Operational Information Geometry — From Response Limits to Certified Experiments

No fixed finite grid reproduces the normalized late continuum response for every time scale. In the declared two-port Neumann model, the theorem instead grows resolution with the diffusive scale: the finite-to-lattice error is bounded by 23√τ/n in the L2 source metric and (23/10)√τ/n in the declared H1 metric. The continuum-to-atomic errors are bounded by 2/(3τ) and 1/(15τ).

Sources: [1] [2]

With data y=Hx+Bz+η, output precision W, and exact W-orthogonal profiling P of nuisance, the requested linear query Lx is identifiable precisely when ker(PH) is contained in ker(L). A successful certificate contains a nuisance-invariant decoder; a failed certificate returns an exact kernel witness instead of a numerical rank guess.

Sources: [1] [3]

The engine compares only candidates with the same source metric, query, query metric and noise-radius convention. For a finite sealed library, the global optimum lies between the minimum certified lower and upper bounds; a candidate is called uniquely best only when its upper bound is strictly below every other identifiable candidate's lower bound.

Sources: [1] [4]

A coefficient shared across several protocols is not equivalent to independently refitting one nuisance coefficient per protocol. Correlated bounded nuisance is represented by its common-generator zonotope and charged through its exact support function. This keeps nuisance semantics visible rather than hiding them inside an entrywise box.

Sources: [1] [5]

Finite model secants, tangent/kernel angles, response tubes and nominally blind coordinates are audited separately. A positive ambient information floor cannot hide a query-relevant model collision. Structured additive nuisance and response-operator uncertainty are therefore not interchangeable proof obligations.

Sources: [1] [6]

The public control selects the scalar response H=[2] over H=[1] and a blind candidate, then reuses the same response and metrics across the structured-nuisance and response-tube layers. The resulting inequalities are exact for the pinned declared model, not an empirical fit.

Sources: [7] [8]

Each layer serializes declarations and witnesses, and standalone verifiers reconstruct them rather than trusting theorem flags. Exact arithmetic defines quotients, identifiability, design bounds and tamper decisions. The pinned integrated certificate is linked with its SHA-256 in the public manifest.

• The focused protocol-engine suite reports 155/155 passing.
• The independent Atlas-integration adversarial publication matrix reports 126/126 passing.
• The complete repository at the canonical integration state reports 920 tests passing with one expected skip.

Sources: [2] [9]

Within the declared finite and continuum models, the engine proves the stated transfer, query, candidate-library, structured-nuisance and pinned integration consequences, provided the external response enclosures, candidate completeness and model premises are accepted as inputs.

Sources: [1] [8]

The global analytic transfer schedule is conservative, the compact Arb cover stops at τ=6/5, and a finite candidate-library optimum is not a continuous-design optimum. Candidate-library completeness is a scientific premise, and matched modal sensors are global linear combinations rather than claimed local hardware.

• The engine does not prove that an external physical system satisfies the declared model.
• The radio/acoustic continuation is a plausible application target, not a validated instrument or propagation model.
• No result establishes a theory of spacetime, matter, information as the substrate of reality, or any other physical law.
• The work has not undergone independent specialist peer review and makes no unqualified literature-priority claim.

Sources: [10]

The immutable repository contains the synthesis, theorem notes, engines, dedicated dependencies, pinned integration program, certificate and adversarial tests. The compact Arb-cover test is slower and can be run as an additional verification step from the manifest.

• git checkout 63068b62241359e51f1f98649d2718dc5b81145c
• python -m pip install -r oig_protocol_engine_requirements.txt
• python oig_atlas_protocol_integration.py --verify certificates/oig_atlas_protocol_integration.json
• python -m unittest -v test_oig_protocol_artifacts.py

Sources: [2]