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IndisputableMonolith.Verification.RecognitionStabilityAudit.FrontEnd

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Front-end layer of the Recognition Stability Audit: it packages the analytic “sensor” interface that detects poles (norm blow-up on a punctured neighborhood) and ties those blow-ups to boundary hits and obstruction data. Stability auditors and anyone wiring RSA into a larger verification stack would import it. The file is mostly definitions and short transfer lemmas from Core and Cayley, not a deep existence proof.

claimA sensor $\mathcal{J}$ blows up at $z_0$ when $\|\mathcal{J}(z)\|\to +\infty$ on every punctured neighborhood of $z_0$. From that pole condition one obtains a boundary hit for the associated phase/angle map, a sensor built from an obstruction certificate, and a front-end witness that an obstruction forces sensor divergence.

background

Recognition Stability Audit (RSA) is the Lean formalization of the audit in papers/tex/Recognition_Stability_Audit.tex. Core presents RSA as a compiler-style interface (RL-friendly hooks for certificates and checks). Cayley supplies the purely algebraic plumbing: the Cayley transform between the closed right half-plane $\mathrm{Re}(z)\ge 0$ and the disk, used repeatedly to move stability questions into bounded domains.

FrontEnd sits on top of those two layers. Its central analytic notion is a sensor $\mathcal{J}$ and the pole condition “blows up at $z_0$”: the norm tends to $+\infty$ on a punctured neighborhood. Sibling names make the intended dictionary clear: obstruction data produce a sensor; tendsto-zero hypotheses upgrade to blow-up; blow-up implies a boundary hit for the angular/phase readout; and the package yields a front-end certificate that an obstruction is visible as sensor divergence.

proof idea

This is an interface and transfer module, not a single deep theorem. Definitions introduce the blow-up predicate for a sensor at a point and the sensor extracted from an obstruction. Short lemmas then chain standard limit facts: if a quantity tends to zero in a way that forces the sensor norm to infinity, conclude blow-up; from blow-up, deduce the corresponding boundary-hit statement for the phase map; finally package obstruction $\Rightarrow$ sensor $\Rightarrow$ blow-up into a front-end witness. Algebraic movement between half-plane and disk is delegated to Cayley; certificate shapes come from Core.

why it matters in Recognition Science

RSA needs a thin analytic front end so that algebraic obstruction certificates become checkable divergence statements without forcing every consumer to rebuild limit and boundary-hit arguments. This module is imported by the umbrella RecognitionStabilityAudit, which re-exports the RSA surface so downstream code can depend on one import. In the broader Recognition stack it is verification infrastructure rather than a T0–T8 forcing step: it does not derive $\varphi$, the eight-tick octave, or $D=3$, but it is how stability failures are meant to surface as concrete sensor poles once Core and Cayley are in place.

scope and limits

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