IndisputableMonolith.Verification.RecognitionStabilityAudit.Core
Core interface for the Recognition Stability Audit (RSA): Schur bounds on a region, boundary-hit predicates, the audit problem package, and the Cayley field built from a sensor. Analysts cite it when wiring front-end obstruction sensors to back-end Schur/Herglotz pinch arguments. The module is definitional scaffolding plus shared predicates; proofs live in FrontEnd and BackEnd.
claimRSA core objects on a region $\Omega$: the Schur (disk) bound $\|f(z)\| \le 1$ for all $z \in \Omega$; the boundary-hit predicate at a point; the audit problem package; the Cayley field $\Xi$ obtained from a sensor $\mathcal{J}$ via $\Xi = \theta(\mathcal{J}) = (2\mathcal{J}-1)/(2\mathcal{J}+1)$; and the front-end / back-end / correctness interface tying obstruction sensors to Schur pinch.
background
Recognition Stability Audit (RSA), from papers/tex/Recognition_Stability_Audit.tex, checks whether a holomorphic defect representative can force a boundary hit on an audited region, or whether a Schur bound plus analyticity rules hits out.
Upstream Cayley plumbing supplies the algebraic map from the closed right half-plane $\mathrm{Re}(z)\ge 0$ into the disk. The front-end story is: obstruction $G$, sensor $\mathcal{J}:=1/G$, Cayley field $\Xi:=\theta\mathcal{J}=(2\mathcal{J}-1)/(2\mathcal{J}+1)$; a pole of $\mathcal{J}$ drives $\Xi\to 1$ on a punctured neighborhood (boundary hit). The back-end assumes a Schur bound $|\Xi z|\le 1$ on $\Omega$, holomorphy, and nontriviality, then pinches away boundary hits.
This Core module names the shared predicates and problem shape (Schur-on-$\Omega$, boundary hit, $\Xi$ from sensor, FrontEnd/BackEnd/correctness) that both ends import. Cost is imported for the ambient recognition-cost setting; Mathlib supplies the analytic toolkit.
proof idea
This is a definition and interface module, not a theorem file. It introduces the Schur-on-region predicate ($|f z|\le 1$ on $\Omega$), boundary-hit-at, the audit Problem bundle, XiFromSensor via the Cayley transform from the Cayley import, and the FrontEnd / BackEnd / correctness hooks. Substantive arguments (pole implies hit; Schur plus analyticity plus nontriviality imply no hit) are discharged in the FrontEnd and BackEnd modules that import this core.
why it matters in Recognition Science
RSA Core is the shared vocabulary for the stability audit that sits under verification in the monolith. The umbrella RecognitionStabilityAudit re-exports it so consumers need one import. BackEnd consumes the Schur-bound interface to run the Schur/Herglotz pinch (no boundary hits). FrontEnd consumes the sensor-to-$\Xi$ and boundary-hit interface to turn obstruction poles into hits. Correctness of the audit is the glue between those ends. In the broader Recognition framework this is verification infrastructure for holomorphic defect claims, not a forcing-chain (T0–T8) step; it stabilizes analytic side-conditions used when auditing recognition observables on regions.
scope and limits
- Does not prove pole-implies-hit; that lives in FrontEnd.
- Does not prove Schur pinch or absence of boundary hits; that lives in BackEnd.
- Does not establish holomorphy, nontriviality, or a concrete Schur bound for any physical observable.
- Does not derive J-cost uniqueness, phi, eight-tick structure, or D=3.
- Does not replace the Cayley algebraic core; it imports and packages it.