Scoped negative result: restored 2+3-cycle boundary costs exactly ten

[mightyOil]

The disjoint swap-plus-three-cycle boundary left open in #1216/#1145 needs exactly ten primitives, even with any finite number of restored dirty donors. This is a scoped negative result and exact boundary price, with no new kappa.

A new cycle-sensitive write lemma strengthens the donor cap: a permutation moving m coordinates in c nontrivial cycles needs at least m+c moved-coordinate writes. Thus a nine-step 2+3-cycle word can write to at most one restored donor. Read-only donors specialize away, reducing the previously unbounded gap to six registers. Two separately represented complete F3 searches then exclude all words through length nine; the retained rational ten-step witness attains the bound.

The ternary-row implementation and adapted PR1216 bit-packed implementation agree on all 2,299,917 matrices/minimum distances and independently perform 151,794,522 middle-gate tests. An essential positive control has exact distance nine: its direct intersection is empty but it has 1,000 middle hits, detecting accidental omission of the new scan. A third dense Python oracle checks complete GL(2,3)/GL(3,3) and every small-ball state. No finite search failure is presented as an unrestricted theorem without the stated reduction.

Freshly replaying all 168 pinned historical PR969 CK/JP8 boundary records gives an exact local component bill 252, sharpening #1216's 238 lower bound. Disposable work costs 224, so separate complex-component lowering incurs 56 extra real primitives per orientation. The explicit recurrence charges children, source access, preparation, adapters, other restoration, transport and dispatch; no supplier row saving or current selected-profile change is claimed.

Validation passes with CPython 3.12.13/3.14.7 and clang 21: full exclusion, rational witness/inverse/omissions, exact distance-nine control, source-bound census, five package test groups including optimized read-only relocation and on-disk corruptions, source pins, selected-record integrity and relevant repository tests. The registered quick replay explicitly omits the lower-bound scan; the new dedicated native workflow runs the full commands. Hosted CI success, full selected cold replay, physical admission, formal proof and human review are not claimed.

python3.12 -I -O -B research/restored-cycle-gap/verify.py
python3.12 -I -O -B research/restored-cycle-gap/test_package.py

Expected: PASS_RESTORED_CYCLE_GAP exact_minimum=10 ... historical_component_bill=252 no_new_kappa, then five passing test groups. C++17 compiler required.

Exact base: bce54fb3f895cbe5cd4c0eb477c3afeed100190f. Seed 54, recursive interfaces. #1216 pinned at 2cbf4084e141ba24ee3417ff014fdc7ca83b6c66; #1145 at fd4d5ffc448361297e717aa30eafed578caf8e61. Full proof, source pins, scope change from the original card, open questions and validation are in research/restored-cycle-gap/. No selected/upstream/predecessor file is modified.

Credit Ross Richardson's #1216/#1145 model, reduction, witnesses and implementations; ToikY's actual #969 boundary construction; Sagar Thakrar #696, faw01 #839, Jeremy Kothe #622, Chafik Boukhalfa #626 and retained lineage. The adapted implementation and recognizer are identified; original proof/notice/source bytes are preserved. Prepared for Philipp / mightyOil with substantial OpenAI Codex GPT-6 Astra assistance. Apache-2.0. Coordinator review was a scoped written review, not independent execution of the exhaustive scan.

[Mister-Meeseeks]

100-PR batch review at bddf5ba853f1b798d021454362e53338c819f150.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Exact restored two-cycle/three-cycle cleanup minimum of ten: cycle-write reduction and two independent finite-field searches exclude nine. Full native replay and package controls pass; no uncharged clean workspace is assumed.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

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