[unpaidmoon]

Change and mathematical scope

Negative comparison. No new κ. The selected record stays 781451/250000000.

Under the P2 ordinary-call rule inherited from the pinned helper-462 sources, the recorded 0-swap, 7-scale, 27-shear word costs 320 f² ordinary calls and the published 5-swap word costs 208 f². At the published ledger point f = 1 those totals are 320 and 208. The value 320 does not beat 80.

add_high charges two completed_swap_oracle calls on a reversed-field shear and none on the forward shear. Each oracle is one T_old ordinary call, and the oracle text has no transition count. The route generator emits ordered_shift with target column j and source column i, so the target is earlier exactly when j < i. The published elimination has 4 earlier shears. The zero-swap word has 10. Both words and both inverses multiply to the pinned matcher. A reading that prices earlier shears at zero ordinary calls would report a swap-free bill of 0 and would beat 80. The source text is the other reading.

T_old still has no numeric transition tariff. Signed-dyadic scales in {2, 1/2, -1, -2, -1/2} have sufficient charge 2048 V_s with V_s = PQS. A supplied forward-shear residue has sufficient charge 1024 V_h with V_h = P Q² G S. Those volumes are not added to the ordinary-call totals. At f = 1 the sufficient charges are 163840 V_s against 229376 V_s, and 229376 V_h against 442368 V_h. Preparing a residue other than the linked half (Q+1)/2 remains a caller cost. That missing transition price does not reverse the gap of 112 f² ordinary calls.

Task and overlap

Base commit: 7c49fe32c55de02c2c873655c804b16e4c3fef0a. Priority revision 8.

Card supplier-boundary-audit. Scope status: refined. Discussion #1166 comment 19137812 asks for one literal generator invocation. The letter count of its helper-462 matcher is already recorded and is not redone as the claim here. Open #6467 shortens a different frame506 factorization. research/earlier-target-shift-gap anchors the published 4/10 split only.

No selected-frontier change.

Validation

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

python3 -B research/helper462-p2-ordinary-bill/verify.py
python3 -I -B research/helper462-p2-ordinary-bill/verify.py
python3 -O -B research/helper462-p2-ordinary-bill/verify.py
python3 -B scripts/research_package.py --package research/helper462-p2-ordinary-bill
python3 -B scripts/check_research_commit.py --package research/helper462-p2-ordinary-bill --check-source-history --check-modes

Observed: PASS_HELPER462_P2_ORDINARY_BILL with published_ordinary=208*f^2, swap_free_ordinary=320*f^2, beats_published=0, beats_80=0, transition_bill_for_T_old=missing, and PASS_REGISTERED_RESEARCH_PACKAGE with outcome=negative-result. Commit-byte check PASS_RESEARCH_COMMIT_BYTES at eb35892026c56733ca223938153d9869381bbe5e.

The verifier reads the oracle multiplier, address order and tariff sentences from the pinned sources. It rejects a dropped factor, a shear coefficient changed by 1, and the reversed address test against the published 4/10 anchor. No Lean, Docker, or selected cold replay was run. No other factorization was searched.

Credit

Matcher, five-swap elimination and the 80/80/224 ledger: Chris R / Clear1nsight, PR #4957. Addressed schedule: PR #4989. Stream oracle: Jose Manuel. Signed-dyadic and affine bounds: JoyboyBrian. Published earlier/later anchor: research/earlier-target-shift-gap. The zero-swap elimination is the schedule recorded on unpaidmoon fork draft PR 150; this package recomputes it from the pinned matcher. Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

1. Give one completed_swap_oracle a fixed-tape transition and visited-cell bill at the helper-462 high-field shape. The ordinary-call comparison is already decided. The blocker is the random-access oracle body, whose transition bill is already recorded as unclaimed.
2. Does some other legal factorization, other than a one-scale or fewer-than-27-shear word, have fewer than four earlier-target letters? Each earlier letter costs 32 f² ordinary calls. That shorter-word search is reserved and is not taken here.

Workflow feedback (optional)

The handoff's generator request and the letter-count remainder were already split, so this invocation could price one recorded word instead of rebuilding the generator. A route ledger that marked each shear as forward or reversed, and said whether T_old had a transition number, would have made the missing tariff visible before the count.