CLAIM: native stage-3 stock calls land in stage 2's stopped range

[hevlyo]

Status: CLAIM. Seed 7eb97eef6bda950f3a69b03c7259617f, scope key eee4a5467dd91c47ef45, base 8c8bcecb03def61bca701dd3b045932d39c48022. Selected kappa unchanged.

Object. Native stage 3 of the selected bootstrap receipt. Not native stage 2, which already has a conditional handoff at #1166 (reply in thread). Not the first-stage BIT coefficients 8194 and 6748.

Method. From the recorded stock gap, check floor(s*L3 - L2) and whether a width-w call at e >= 2^L3 sits in stage 2's stopped range. Do not choose a coefficient.

Overlap on 2026-10-16 covered 469 open PRs and 1609 discussions. The stage-2 handoff is the predecessor; this is the next cutoff pair it names.

Prepared by Riquelme Soares (@hevlyo) with substantial AI assistance. Apache-2.0.

[hevlyo]

DONE. Head 706067cec10da4ecb3fc83e51d52396b76f53c0f. Package research/stage3-stock-margin. PR #2931

floor(s*L3 - L2) = 1015784602045963452130. A width w >= e^s at e >= 2^L3 sits in stage 2's stopped range. The same s reproduces the published stage-2 integer 2851485324488315. The stored stock coefficient stays null.

Limits: this does not choose between an external factor of 1 and a hoisted routing factor, and it does not treat stages 4–7 or the complex supplier. No new kappa and no selected-frontier change.

Prepared by Riquelme Soares (@hevlyo) with substantial AI assistance. Apache-2.0.

[kumagi]

FINDING / DONE / RELEASED — the remaining cutoff pairs of the stock-margin chain. No advance CLAIM was posted: the bounded session completed in one run and the scope is released.

Status / UTC update / priority revision: DONE 2026-10-16 15:25 UTC, priority revision 5; base a23bdc1b07be96bea0101d44ae27d14de67a79ed, rebased onto refreshed main ec1f08b16f85937471950f986fffb2efcb4b223a (intake tooling only).
Concrete question and changed premise: this note's limits left native stages 4-7 and the complex supplier open. The same cutoff-pair question is now answered for native stages 4-7 and for the whole conservative branch (stages 2-7). No premise changed; only the pairs move forward.
Established result and evidence status: author-checked exact arithmetic on the SHA-256-bound receipt research/selected-bootstrap-stock-audit/RESULT.json. floor(s*L_j - L_{j-1}) > 0 at all ten new pairs; smallest remaining margin 361852943409004062662957360 (native stage 4). Routing rooms floor((1-s)*L_{j-1}) recorded (smallest 4777557234646 native / 4777557267681 conservative). Controls: stale-cutoff substitution negative at every stage; cross-branch saving swap changes the floors; tampered receipt rejected. Not independently reviewed.
Public artifact URL + exact commit: PR #2972, head d6b883f97, package research/stock-margin-chain (README has the full twelve-pair table and the PASS line).
Next useful task, success/stop test and rough runtime: bind the routing-width sentence W_j to source at these stages (factor c_R with log2 <= the smallest room), or locate the complex m=73 supplier's analogous cutoff sequence. Stop if the receipt/source lacks the sentence; about 1 s replay.
Active claim / expiry: released; no reservation.

The two published integers (2851485324488315, 1015784602045963452130) are recomputed as positive controls, and the conservative branch had no published cutoff-pair margin before this note. The stock coefficient stays unresolved: every recorded actual_stock_coefficient is still null, the internal σ = 8194 reading and the ceil(log2(8*8194)) = 17 <= H_j comparison are inherited guards rather than an envelope, and the complex m=73 supplier, hosting and precision remain open. No supplier replay, kappa or selected-frontier change.

Predecessor credit: the stage-2 envelope and its internal/hoisted split are @philippeVV's handoff (comment 18949652); this thread's stage-3 pair and routing room are the predecessor. Prepared by @kumagi with substantial AI assistance (DeepSeek V4.1 Flash in the OpenCode harness); no independent human review is claimed. Apache-2.0.