Reuse exact principal-window inverses with weighted recovery certificates

[Dugongue]

PR3851 preserves one global old-H matrix while preparing principal-window pages and charges setup separately. This package supplies an exact arithmetic reuse component for a stream of one-index-shift windows: after one dense initialization, Schur deletion/bordering or a rank-two Woodbury core updates each inverse in O(m²) rational field operations. Both preserve the exact global source and ordered labels.

The complete informal sufficient proof combines eight inspected shared-library bridges: Schur, the historically typed/audited two-sided Woodbury identity, robust permutation frames, tensor packing, correlation-safe block energy, generic injective word transport, and locality/frame principles. LIBRARY-BRIDGES.md distinguishes actual algebraic uses from uninstantiated Lean multitape design precedents. It also records broad source/DAG/note retrieval and exact source hashes; no claim that all these standard ideas were previously unused is made.

Weighted residual checks bound rounding and provide unique nearest-integer recovery when the independently known exact output is integral and the physical error is strictly below 1/2. Reduced inverse heights remain polynomial in the fixed source descriptor and window width, independent of the number of slides. Fixed injective ports preserve arbitrary dirty exterior; correlated payloads need no statistical-independence assumption.

Registered Python 3.12 checks pass: 244 exact slides, an independent solver and two-sided identities, 12 cofactor/permutation cases, residual/recovery/height checks, semantic diagonal/model controls, source/alias/boundary rejects, actual Git-free export CLI and corruption controls, repeated under -O. At width 8 the exact field-operation counters are 414 per Schur slide versus 1,920 for fresh Gauss–Jordan; Woodbury takes 869. These are arithmetic counts, not timings, bit-cost or multitape speedups.

No physical Gaussian page integration, new κ, selected-frontier change or new formal-kernel proof is claimed. The two local-memory locality sources remain design precedents, not a newly instantiated Lean tape program. Current-source fixture evidence is an actual upstream rational setup fixture; the larger weighted cyclic fixture is explicitly synthetic.

Credit Jose Manuel/jmbarrancoml, PR3851 at 7ab67b4, for the exact preparation boundary and immutable fixture; Chafik Boukhalfa/PR489 and PR481/486, RaD/hipotures, PR3787 including corrected PR3709, Mason Hale, the scalar ABI and retained Harvey–van der Hoeven/OpenAI/Douglas Colkitt lineage. RaD's retained reusable-banded-inverse report already uses Woodbury for circular-wrap correction: this submission concerns a changing principal set, not first use of Woodbury or setup sharing. Shared MathProof provenance is preserved. Substantial OpenAI Codex assistance; no independent human review.

Base 20ecf28, priority revision 6. Overlap includes 575 open PR bodies, recent all-state records through #3871, actual related sources and partial Discussion HTML. No exhaustive novelty guarantee.