Research: dirty arbitrary-stride cyclic inverse on two tapes (no new kappa)

[aliromman]

Result

Implement the borrowed-array form left open by PR #846 for constant stable coefficients and supplied unit gauges. This research construction adds an arbitrary-stride cyclic inverse to a dirty target, restores the source exactly, and uses no extra data array inside a leaf. It uses a constant number of clean arithmetic registers plus an index stack. The certified PR #628 kernels use their original ceil(log2(r-1)) borrowed arrays, routed over two physical tapes.

Review files: Proof and scope · Evidence · Source pins and credit.

Source-prefix closure reuse and reversible block transport give O(L) rounded scalar operations and O(L) data-record movement per leaf. PROOF.md includes rounding, scalar coefficient preparation, complete recursion, temporary magnitude, and tape costs. The reference uses exact rational arithmetic with explicit rounding; it is not a fast-bit compiler or a runtime speedup claim. The precision budget is conservative and does not import the stronger bounds in PR #877 or PR #905.

The rounded increment can depend on the initial target. A length-three witness and a deliberately wrong inverse order check this distinction. Negative calls reverse the complete word.

Reproduce

With standard-library Python 3.11 or later:

python3 -I -O -B research/dirty-stride-source-reuse/verify.py
python3 -I -O -B research/dirty-stride-source-reuse/test_package.py

The primary receipt checks 8,256 geometries, 2,322 rounded powers, 3,456 rounded leaf executions, 54 cost fixtures, and 80 executions of all ten original kernel fixtures through radix 16. All leaf and kernel numerical cases have nonzero rounding error. A separate geometric-sum implementation and the pinned dense rational solver supply the numerical oracles. The checks cover exact source/scratch restoration, complete-word inversion, 128-bit kernel accuracy, two physical tape heads, head returns, and intermediate magnitudes. The source data, targets, and borrowed arrays have odd lowest working bits.

Local validation on macOS arm64 / Python 3.14.7 passes under isolation and optimization. Each input-validation loop reads a value once into a scalar. A separate array observer checks every indexed read and write for both signs of a leaf and factor word, and rejects a repeated uncharged read. The final full mathematical replay passed in 752.66 seconds; all ten short fault checks passed. Receipt SHA256 remains 4545a0f63837efa8be0715be509fb0a2ac6a8c4835a118b871653235b9c907d2.

The complete standalone harness passed at the prior source commit 9df42a99dd8497b6e7d46cd2507bb89071372640: ten faults, including an integer-to-Boolean certificate mutation, and exact regeneration from a read-only relocated copy. Its duration was 1329.85 seconds. That two-replay harness was not repeated after the read-once correction; the changed access path has the new observer, mutation and full mathematical replay. VALIDATION.json binds both source freezes. These durations describe verification, not performance.

make selected-record-check and all 17 selected-result tests pass at the exact experimental base. Executable files and retained dependencies match the verified source freeze. VALIDATION.json records the evidence and omitted checks. The full repository suite and selected cold replay were not run for this isolated package. The scoped Python 3.11/3.14 workflow runs the complete package harness; hosted CI results are separate from local validation.

Scope and provenance

Base: 47481c89fd30a43f8f882eb4b391e89c29273fd0. PR #846: 4bdb3e755ea7118170a7a34764df955880dec282. PR #628: 0768f97d06c623b8211e651543c66135796b62bf. Retained source files have exact SHA256 and Git-blob pins in SOURCE.json.

Credit Rohan Guliani (@Rohansguliani)'s PR #846 for the Euclidean decomposition, Chafik Boukhalfa (@chafreaky)'s PR #628 for factor preparation and the dirty commutator, Charles Bethin (@cbethin)'s PR #764 for the shared-suffix estimate, and PR #621 and its retained kernel lineage. The concurrent PR #951 has two grouped additive calls and larger clean scalar storage; its arbitrary-stride tape routing remains open. This result supplies a distinct arbitrary-stride transport mechanism. It does not combine PR #951 or improve its arithmetic count or precision. It keeps the original logarithmic borrowed-array budget.

PR #977 appeared during final verification. Its proof keeps PR #846's clean scratch model while improving its precision. This dirty construction retains its stated admission and conservative precision; the PR #977 argument is not imported.

No new kappa is claimed. The selected certificate and upstream/ are unchanged. The experimental base selects PR #890. Submission main 407d52ff15b2217b6e22bce44728b4c3907b6515 selects PR #942 at 1661960547713947/10^18; CLAIM.json records this refresh. Variable site phases, the complete transform, common-label/Clifford compilation, physical supplier hosting, and the multiplication reduction are outside this package. PR #1038 supplies a separate paid quadratic-phase extension. The finite receipt is supporting evidence, not formal verification or independent human review. NOTICE.md records Ali Romman (@aliromman)'s contribution and substantial OpenAI Codex assistance. The phase-solver lane found the validation-read defect; the coordinating agent independently reproduced and corrected it.

[Mister-Meeseeks]

100-PR batch review at da1cdf8ed4ac9b1b8378dfec73f77ff4e81a4f70.

This remains open after scoped triage. Next review step: Dirty source-reuse/two-tape solver requires a dedicated restoration, precision, physical routing and source-domain proof audit.

This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations.

Batch review, attribution and evidence. Thank you for the contribution.