOBAL_GEOMETRY_II_FOUNDATIONS.md Proposition 8.1",
      "result": {
        "isometricLimits": false,
        "squareExtremePoints": 4,
        "triangularExtremePoints": 6
      },
      "schemaVersion": 2,
      "scope": "Infinite square and triangular coordinate graphs with their word metrics, rescaled by lattice spacing on bounded pointed sets.",
      "sourceUrls": [],
      "status": "proved",
      "tests": [
        "bounded integer-coordinate breadth-first fixtures",
        "unit-ball extreme-point fixture"
      ]
    },
    {
      "artifacts": [
        "formula:lattice-step-moments",
        "formula:lattice-step-characteristic"
      ],
      "assumptions": [
        "uniform independent increments",
        "declared Euclidean embeddings",
        "fixed finite observation times",
        "diffusive n^{-1/2} spatial scaling"
      ],
      "basis": "proved-here",
      "claim": "Uniform simple random walks on the orthogonal square and equilateral triangular step sets have the same covariance-normalized Gaussian finite-dimensional diffusion limit.",
      "dependencies": [],
      "digest": "f95165e6",
      "digestAlgorithm": "fnv1a32-canonical-json",
      "falsifier": "A declared step moment differs from I/2, or a fixed finite collection of rescaled-time characteristic functions has a non-Gaussian or family-dependent limit.",
      "id": "ggii.theorem.p8.2.square-triangular-gaussian-fdd",
      "limitations": [
        "does not prove path-space tightness",
        "does not identify graph metrics",
        "does not cover boundaries or disordered conductance"
      ],
      "method": "Prove the symbolic zero mean and covariance I/2 identities, expand each finite-support symmetric characteristic function at the origin, and apply Cramer--Wold after factoring joint characteristic functions over disjoint time increments.",
      "proofAnchor": "GLOBAL_GEOMETRY_II_FOUNDATIONS.md Proposition 8.2",
      "result": {
        "covarianceAtTimeT": "t*I/2",
        "limitingCharacteristicFunction": "exp(-t*|xi|^2/4)",
        "squareCovariance": [
          [
            0.5,
            0
          ],
          [
            0,
            0.5
          ]
        ],
        "standardBrownianTimeAccelerationAtEdgeScaleH": "2/h^2",
        "symbolicCovariance": "I/2",
        "symbolicMean": "0",
        "triangularCovariance": [
          [
            0.5,
            0
          ],
          [
            0,
            0.5
          ]
        ]
      },
      "schemaVersion": 2,
      "scope": "Independent-increment walks using exactly the declared physical step vectors; convergence of finite-dimensional distributions under n^{-1/2} spatial scaling.",
      "sourceUrls": [],
      "status": "proved",
      "tests": [
        "symbolic covariance identity with binary64 residual audit",
        "multi-time finite-n characteristic convergence audit",
        "distinct fourth-moment microscopic control",
        "derived-phase overflow rejection"
      ]
    },
    {
      "artifacts": [
        "formula:uniform-whitened-characteristic-expansion",
        "artifact:calibration-v1.json"
      ],
      "assumptions": [
        "iid increments",
        "zero mean",
        "uniformly bounded support",
        "uniformly positive-definite covariance",
        "covariance whitening",
        "fixed finite observation schedule"
      ],
      "basis": "proved-here",
      "claim": "Centered iid bounded-range step laws with uniformly nondegenerate covariance converge uniformly over the declared bounded basin, after covariance whitening, to common standard-Brownian finite-dimensional laws.",
      "dependencies": [],
      "digest": "a8f96d29",
      "digestAlgorithm": "fnv1a32-canonical-json",
      "falsifier": "A law inside the declared bounded centered nondegenerate basin has a whitened fixed-time characteristic function that does not converge uniformly to exp(-|xi|^2/2), or the uniform Taylor remainder bound fails.",
      "id": "ggii.theorem.p8.3.robust-whitened-gaussian-fdd",
      "limitations": [
        "finite-dimensional laws only",
        "does not prove path-space tightness in this package",
        "does not cover estimated whitening",
        "does not cover state-dependent, correlated, boundary, or degenerate increments"
      ],
      "method": "Whitening gives identity covariance and a uniform support bound M/sqrt(kappa); a third-order characteristic-function remainder is O(n^-3/2) uniformly, and independent increment blocks give uniform finite-dimensional convergence.",
      "proofAnchor": "GLOBAL_GEOMETRY_II_FOUNDATIONS.md Proposition 8.3",
      "result": {
        "convergence": "uniform finite-dimensional after covariance whitening",
        "limitingCovarianceAtTimeT": "t*I",
        "robustnessParameters": "fixed finite M and kappa>0"
      },
      "schemaVersion": 2,
      "scope": "Families of centered iid laws on R^d with support norm at most M and covariance eigenvalues in [kappa,1/kappa], for fixed finite observation times and Cramer--Wold coefficients after exact covariance whitening.",
      "sourceUrls": [],
      "status": "proved",
      "tests": [
        "four-law perturbation basin",
        "anisotropic unwhitened negative control",
        "whitened covariance residual audit",
        "three-direction finite-n convergence audit"
      ]
    }
  ],
  "spectralCalibration": {
    "candidateStatus": "calibrated-profile-candidate",
    "conformsToFrozenProtocol": true,
    "evidence": {
      "artifacts": [
        "manifest:ab2843e4",
        "result:fnv1a32-canonical-json:87063714"
      ],
      "assumptions": [
        "periodic unweighted regular lattices",
        "continuous-time heat semigroup of the normalized graph Laplacian",
        "predeclared finite-size window"
      ],
      "basis": "finite-computation",
      "claim": "Closed-form square and triangular spectra evaluated in binary64 agree within the frozen finite spectral-dimension profile tolerances on every eligible intermediate window, and the cycle control remains within its registered one-dimensional tolerance.",
      "dependencies": [
        "ggii.hypothesis.spectral-profile.calibration.v1"
      ],
      "digest": "7a316ba3",
      "digestAlgorithm": "fnv1a32-canonical-json",
      "falsifier": "Invalidate this result if its bound result checksum does not reproduce, a finalized evidence or manifest digest fails, or recomputation changes any gate under the same protocol and runtime contract.",
      "id": "ggii.result.spectral-profile.calibration.87063714",
      "limitations": [
        "profile agreement is weaker than full geometry",
        "bounded planar and disordered ensembles are required before a universality claim",
        "finite-size thresholds are research protocol choices"
      ],
      "method": "Evaluate Fourier eigenvalue formulae in binary64, compute d_s(t)=2t·Σλe^{-tλ}/Σe^{-tλ}, mask scales by finite-size and zero-mode rules, compare matched windows, and apply the frozen target and cycle-control bounds.",
      "proofAnchor": null,
      "result": {
        "candidateStatus": "calibrated-profile-candidate",
        "conformsToFrozenProtocol": true,
        "eligibleRefinements": 4,
        "resultDigest": "87063714"
      },
      "schemaVersion": 2,
      "scope": "Binary64 evaluations of closed-form finite normalized-Laplacian spectra and the heat-trace analytic-log-derivative estimator only; this does not assert graph isometry, a common metric limit, full marked metric-measure-operator equivalence, or a continuum theorem.",
      "sourceUrls": [],
      "status": "computational",
      "tests": [
        "analytic spectra versus release-1 dense eigensolver on small lattices",
        "deterministic replay",
        "one-dimensional cycle rejection control"
      ]
    },
    "experiment": "spectral-profile-calibration",
    "hypothesis": {
      "artifacts": [
        "source:global-geometry-ii-core.js#CALIBRATION_PROTOCOL"
      ],
      "assumptions": [
        "periodic unweighted regular lattices",
        "continuous-time normalized-Laplacian heat semigroup",
        "binary64 evaluation of closed-form Fourier eigenvalue formulae"
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