RecognitionRatioBridgeStatus
plain-language theorem explainer
Four boolean status flags that audit the recognition-ratio bridge: paper odd-ratio encoded, negative-deficit witness proved, stationarity derivation still open on the bare ledger, and the old even deficit form refuted. Gravity auditors cite it when checking Seven Gaps Phase 0a closure. It is a pure documentation structure; the mathematics lives in the named theorems it indexes.
Claim. A status record with four booleans: (1) the paper's odd ratio admissibility $\log x_\sigma = \kappa_\sigma\,\delta_\sigma + R$ with $|R|\le C h^3$ is encoded as an explicit hypothesis; (2) a strong exact unit-coupled witness with strictly negative geometric deficit for some $d>0$ is theorem-tier; (3) derivation of the ratio from the bare recognition ledger (no constitutive action) remains open; (4) the old even/nonnegative deficit-equality bridge form is refuted.
background
Seven Gaps Phase 0a replaces a refuted ledger-to-geometry bridge with the paper's odd recognition-ratio form. The old form equated ledger deficit to a signed geometric hinge deficit. That fails: ledger deficits are nonnegative and even in the deformation, while signed Regge response is odd (the sign no-go in LedgerBridgeNoGo).
The paper instead posits, at each hinge $\sigma$, a positive comparison ratio $x_\sigma$ obeying $\log x_\sigma = \kappa_\sigma,\delta_\sigma + R$ with $|R|\le C h^3$. The structure RecognitionRatioBridge packages $x$, $\kappa$, signed $\delta$, mesh scale $h$, and remainder bound as an explicit MODEL hypothesis (Def 6.2 clause), not a derived law.
Kernel-checked theorems then reconcile this odd clause with the no-gos: an exact unit-coupled two-hinge witness admits geometric deficits $d$ and $-d$; every bridge induces a genuine recognition ledger whose cost is the $J$-cost of the ratio quotient; on that ledger the deficit stays nonnegative and even while geometry keeps the sign. Two observables, no contradiction.
proof idea
No proof body: this is a four-field documentation structure. Each field is a bare Bool annotated by a doc-comment that points at the real mathematics (the MODEL structure, the negative-deficit witness, the stationarity residual, and the no-go refutation). The canonical inhabitant sets all four flags to true and does not introduce new lemmas.
why it matters
Gives a single audit surface for the recognition-ratio bridge inside Gravity / Seven Gaps. Downstream, recognitionRatioBridgeStatus freezes the canonical snapshot: paper relation encoded, negative-deficit witness present, old even form refuted, and derivation-from-stationarity still flagged open.
The open flag is intentional after the 2026-07-15 stationarity closure: the constitutive form is inhabited from sourced $J$-stationarity, but the deficit-source coupling inside the sourced action remains a MODEL premise, so bare-ledger derivation is unfinished. That split keeps the status honest relative to the forcing chain and the ledger cost $J$ without claiming T5–T8 content here.
Anyone tracking which Seven Gaps clauses are MODEL vs THEOREM vs OPEN reads this record rather than re-deriving the module narrative.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.