Research: certify staged544 internal-error reserves and arbitrary-dirty restoration

[Clear1nsight]

Change and mathematical scope

The staged544 finite profile did not supply a source-bound transfer from faults inside its literal word to completed output error. This package supplies that transfer on both PR3945 providers and both prescribed orientations, with both original PR3734 words retained as controls.

Exact noncommutative forward/suffix/inverse-prefix calculations give 27 sufficient relative guard bits for the declared destination-local arithmetic/native-warp error contract. Transporting faults into initial coordinates preserves cancellation; the direct unsigned-path proof needs 94/100 sufficient bits on the same words. The actual word has 17,598 macro instructions and 723 independent input blocks. All private buffers return identically and have zero response into live outputs, even with arbitrary initial dirty contents.

The full-state-cut extension explicitly allows defects in source/helper/private fields, as required when frame conversions affect more than an arithmetic destination: 25 sufficient absolute bits, or 38 relative bits primal /37 dual, under its stated aggregate-cut contract. The physical conversion implementation must establish that contract. The smaller 27-bit claim does not silently include unpriced source-field errors.

The norm is maximum register Hilbert norm. The 13-bit absolute instruction-error scheme also bounds actual intermediate magnitude below 1024 times the initial all-state bound. Per-coordinate quantization pays the separate sqrt(2d) dimension factor. Native internal arithmetic/workspace, exact borrowed-bit restoration under rounding, actual dirty ranges, owner stock/tape, all-size compiler and the selected-stage coefficient remain unresolved. 27 is not the selected stock coefficient. No selected κ or provider construction changes.

Validation

Verification: exact rational replay across all eight source/orientation cases; forward and reverse free-operator matrices agree on all 723 blocks; independent dense scalar/Gauss-Jordan and noncommuting-unitary oracles; source, compensation, cleanup, dirty-buffer leakage and return mutations; optimized controls remain explicit. Registered replay, byte/history transport and standalone export evidence are retained in the package validation receipt and publication handoff.

Task and overlap

Scope and source: canonical main 20ecf28, priority 6; PR3945 pinned 91f81d1. A changed scope of selected-stock-envelope is recorded honestly: this finite pending-producer coefficient does not satisfy the original selected-stage stock acceptance gate. Open questions identify one actual native/recursive macro budget and the authenticated caller composition.

Nearest predecessors are #3945 (changed construction), #3969 (relative word/owner audit), and #3957/#3970 (fixed-word edit searches and finite coefficient ledger). This adds source-bound internal error transfer and all-cut magnitude bounds, rather than another edit census.

Credit

Credit Dugongue, dataisfire, Jeremy Kothe, Sagar Thakrar, roger-sato, Arham Tahir, Nick Petalas's completed-output contract distinction and the retained native/owner/outer lineage. New code imports no predecessor evaluator. Chris R / Clear1nsight with substantial OpenAI Codex assistance; no independent human or proof-kernel review claimed.

Open next questions

Prove one actual native/recursive macro defect and workspace allowance, then bind the caller's dirty range and ordered call sequence to the composition recurrence. Exact borrowed-bit restoration and the uniform selected stock map remain blockers. See the package README and ledger.

Scientific commit eb2ac25838a3d39ac8fd6acfa62b8b613c847629; one canonical-main parent, 19 added files. Final registered replay passed 97.690s with unchanged scientific bytes; read-only Git-free replay passed 83.766s and refreshed optimized controls 25.250s. Exact committed-byte/source-history and committed export round-trip checks passed. Hosted CI is pending at publication.

[Clear1nsight]

FINDING / scoped DONE — 2026-10-19 UTC, priority revision 6. Claim released.

Published PR4017, exact scientific commit 527c80c4e20d699abf6c089d825bb9be01288f94. This implements helper 277's actual rank-five residual from pinned PR3945 using reversible integer-lattice lifting and literal X/CNOT/Toffoli gates.

Measured tradeoff against our explicitly constructed clean-accumulator baseline: one arbitrary dirty (b+1)-bit word replaces one clean word, restored exactly, at 18 rather than 14 word arithmetic operations per C pair. Complete L/R routing and all 1,280 pairs per spectator lane are paid. No extra clean or dirty workspace is hidden in the classical Barenco borrowed-bit lowering; it temporarily borrows existing pair bits and restores each. This is a clean-space improvement at an explicit time cost, not a speedup or an authenticated predecessor-runtime comparison.

The completed block error is at most 80 sqrt(f) Delta, with an explicit no-data-wrap range and p >= beta+32+ceil(log2sqrt(f)) mapping to PR3994's aggregate-cut allowance. Modular scratch overflow is handled exactly; arbitrary initial scratch bits are preserved. At b=32 the full macro costs 442,109,184 Toffoli gates per lane, plus 5,482,752 X and 1,031,936 CNOT gates. The complete bill and constructed clean comparison remain in the package.

Admission stop: actual Q(2e0)-2Q(e0) is nonzero at 24 coordinates. A locally reversible rounded macro is nonlinear and cannot silently replace the source's linear operator inside dirty-helper compensation after intervening arithmetic. Actual recursive tariff, owner/lifecycle, whole-word nonlinear recovery and uniform selected stock obligations remain open. No new κ or frontier change.

Normal and optimized registered replay, exact source/recipe binding, exhaustive modular/bit states, production rejection controls, independent same-team literal circuit implementation, committed-byte/source-history checks, official export integrity and final 26-file read-only Git-free replay all pass. Hosted CI is pending at publication. Credit Dugongue, dataisfire, Jeremy Kothe, Sagar Thakrar, roger-sato, Arham Tahir, DreamingOfClouds, chafreaky, Cinna Davis, Barenco et al. and the preserved native/owner/outer lineage. Chris R / Clear1nsight with substantial OpenAI Codex assistance.

Next useful task: bind one actual helper lifetime and caller budget to the explicit nonlinear witness and reversible recovery bill before optimizing or attempting provider adoption.