[unpaidmoon]

Change and mathematical scope

Partial route-schedule result. No new κ and no selected-frontier change. The selected value stays 781451/250000000.

The pinned helper-462 matcher inside research/bit-completed-backend-api has determinant -16. In the elementary alphabet of axis swaps, single-coordinate scales and shears, every factorization satisfies

(product of the scale coefficients) * (-1)^{number of swaps} = -16.

A word with no scale would have determinant ±1, so at least one scale is required. Elimination without axis swaps produces an explicit word with 0 swaps, 7 scales and 27 shears that multiplies to the pinned matrix. The published five-swap Gaussian schedule is therefore not a lower bound on ordinary chunk interchanges for this matrix.

Under the predecessor's own high-row rule, the new pair bill is 0 ordinary chunk interchanges, 112 unit scalings and 432 linear ordered shifts, against the published 80 / 80 / 224. Seven scales and twenty-seven shears are not claimed to be minimal, and no tariff comparison between a chunk interchange and a shear is made.

This does not emit owners, restored ROW, fallback, tape, precision or a physical N-dimensional generator. It does not discharge P1–P3.

Task and overlap

Base commit: 7c49fe32c55de02c2c873655c804b16e4c3fef0a. Priority revision 8.

Card supplier-boundary-audit. Scope status: refined. The card's #5717/#5719 admission experiment is not this task. The work takes the still-open next step in Discussion #1166 comment 19137812: one fixed invocation of the route generator left by PR #4957. The invocation used here is that package's published helper-462 matcher, and the result is only its elementary letter count.

Ordered eligible list for session r111, item #4, after excluding handoffs already answered by unpaidmoon PRs, fork cursor/* branches, or a PR found by title search:

1. Handoff 03 — physical entry word after the Price an actual centre-chain terminal and certify its scoped cost loss (no new κ) #4839 terminal loss.
2. Handoff 04 — one changed resource policy after the Emit shared-port fusion and bound its free five-target completion (no new κ) #4856 free pre/post closure.
3. Handoff 05 — one changed-ownership premise outside the fixed-224 serial model.
4. Handoff 09 — literal stock/role/route generator for the A0→A1 API (this item).

Handoffs 01, 02, 06–08, 10–14 and 17–32 were excluded as delivered, reserved-closed, or already refined by the listed unpaidmoon work or by an open/merged PR. Handoff 09 is the fourth remaining open handoff in discussion-comment order.

Nearest work: PR #4957 and research/bit-completed-backend-api publish the five-swap ledger and name the generator as open. No open-PR title found for a swap-free helper-462 route. Overlap title search is not a novelty certificate.

Validation

Python 3.12.3, standard library only. From the repository root:

python3 -B research/helper462-swap-free-route/verify.py
python3 -I -B research/helper462-swap-free-route/verify.py
python3 -O -B research/helper462-swap-free-route/verify.py
python3 -B scripts/research_package.py --package research/helper462-swap-free-route
python3 -B scripts/check_research_commit.py --package research/helper462-swap-free-route --check-source-history --check-modes

Observed: PASS_HELPER462_SWAP_FREE_ROUTE, PASS_REGISTERED_RESEARCH_PACKAGE with outcome=partial, and PASS_RESEARCH_COMMIT_BYTES at 60ff33d90472d69bce722549fa0aaf863d0b21bb.

The verifier recomputes the published word from the pinned factor matrices, checks the determinant identity for both words, reproduces the pinned pair ledger 80/80/224 from the factor counts, and rejects a dropped shear, a shear coefficient changed by 1, and any scale-free signature for this determinant. The identity matrix is a control that does not require a scale. No Lean, Docker, or selected cold replay was run.

Credit

Matcher, five-swap elimination and high-row ledger: Chris R / Clear1nsight, PR #4957, research/bit-completed-backend-api, using ai-nanachi #4760/#4814 and the ordinary lineage credited there. Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

1. With the inherited P2 tariffs, does any legal word beat the published pair on the completed ordinary bill? The zero-swap schedule removes 80 interchanges and adds 32 scales and 208 shifts. Those tariffs are not proved here.
2. Is there a zero-swap word with one scale, or with fewer than 27 shears? One scale is necessary. The constructive count is only an upper bound.

Workflow feedback (optional)

The handoff thread's structured HANDOFF blocks are still the usable index; many of them describe finished work that was never edited to DONE. A one-line remaining-question field would make the next invocation easier to tell from the completed scope.