stabilityThreshold_raw
plain-language theorem explainer
Defines the raw stability threshold 0.01 (uncertainty 0.005) as a quarantined measurement result for perturbation bounds, tagged as computed from a Cauchy–Schwarz overlap analysis. Anyone wiring calibration constants into classification or coercivity checks cites this record. The body is a pure structure literal: value, optional error, and provenance metadata only.
Claim. The stability threshold is the measurement result with value $0.01$, optional uncertainty $0.005$, and provenance marked computed from a Cauchy–Schwarz stability bound (private calibration ledger, dated 2026-01-06). It is the raw empirical input used for perturbation bounds on classification.
background
The Data Provenance module is quarantine infrastructure: every empirical constant that might touch verification must sit inside a MeasurementResult, which pairs a value and optional uncertainty with a DataProvenance record (source, hash, generator, date). Certified theorem modules are forbidden from importing this tree; only preregistered tests may bridge both sides.
The stability threshold is the scale below which a perturbation is treated as not flipping a classification decision. The doc-comment ties it to overlap perturbation analysis; the provenance string names a Cauchy–Schwarz bound as the computational origin. Sibling raw constants (classify threshold, net/projection/energy coercivity factors) follow the same wrapper pattern so calibration can be audited without leaking into the certified surface.
Upstream foundation edges (finite-dimensional Stone generators, primitive distinction reductions, certified analytic value extractors, Cauchy ledgers) supply the analytic language in which such bounds are eventually stated; this definition itself does not invoke them.
proof idea
Not a proof: a structure literal for a measurement result. It hard-codes value $0.01$, sets uncertainty to some 0.005, and fills provenance via the computed constructor with source text "Stability threshold from Cauchy-Schwarz bound", empty hash, generator "private calibration assumption ledger", and date "2026-01-06". No lemmas are applied.
why it matters
Keeps the stability scale out of the certified surface while still making it machine-readable for audits. Downstream, calibrationSummary lists it beside the other raw constants so a single table exposes every quarantined number and its source string. stabilityThreshold_hypothesis lifts the same record into a DataHypothesis whose intended claim is that perturbation changes classification only within this threshold, with the stated closing path "Prove tight bound from overlap_perturbation_bound".
In the broader Recognition stack this is bookkeeping, not a forcing-chain step: it does not establish J-uniqueness, $\varphi$, the eight-tick octave, or $D=3$. It only isolates a private calibration assumption so that any later certified perturbation or CPM coercivity argument can cite a named hypothesis rather than a naked float.
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