[Clear1nsight]

Change and mathematical scope

The physical interpretation of Nick Petalas's #5083 needs a direct-comparator price gate in addition to its sound formal five-call saving. This package retains the source extraction, exact derivation and independent direct-only review, with unchanged scientific bytes and portable bounded replay.

The formal word costs c1+4c2, against 3c1+3c2. With unweighted reversed BIT generators, however, F12 F23 F12 produces ordinary J13, including restoration of the middle chunk. The source supplies a direct ordinary-swap recipe costing at most 3F+6Q for the three target owners. A candidate therefore needs

B < (2F+6Q-Delta)/4, where Delta=wNew-wDirect counts only outside-call work.

F and Q are complete same-volume reversed-call prices at widths f and floor(f/2); B is the complete cap-two owner transaction. Uniform label/pair tariffs, actual weights, orientation, precision, all independent outputs and arbitrary dirty spectators must match. This is an exact comparison to a constructive upper recipe, with no optimum claim.

In the explicitly hypothetical tariff model F=K*f^(1-C), Q=K*floor(f/2)^(1-C), B=2^(1-C)F, Delta=0, the nominal proposal loses throughout 0<=C<=17/5000: the necessary B/F is below 333/266, while the nominal value exceeds 399/200; recursive disadvantage exceeds 19767/6650 F. Exact integer/rational checks establish this screen. Unknown physical prices or overhead remain blockers.

Task and overlap

The exact canonical base is 81e9bd69e4a5b00ba9c713a1620e36d576d5522e. The actual bit-new-register-model card is retained verbatim, with scope explicitly changed to the physical ABI, ordinary/reversed orientation and direct price comparison. #5083 owns the predecessor formal construction; this package neither duplicates its formal replay nor supplies an emitter or new κ. A fresh all-author created-and-updated PR scan covered activity through 2026-10-23T09:18:17Z (cursor #5098), with direct reads of the canonical #4930 investigation and #5083 comments and head. No exact competing scope was found in that coverage. The canonical main ref remained81e9bd69e4a5b00ba9c713a1620e36d576d5522e at 09:18:52UTC. This is bounded metadata/body/known-claim coverage; arbitrary diffs and unpublished work are not covered, so it is not an exhaustive novelty claim.

Source head d2b3f35275cab6fbf18bee40e3fb411496732e54 was not ancestral to the canonical base. A provenance-only ours merge ea40685a28ebf1489f74e91e39b143930dbfee53 retains that exact history without changing the tree. Original source paths and head pins remain provenance; all retained live inputs are pinned at their same paths in ancestor a84a22d3f6e0ce75a9e433c6438f01cf25ed384c. The #4610 source/arithmetic head 20bb93cd990d2ff683e4d0fc56b87a42cd5d3296 was already ancestral. No silent repin or scientific rewrite occurs.

Validation

Exact package commit: acc79887d532095330ece3e6ed048d25f6a6a5e5.

python3 scripts/research_package.py --package research/three-swap-cap2-physical-ceiling
python3 -B scripts/check_research_commit.py --package research/three-swap-cap2-physical-ceiling --check-source-history
python3 -I -W error -B research/three-swap-cap2-physical-ceiling/verify.py
python3 -I -O -W error -B research/three-swap-cap2-physical-ceiling/verify.py

All pass locally. The registered commands each cap execution at 180 seconds; the full registered normal/optimized pair took about three seconds. Frozen author and independent direct receipts reproduce byte for byte, including meaningful sign/equality, floor, complete-price, orientation, reserve and source-corruption rejection controls. The adapter stages original relative paths privately and preserves scientific checker bytes. All 51 retained evidence files, their manifests and the relevant entries of the original independent freeze are authenticated. Unrelated centre-p2 material is not replayed.

Committed-byte/source-history checks and the official exporter pass. A checked export passes both direct modes with Git absent and all extracted files/directories read-only; all exported bytes and modes remain unchanged. Validation receipts are retained locally. Inherited GIT_* variables were removed for these explicit-root operations. Local validation and hosted execution are distinct from scientific admission.

Hosted CI run 39931317193 passed at acc79887d532095330ece3e6ed048d25f6a6a5e5 on 2026-10-23 at 09:27:28 UTC. Planning/helper checks completed a 400-test suite with 17 expected skips. The sole selected package replay passed normal and optimized modes, reproducing the author and independent direct receipts byte-for-byte and rejecting two corrupted scientific inputs. It preserves physical_supplier_verified=false, unchanged committed inputs and new_kappa=null; hosted success is not physical supplier or scientific admission.

Credit

Prepared by Chris R / Clear1nsight with substantial OpenAI Codex assistance in research, independent review and packaging. Nick Petalas retains credit for #5083; David Arias, Ross Richardson, Adam Gall and the retained group/cut lineage retain their mathematical credit. The source BIT, native, row-cover, Clifford, precision/compiler and analytic contributors include Cao Yifan, Cinna Davis, zxv, Dugongue, Jacob Alan Sussman, eumemic and their predecessors. The frozen reports retain their full attribution and notices. Predecessor authors are sources of credited work, not commissioning clients. Apache-2.0.

Open next questions

Bind one eligible chronological caller to the exact cap-two ABI and a complete same-volume F,Q,B,wNew,wDirect bill, including independent owners and dirty-spectator restoration. Test the strict direct-recipe threshold; stop that candidate on failure, and retain missing costs as blockers. Only after a pass is a separately scoped orientation-discriminating physical fixture useful, followed by a uniform exact argument and the full complex supplier/finite-work/tails/compiler/outer audit.

No physical supplier, actual eligible occurrence, new P/T histogram, native emitter, universal obstruction, optimal direct comparator or new κ is established. Publication and hosted CI are separate from this local verification.