Richardson G–Σ–P–L Subspace: A Local TWA Certification with Mapping and Falsifiable Testing

This significant manuscript introduces a certified, two-engine pathway for ultrafast squeezing control that did not previously exist. A compact Hilbert baseline establishes a plateau contract and calibrates capsule-local allowances and guard bands; a Truncated Wigner Approximation (TWA) engine then executes production screening inside a fixed G–Σ–P–L “Richardson subspace” with replayable ledgering and drift-aware sentinels. Engine-invariant parity probes (odd/even Z-flip), disable-L, and a no-backflow slope sentinel enforce hygiene, while a parity-first triage separates structural failures from variance effects. The posture is short-side by construction—TWA cannot promote looser than Hilbert—so scaling never erodes falsifiability. A twelve-tile study shows cross-engine parity stability and confines disagreements to flatness under small ensembles, where the variance-suspect path (adaptive averaging or lower-variance observables) resolves false fails without creating false accepts. Historically, the work operationalizes the long-standing two Hilbert steps (zero-centered triads with reversible tokens, and preregistered acceptance lines) locally inside each capsule, paired with eight containment conditions (E1–E8) that pin constants, freeze run-uniques, enforce Σ-hygiene, gate geometry, separate no-backflow from oblique handoffs, drill independence (flip-only Z, disable-L), require a two-green admit, and log a replayable bundle under invalidate-off-plateau discipline. These elements—developed across the last 8–10 articles—make the Hilbert→TWA handoff practical and falsifiable at scale: a theory-clean Hilbert plateau becomes a portable certification protocol that runs on modest hardware, with subspace settings transferred as audited artifacts and safety guaranteed by short-side bounds.