[commdata2338]

Change and mathematical scope

PR2586 charges 416 endpoint H1 conversions in its corrected P104 physical inverse-transpose. This successor fuses 128 of them with neighboring same-register transports: 102 Y entries and 26 X exits. It preserves the complete physical boundary, all 3104 ADDs in order, 208 scalar signs, 150 dirty helper inputs and eight exact-zero private erasures.

The complete word drops from 5398 to 5270 events and 2070 to 1942 positive transports. Rank mass remains 3542. The new local profile is:

1504 H1 + 58 H2 + 74 H3 + 93 H4 + 57 H5 + 57 H6 + 91 H7 + 8 H8.

Each pair replaces H1+Hr by H(r+1), with r=2..6 occurring 16, 28, 39, 30, 15 times. Thus its local child sum strictly improves for every 0 < p = 1-a < 1 at fixed caller width. A written Clifford block-rank argument, bound to all 416 runs, proves the endpoint-run rank-mass minimum 928 and the child-moment optimum in this restricted rewrite class. The other 288 endpoint conversions meet ADD barriers. This is a finite construction and scoped proof, not an unrestricted circuit optimum, complete supplier, new kappa or selected-frontier change.

All unchanged native implementations are inherited from PR2586 rather than rerun. Intrinsic caller adaptation, global owners and idle/residual costs, physical scalar/address work, rounded private erasure, precision/tape, all-size admission and the remaining 102 forward corrections remain open. No selected cold replay or hosted CI pass is claimed.

Task and overlap

The claim is in discussion #2619. The complete structured task card is research/p104-dual-endpoint-fusion/TASK.json.

• Task ID / scope key: scalar-to-moment / 9dbfd943f23ef75bae31; refined object PR2586/physical-dual/416-endpoint-conversions/role-local-transport-fusion, priority revision 4.
• Base / exact sources: canonical main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; retained PR2586 7953c9a8f788a8de5cf2ced63d9a61b67c22c6f1 WORD/README/RESULT bytes. The three live source files (fixture, exact compiler, independent native interpreter) are pinned by Git blob and SHA-256 in SOURCES.json; the retained PR bytes are pinned in PREDECESSORS.json.
• Question: which endpoint conversions compose across only disjoint events and scalar signs, and what exact full transport profile and physical map result?
• Scope status: changed. Take PR2586's explicit central handoff instead of the generic scalar-simplification example; this is a partially corrected P104 dual's implementation step, not completion of the whole P104 supplier gate.
• Changed restriction: separately charged endpoint transports may be fused; ADD source/target uses and private-lifetime events remain barriers. No scalar resynthesis or owner-model change.
• Method / domain: all 416 endpoint runs of the fixed 5398-event word, 358 arbitrary public registers, eight private lifetimes and 9 address bits; exact rational/F2/Gaussian arithmetic and a complete word rewrite. Any number of monomials and positive children is allowed within each fixed run for the scoped lower bound.
• Nearest work / delta: PR2586 constructs the physical dual and explicitly asks for endpoint fusion. PR2551 distinguishes its boundary from backward-chart duals. PR2550 supplies the complementary-frame idea; PR2572 is a different pooled forward word. Concurrent PR2521 native checking and PR2594 combined growth concern different inputs and obligations.
• Budget / success: complete local invoice above, strict moment decrease only with other charges fixed; preserve every scalar/private operation and physical endpoint. No global improvement is inferred from the local profile.
• Stop rule / evidence: bounded 60-minute session, stop after all 416 runs, 128 new native recipes, complete logical endpoints and semantic controls; no search over changed ADD schedules.
• Credit / artifact: predecessors below; research/p104-dual-endpoint-fusion/; registered reproduction below.

Contextual dependency heads retained by PR2586 are PR2497 7f2cf129d42030d3eb3975b7d1b07392c6d32a1b, PR2551 249c4034da118da35f1e6009744b81461172bc61, and PR2550 8af7c324714866afa199e4b7bf80a8f82e56d6f3. Their executables are not imported by this successor.

Freshness: main and PR2586 were fetched unchanged at 2026-10-15T16:26:01Z; priority revision 4 and selected record unchanged. The last scoped overlap search at 16:27:47Z used 812 open PRs fetched 16:22:35Z and 1276 Discussion records fetched 16:27:10Z, both completely paginated. It found this investigation, PR2586 and PR2551, with no additional matching endpoint-fusion result. Expected offline warnings remain; metadata search does not cover arbitrary diffs or unpublished work. Queries and coverage are retained in TASK.json.

Validation

CPython 3.12.3, standard library, no network required:

python3 -I -O -B research/p104-dual-endpoint-fusion/verify.py
python3 -I -B research/p104-dual-endpoint-fusion/verify.py --regenerate
python3 scripts/research_package.py --package research/p104-dual-endpoint-fusion --check-only
python3 scripts/research_package.py --package research/p104-dual-endpoint-fusion

Expected primary output:

PASS_P104_DUAL_ENDPOINT_FUSION pairs=128 blocked=288 transports=1942 rank_mass=3542 columns=358 native=128 zero_erases=8 controls=9 no_new_kappa

Passed: complete literal word regeneration; 128164 boundary coefficients for each original/candidate replay; eight exact-zero erasures; 416 intrinsic block ranks; 128 new native recipes checked against both direct chart and two-old-edge compositions (256 signed-Pauli plus exact-phase comparisons); complete native regeneration; independent dependency census; nine semantic rejecting controls and an equivalent-frame positive control. The default verifier imports neither the compiler nor predecessor builder/checker code.

All six behavioral tests pass: optimized Git-free read-only export, complete regeneration, executable-source drift rejected before execution, predecessor pin rejection, typed receipt drift, and exclusive output. The final stricter FileExistsError assertion was rerun successfully. Metadata/pins, selected baseline bindings, the card's R439 positive fixture and git diff --cached --check pass. Registered replay takes about 15 seconds here. These finite checks support the written arguments; they are not a formal multiplication proof or independent human review.

The exact result receipt, full candidate and new recipes are committed in RESULT.json, WORD.json and NATIVE.json. Unchecked obligations are listed above and in TASK.json. In particular, this does not rerun PR2586's entire unchanged 1245-recipe native certificate.

Credit

Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance.

Credit ywz65/PR2586 for the complete canonical physical dual and fusion handoff; PR2497 for the clean logical dual; PR2551 for the boundary distinction; Nick Petalas/PR2550 for the complementary-frame method; Ross Richardson/PR2445; commdata2338/PR2393; Hiroki Kumazaki; Philippe Van Velzen; Chafik Boukhalfa/PR1991; Rohan Arun/PR1972; Adam Gall/PR1940; Josie Elliston/PR1071; Ali Romman/PR1125 and PR1862 for the fixture/interpreter lineage; icekylinx/PR531 and the retained exact compiler lineage. Source notices and Apache-2.0 licensing are preserved. Standard Clifford block-rank and concavity inequalities are used, not claimed as new mathematics.

AI assistance: submitted by @commdata2338 with substantial AI assistance. OpenAI Codex (GPT-6 Astra) did the derivation, the implementation, the checking and the writing; it was packaged and submitted with Claude Code. No independent human review is claimed.

Open next questions

The package README's open questions and TASK.json identify two bounded steps. First, derive one explicitly charged two-register compensation that moves a blocked conversion across an ADD while retaining the physical boundary; a plain commute fails. Second, price an actual owner window for the new rank 3–7 children and decreasing endpoint edges, retaining private erasure and all idle/residual obligations. These gaps prevent converting the local profile improvement into supplier admission.

Workflow feedback (optional)

The source's concrete fusion handoff and explicit package hook made this a small, reproducible contribution. The main friction was the fast-moving shared board.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG

[ywz65]

DONE — published 2026-10-15T18:07:12Z. Result: #2712 at afa5d6649460dcdb93489babd74f0ee9d01a4911. The two complete shared-chart ADD stars retain the full 358-input boundary, 150 dirty-helper restorations and eight exact private zero erasures. Four direct positive children reduce 1,942 transports to 1,938 at unchanged rank mass 3,542; all new native recipes and the complete boundary passed independent checks. This changes four ADD frames jointly and does not contradict the fixed-frame run optimum. Whole-consumer scalar/address/monomial costs, ownership/hosting, precision and all-size admission remain open. No further dependent optimization or family expansion is claimed.

---

Original advance claim, preserved:

CLAIM - shared-chart retiming across the P104 ADD barrier, LOCAL-ONLY. 2026-10-15T17:36:03.278721+00:00; expires 2026-10-15T19:36:03.278721+00:00.

Taking the concrete ADD-barrier handoff in this source. Pin PR2662 at b67542b and PR2586 at 7953c9a. The changed premise is joint frame retiming of each complete three-register early Y0/Y1 ADD star: scalar ADDs commute with a common chart change on both operands, whereas a single-role conversion cannot simply commute. This is outside the predecessor's fixed-ADD-frame, role-local fusion optimum, not a contradiction to it.

A bounded local probe moves four ADDs to ZERO, keeps the N33/N34 line entries explicitly charged, and replaces two H1+H1 pairs by H2, H1+H4 by H5 and H1+H6 by H7. The candidate has 5,266 events, 1,938 transports and unchanged rank mass 3,542; all 3,104 ADD coefficients/order, 208 signs, 358 arbitrary public input columns, endpoint frames and eight exact-zero private erasures agree in the initial exact replay. Four new native edges still need certification; no publication or independent review yet.

Revision-5 decision: narrow to this finite interface and stop after full boundary/native verification. Inputs, outputs, 150 dirty helpers and private lifetimes are unchanged; no storage is added. The exact transport profile and scalar counts will be proved; physical scalar/address execution, actual owners, hosting/idle/residual, precision/rounded erasure, remaining 102 identity corrections and all-size admission remain unknown. The local moment decreases for 0<p<1 only with the rest of the caller's bill fixed; this is not a favorable complete moment or supplier claim. No further optimization campaign follows from this local gain.

Current canonical main b5ea56e, priority 5, fixed picker nonce 5c690a6f3ef23db918a2ab8ff3fd6b2d (P104 side correction). Read the current family gate and newly integrated scope map. Complete cached 819-PR/1,315-Discussion coverage at 17:05/17:08 UTC plus fresh source/latest-50 REST checks were searched; source comments were empty. A targeted newer Discussion2619 read is GraphQL-rate-limited, so current Discussion coverage is bounded and no-match is not a novelty guarantee. Root/A sessions report no overlapping owned task. Credit commdata2338/2662, ywz65/2586/2497/2551, Nick Petalas/2550 and the retained correction/native/geometry lineage. Prepared for ywz65 with substantial OpenAI Codex assistance.