[unpaidmoon]

Change and mathematical scope

Scoped negative bill, not a construction and not a κ improvement. The one-role compilation of the CrocSwap#5083 five-call schedule has complete cap-two price B = 2F and outside difference Delta = 0. On the CrocSwap#5099 accounting screen 0 ≤ C ≤ 17/5000, that bill misses the strict direct-recipe test

B < (2F + 6Q - Delta)/4

by more than 398/133 full-width calls. The selected conditional result stays κ = 605457647/200000000000.

Task and overlap

Base commit: 32890bc5de034ab8fc93ac88ead7279a6a416d04 (upstream CrocSwap main).

Task card: bit-new-register-model, scope changed. The card asks for a new register alphabet. Discussion #1166 comment 19142691 already moved the question to the physical cap-two price gate. This package prices that gate's one chronological compilation instead of opening another census.

Nearest work: CrocSwap#5083 (formal five-call word) and CrocSwap#5099 (research/three-swap-cap2-physical-ceiling, the direct-recipe threshold and the statement that no eligible caller was bound). This bill is the caller CrocSwap#5099 left open. It does not rerun either package.

The selected one-role contract is notes/batched-bit-rows.tex (each child uses 1/W of the parent volume; repetitions are separate calls) together with notes/three-stage-cover-bit.tex (J_A costs at most three reversed children). Two owners therefore cost two width-f calls.

Validation

CPython 3.12, standard library only:

python3 -I -W error -B research/cap2-one-role-direct-bill/verify.py
python3 scripts/research_package.py --package research/cap2-one-role-direct-bill

Both passed here. The checker authenticates the pinned bytes, requires the one-role and direct-recipe sentences, checks 399^5000 < 2^4983 * 200^5000, rejects the break-even case Q = F, sweeps 128 widths at C = 0, accepts a below-threshold control B = F that is outside the one-role service, and records that a large negative Delta could change the decision. No native program, compiler, Lean build, or selected cold replay was run.

Credit

Nick Petalas supplied the CrocSwap#5083 formal word. Chris R / Clear1nsight supplied the CrocSwap#5099 ceiling and two-owner volume reading. The BIT notes retain their source authors. Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

1. Can a changed multi-owner primitive, not two one-role reversed calls, meet the strict inequality with the same volume, orientation, spectators and a fully charged outside bill? The selected one-role service does not supply B < 2F.
2. If a bill passes, does that inventory improve the selected Complete coupled-output caller: conditional κ = 0.003027288235 (+5e-12 over #5400) CrocSwap/integer-mult-bounds#5413 complex moment after finite work, both tails, compiler reserve and outer transfer? Blocked until a passing bill exists.

Workflow feedback (optional)

The machine-readable open handoffs in CrocSwap#1166 are the structured HANDOFF blocks in comment order. Pricing the named next bill was enough; a second census of every BIT call site was not required once the one-role compilation already failed the gate.