Research: cubic arbitrary-stride inversion without a length admission (no new kappa)

[chafreaky]

PR846's arbitrary-stride cyclic inverse has a precision admission depending on log log L. This removes that condition and combines the unchanged solver with PR862's common-operator bound to give working precision W <= p+m+9r^3 at every cycle length and stride, under the inherited certified prime-power preparation hypotheses. No new kappa.

For margin beta=2^-g and working precision W>=2g+8, rounded chain coefficients vanish after at most 2g+ceil(log2 W)+4 effective levels. A zero-coefficient subtree in the original solver returns exactly the once-rounded data. An explicit early-exit version therefore has identical output, letting the accuracy proof use the bounded effective depth while the unchanged implementation retains its original 40L record-traffic bound. The optional early-exit version costs at most 44L, including the coefficient scan and head return.

Its local error fits PR862's existing partial-inverse argument. The package supplies exact cubic budgets for execution, root preparation and integer guards; the supplied-phase cost is soft-O(r^3(p+m+r^3)) + O(rL) M(A+B_tau) + O(rL(A+B_tau)), with A=max(p,w)+2m+16r^3. Phase-oracle/input costs remain explicit. The Python reference does not claim to implement the inherited fast factorizer or asymptotically fast integer arithmetic.

Validation on the frozen package:

• Complete macOS/Python 3.11 and Linux/Python 3.14 replays with identical full mathematical receipts, under isolation and optimization.
• 423 array cases, 90 coefficient-decay paths, all 300 original PR846 kernel cases and 64 actual cubic-budget kernel executions. The latter round prepared roots to the stated width, verify every common-operator hypothesis and meet the 128-bit target with arbitrary odd lowest working bits.
• 216 exact budget rows, three nonnegative polynomial identities, 54 admission checks, 1,545 logarithm boundaries, 12 new mathematical controls and four inherited controls. Traffic checks cover lengths through 131,072.
• Eleven package rejection controls and a complete read-only relocated replay on each platform. Linux also runs the supplied source package read-only under a supervisor with exit status zero.
• All 12 retained source files match their pinned SHA256 and Git objects. Selected-record consistency passes on current base bbc600db2fc15007b7c914f4f2b2ed55fa909c87; staged whitespace and file-byte checks pass.

Reproduce with python3 -I -O -B research/cyclic-stride-effective-depth/verify.py and python3 -I -O -B research/cyclic-stride-effective-depth/test_package.py. Scoped Python 3.11/3.14 CI is included; hosted results are separate from local validation.

Only the construction/validation directories and their workflow are added. This remains PR846's clean scratch tape model, separate from PR951's neighboring-cycle dirty-array work. It does not provide bit-reversible arithmetic, common labels, full transform composition or the multiplication reduction. Finite checks and the written all-size argument are distinct; no independent human review or formal verification is claimed.

Credit Rohan Guliani's PR846, Charles Bethin's PR764, Chafik Boukhalfa's PR628/862 and Ali Romman's PR621, with their retained notices and classical sources. New integration by Chafik Boukhalfa with substantial OpenAI Codex assistance.

[Mister-Meeseeks]

100-PR batch review at 2846af720af190cb75b45ebddbb0357dec1121ec.

This remains open after scoped triage. Next review step: Uniform effective-depth and accuracy extension depends on the #846 solver and #862 analytic interface; review as a single proof family.

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.