Reuse exact principal-window inverses with weighted recovery certificates

research/sliding-window-inverse/.gitignore

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+__pycache__/
+*.pyc

research/sliding-window-inverse/INPUTS.json

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+{
+  "inputs/gaussian_check_setup.py": "46e234fbadbbf934cb02f609d7aa14355789c42f82e384cf624d31e57bd05a3a"
+}

research/sliding-window-inverse/LIBRARY-BRIDGES.json

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+{
+  "schema_version": 1,
+  "concepts": [
+    {
+      "id": "schur-elimination",
+      "source": "Mathproof/LinearAlgebra/SchurBlockElimination.lean",
+      "sha256": "b865c41950e67c86d3e2961e5a5682d0cbf1a49ad9e11612730e0c198c16ddb3",
+      "declarations": [
+        "schur_block_system_iff"
+      ],
+      "role": "Deletion and reattachment of one coordinate; requires the actual two-sided inverse hypotheses.",
+      "catalog_status": "ARTIFACT_PRESENT",
+      "catalog_hash_matches_current": true,
+      "evidence": "Current source read; no new kernel audit of this combined informal application."
+    },
+    {
+      "id": "robust-frames",
+      "source": "Mathproof/Meta/RobustRealTIFrames20261006.lean",
+      "sha256": "47a7f3586e6b1be6497e237df7cd37c73fae5107b69f7242e5e128a2eb7e918b",
+      "declarations": [
+        "Frame.norm_apply",
+        "relative_frame_error"
+      ],
+      "role": "Permutation-frame transport. Positive diagonal weights are separately justified by a pullback norm, not treated as orthogonal.",
+      "catalog_status": "ARTIFACT_PRESENT",
+      "catalog_hash_matches_current": true,
+      "evidence": "Current source read; no new kernel audit of this combined informal application."
+    },
+    {
+      "id": "tensor-packing",
+      "source": "Mathproof/Meta/RobustRealTIRecovery20261006.lean",
+      "sha256": "bffdfcd0b61f4f116c2f7e24566cbbef608fe127f2215fb3d225ad1218ce73d6",
+      "declarations": [
+        "pack_norm",
+        "pack_sub"
+      ],
+      "role": "Finite tensor layouts preserve squared energy; real/imaginary and correlated payload columns share one exact map.",
+      "catalog_status": "ARTIFACT_PRESENT",
+      "catalog_hash_matches_current": true,
+      "evidence": "Current source read; no new kernel audit of this combined informal application."
+    },
+    {
+      "id": "block-energy",
+      "source": "Mathproof/Computability/IntegerTensorBlockNorm20261015.lean",
+      "sha256": "52a61d4d8ed0897f097001b9aac1d1ea46b57a0deec5598734b6badae134c420",
+      "declarations": [
+        "block_energy_prefix",
+        "total_energy_bound"
+      ],
+      "role": "Maximum local depth controls a direct sum without an independence premise; inverse gaps yield explicit local factors.",
+      "catalog_status": "NOT_FOUND",
+      "catalog_hash_matches_current": false,
+      "evidence": "Current source read; no new kernel audit of this combined informal application."
+    },
+    {
+      "id": "word-embedding",
+      "source": "Mathproof/LiGuanCNOTFallout20260905.lean",
+      "sha256": "1b6b13e220370fee7a233ba1ee6b66b7eb9d981e8daa9042da2342eb982972da",
+      "declarations": [
+        "word_map",
+        "within_embedding_iff"
+      ],
+      "role": "The generic monoid portion transports an unchanged finite word through fixed injective ports; no characteristic-two recorder theorem is used over rationals.",
+      "catalog_status": "ARTIFACT_PRESENT",
+      "catalog_hash_matches_current": true,
+      "evidence": "Current source read; no new kernel audit of this combined informal application."
+    },
+    {
+      "id": "footprint-frame",
+      "source": "Mathproof/Computability/MultitapeFrameRule20261014.lean",
+      "sha256": "e5aa9ec056340c67bc6e382eee0a859e6903d9944d3a0e021f2a24a12459cb66",
+      "declarations": [
+        "FootprintedRuns.frame"
+      ],
+      "role": "Arbitrary exterior preservation is a design precedent; the finite-memory API is proved directly, not claimed as a Lean multitape instance.",
+      "catalog_status": "ARTIFACT_PRESENT",
+      "catalog_hash_matches_current": true,
+      "evidence": "Current source read; no new kernel audit of this combined informal application."
+    },
+    {
+      "id": "locality",
+      "source": "Mathproof/Computability/MultitapeLocality20261014.lean",
+      "sha256": "4e5df1bdd9764d335424acb2a3aad8364f647892e632d8b09aec85e45cfb5b31",
+      "declarations": [],
+      "role": "Local scanned-region dependence motivates the exact immutable-source/port contract; not a new tape execution theorem.",
+      "catalog_status": "ARTIFACT_PRESENT",
+      "catalog_hash_matches_current": true,
+      "evidence": "Current source read; no new kernel audit of this combined informal application."
+    },
+    {
+      "id": "woodbury",
+      "source": "research/woodbury-reactor-20260920/Woodbury.lean",
+      "sha256": "8f269e268a026bc659e33f85e8873713b325f618ef0dae9f7d469e911730b27d",
+      "declarations": [
+        "woodbury_two_sided"
+      ],
+      "role": "Two-sided inverse of the 2x2 core gives the exact full rank-two replacement.",
+      "evidence": "Historical typed DAG operation exists; current source read. Not a fresh audit of this new result.",
+      "dag_snapshot": "5cafc7e755c67429021b07c755ddd70e5fef81e1f478c9e6d14f298cca131835",
+      "dag_type_node": "837a84e5d279c06003451565aefc1517bec1e6667bba5fc0a71ce315fc9002ed",
+      "historical_axioms": [
+        "propext",
+        "Classical.choice",
+        "Quot.sound"
+      ]
+    }
+  ],
+  "scope": "Discovery provenance, exact hypotheses checked against written application. Source presence or historical artifacts are not a fresh kernel proof."
+}

research/sliding-window-inverse/LIBRARY-BRIDGES.md

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+# Eight shared-library bridges and nine mathematical concepts
+
+These are actual source statements or explicitly labelled design precedents.
+The new sufficient proofs are fully written in PROOF.md; none relies on an
+unavailable spectral oracle or an assumed unknown circuit. Exact current source
+hashes and historical evidence distinctions are in LIBRARY-BRIDGES.json.
+
+| Shared source | Reusable fact or concept | Concrete use here | Limit |
+| --- | --- | --- | --- |
+| SchurBlockElimination | two-sided Schur system elimination | principal inverse deletion and bordering | Already used in PR3851; no novelty claim for Schur. |
+| woodbury-reactor / typed DAG | `woodbury_two_sided` | a two-column/two-row update and 2×2 inverse replace a dense inverse | Historical audited algebra; combined cache is informal. |
+| RobustRealTIFrames | `relative_frame_error`, exact orthogonal frames | source-label permutations transport inverse/error without changing norm | Arbitrary positive D is NOT orthogonal. |
+| RobustRealTIRecovery | `pack_norm`, coordinate bijection | tensor/column flattening preserves squared energy | Does not prove spectral recovery or supply frames. |
+| IntegerTensorBlockNorm | `block_energy_prefix`, `total_energy_bound` | correlated blocks use maximum local amplification, not total unrelated work | Separate inverse applications, not an unbounded product. |
+| LiGuanCNOTFallout | generic `word_map` and injective word transport | fixed caller-port embedding preserves the same local-map sequence | Uses only generic monoid lemmas, not F₂-only recorder algebra. |
+| MultitapeFrameRule | `FootprintedRuns.frame` | direct finite-memory exterior-frame proof and dirty-value controls | This API is not a new Lean multitape program. |
+| MultitapeLocality | finite-region observational dependence | immutable old-H and injective finite port contract | Design precedent, not an instantiated new execution certificate. |
+
+The additional numerical concept is an actual residual-to-recovery certificate:
+check the full rational residual against the exact weighted old-H matrix before
+asserting a numerical tolerance. It follows the shared robust-recovery practice
+of checking the returned object itself; the inverse-specific proof is new here.
+The exact coefficient-height/minor argument and diagonal similarity cancellation
+are retained from the Gaussian predecessor, not advertised as unused inventions.
+
+The submitted cache, two-sided residual check, weighted rounding, port-map
+implementation and tensor/block controls instantiate the first six algebraic
+patterns and a direct finite-memory frame. The two multitape sources remain
+explicit design precedents; their Lean execution theorems are not newly applied
+to this host-language algorithm. We do not inflate that boundary into a formal
+tape result merely to increase the source count.
+
+## Search coverage and unused status
+
+The existing authoritative source catalogue contains 401,769 registered modules.
+Twenty broad source queries retrieved at most 100 hits each, with bounded
+MathProof-specific follow-ups; twelve typed-DAG/symbol queries and six indexed
+note searches were also performed. Sources include the federated project,
+downloaded libraries and registered archive notes. This is broad retrieval,
+not a complete inspection or semantic search of every registered statement.
+The first unrestricted ranked source query was bounded after slow common-term
+search; the bounded indexed replacement preserved explicit limits.
+
+Actual source inspection then followed the eight bridges above, the local
+Woodbury mission/proof, current Gaussian source and precise predecessor APIs.
+The private search packets retain indexed paths, revisions, snapshots and misses.
+Only the sanitized provenance needed for review is published here.
+
+Schur, weights, minors and Neumann reasoning are demonstrably already present
+in PR3851. The scoped Woodbury sliding-cache application, its weighted residual
+and fixed-port/block contracts were not located in the inspected project sources
+or the 575-open-PR body scan. That is a bounded overlap finding, not a guarantee
+that nobody has applied any of these standard ideas anywhere in the project.
+
+A later actual-source comparison found that RaD's retained
+`review-reusable-banded-inverse.md` already uses Woodbury for a circular wrap
+correction and shares setup across right-hand sides. That predecessor is
+explicitly credited. It does not describe the one-index principal-set deletion/
+bordering cache checked here. Our claim is this scoped composition, not first
+use of Woodbury, residuals, setup reuse or weighted Gaussian inverses.

research/sliding-window-inverse/NOTICE

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+Apache-2.0. New composition, exact host algorithm, proof and checks by Dugongue,
+with substantial OpenAI Codex assistance. No independent human review claimed.
+
+Unmodified vendored source:
+research/physical-gaussian-core/gaussian_check_setup.py from Jose Manuel
+(jmbarrancoml), PR3851 at 7ab67b4a84d28cd562b9711aa315ca5b47822b37.
+Only its literal exact rational setup fixture is consumed by AST parsing.
+Its physical implementation and native dependencies are not imported or rerun.
+
+Retain the predecessor's attribution: Chafik Boukhalfa's PR489 local inverse
+and PR481/486 boundary/halo work; the RaD project (hipotures) Gaussian,
+phase-cell, microbox and reusable-banded-inverse reports; PR3787 word multiplier
+at 9b5474f47b0ea9a3c76bb5b1b577fb36704815e0 including corrected PR3709;
+Mason Hale's interval reference; Dugongue's scalar ABI precedent; Harvey and
+van der Hoeven, the OpenAI manuscript and Douglas Colkitt's framework.
+These source notices are retained credit, not a fresh validation of their full
+physical/analytic claims. PR3763's chirp caller is a separate future integration
+interface, not implemented or re-audited here.
+
+The shared MathProof Schur, Woodbury, robust-TI frames/recovery, block norm,
+CNOT/TI word, locality and frame sources retain their existing authorship and
+provenance, identified by exact source hashes in LIBRARY-BRIDGES.json.
+The matrix identities and elementary norm facts are standard mathematics.
+Woodbury already appears in RaD's reviewed circular-wrap correction; this work
+claims a moving-principal-window cache application, not its first project use.

research/sliding-window-inverse/OVERLAP.md

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+# Current source and overlap
+
+Canonical main fetched at entry and at the final research checkpoint:
+`20ecf2891d80b5acf18d980b2164fb44ea7faa90`, priority revision 6.
+Current AGENTS.md, autoresearch.md and CONTRIBUTING.md were refreshed and compared
+with the same previously read source revision. PR3851's current head remained
+`7ab67b4a84d28cd562b9711aa315ca5b47822b37`. Its actual PROOF, setup fixture,
+window/axis/matrix/production source, README and source manifest were inspected.
+
+The original uniform-transfer-audit card is retained verbatim; the changed scope
+and its actual sufficient conclusion are explicit in TASK.json. The selected
+baseline bindings were checked in the preceding same-main campaign; no new
+selected cold replay is claimed for this unrelated component.
+
+A fully paginated REST snapshot scanned 575 open PR titles/bodies. No body match
+for the scoped sliding principal-inverse cache was located. The repository
+find_overlap.py also searched the snapshot and available local package notes.
+Latest all-state updated records were scanned at entry and a final 30-record
+checkpoint through PR3871. Start-here and handoff Discussion HTML was read, with
+partial possible reply coverage and no complete GraphQL Discussion cache.
+No exhaustive historical closed-PR, arbitrary-diff or unpublished coverage claim.
+
+Actual-source comparison found a crucial existing use: RaD's retained
+review-reusable-banded-inverse.md already uses Woodbury for circular-wrap repair,
+plus setup sharing, rounded row residuals, inverse bounds and coefficient heights.
+Its phase-cell report and PR3851 already use Schur and exact similarity weights.
+Those tools are predecessors, not newly introduced mechanisms. The new delta is
+one-index changes of the principal index set, with exact cache update, source-
+label contracts, weighted residual recovery and a finite-memory port/energy API.
+Neither new broad mathematical novelty nor first project use of the standard
+identities is asserted. The scoped application was not found in the compared
+sources. LIBRARY-BRIDGES.md records the broad DAG/source/note search and limits.
+
+No exact new kappa, selected-frontier change, hosted CI or human review claimed.