Module stability 

Analytic stability claims (PSP-8 System 2).

Perspt’s primary contract is the measured discrete gate (crate::gate). The continuous embedding-space constants alpha (correction strength), beta (drift), delta (disturbance), L (smoothness), and eta (step size) are optional: a domain registers them only when it can instrument a continuous correction coordinate. The coding domain exposes no such coordinate, so these remain NotClaimed for it.

The energy-slope constant mu is the exception — it is combinatorial and is computed from the verification graph in crate::spectral.

When the constants are present and satisfy their preconditions, the SDK reports the input-to-state-stability floor

V_inf = delta^2 / (2 (alpha - beta)^2 mu),   alpha > beta, mu > 0,

and the discrete step-size certificate.

Structs

CertifiedBound

A certified numeric bound with its evidence.

RealizabilityClaim

A domain’s claim to Paper I’s numeric realizability residual (Assumption 6). delta_r lives here and never in StabilityClaim::delta, which is the Papers I–II exogenous disturbance parameter.

StabilityClaim

A registered analytic stability claim (PSP-8 StabilityClaim). A missing constant is an explicit NotClaimed status, never a soft pass.

StabilityParameters

The kernel-facing stability parameters (PSP-8 StabilityParameters).

Enums

AnalyticPathVerdict

Verdict of the analytic-path admission check (PSP-9 system 10).

BoundMode

How Assumption 6’s bound is instantiated. Theorem 12.4’s conclusion weakens to match, so the mode is recorded and a certificate cannot be read as deterministic when the bound was only in expectation.

Traits

ProxyGeometry

Optional domain extension activating the analytic Paper I path (Theorem 12.4 / Corollary 12.5). Coding returns None for this extension: a fraction of edits denied or rewritten is projection_mismatch telemetry, not ‖r_k‖.

Functions

admit_analytic_path

Admit or refuse the analytic path from a claim’s own constants.

c_eta

Geometric contraction coefficient c(eta) = (alpha-beta) - L eta (alpha+beta)^2 / 2.

geometric_factor

Expected one-step geometric factor 1 - 2 eta c(eta) mu from V(x_k) <= (1 - 2 eta c(eta) mu)^k V(x_0).

step_size_upper_bound

Sufficient discrete step-size upper bound (PSP-8 Theorem 12.1):

ultimate_floor

ISS energy floor V_inf = delta^2 / (2 (alpha - beta)^2 mu).

validate_step_size

Check that a proposed step size respects the sufficient bound.