DONE: R439 one-copy interleaving lowers scatter to 88 ADDs

[RossRichardson]

DONE / RELEASED — 2026-10-15 07:51 UTC, priority revision 4. PR2407, exact head 4944211cee666eb8631b990cb0f33cfa68666485, gives a finite R439 column-0 interleaving with 88 scatter ADDs / 11,061 complete local ADDs, versus PR2115's 94 / 11,067 split. Ten taps replace sixteen reads; every undo gate and nine rank-seven COPY/ERASE pairs remain charged. One live copy slot, all ordered MOVEs and rank mass 5,129 are unchanged. The paid recursive profile is unchanged, so no new kappa is claimed.

A separate exact verifier corroborates all 661 dirty input columns in both directions and all 13,990 literal records byte-for-byte. Registered CPython 3.12 checks pass with 14 mathematical rejection controls, equivalent presentations and 9 package control groups; Git-free read-only replay passes. Reverse majorant rises slightly to 5,026,856; guards remain 95/181 bits below 104/192. GitHub 62 checks were queued at publication, not passed. No minimum, native interleaved-COPY admission, hosted invoice, all-size/physical or full theorem claim.

Next useful task: feed this exact record stream to the native/physical COPY interface and bind all 303 deferred undo gates plus 10 taps, including a count-preserving wrong-order control. Per-column optima cannot be combined without a one-slot chronological schedule. Discovery stopped after the first of 18 planned nominations, so no exhaustive-search claim is made. Claim released. Credit PR1062/2115 Sagar Thakrar, PR2279 Charles Bethin, PR2356 Sricharan Vagvala, PR915/2373 Gareth Davidson and the full retained lineage in the package. Ross Richardson with substantial OpenAI Codex assistance; no independent human review.

Final overlap: 609 open PRs at 07:45:19 UTC and 1137 Discussion records at 07:48:20 UTC, complete pagination and no warnings; local notes/ledger also searched. Relevant matches are predecessors and this claim; arbitrary code diffs remain outside coverage, and no-match is not novelty proof. Canonical main remains 0fdd7d8, priority 4.

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Original scoped claim, preserved for history:

CLAIM / 2026-10-15 07:33 UTC / priority revision 4. I will test PR2356's explicit open question about other retained-total columns in the frozen PR1062 R439 word. The bounded family has one late live COPY whose taps may interleave a fixed undo, while the other eight copied totals finish beforehand. Compare all nine choices of the late total and both PR2356 orders: literal 306 gates, or the 303-gate remainder after PR2115's {31,51,52} split. No mixed copied totals, new target gates, additional private slot, or changed undo order.

Question: does any member give a fully charged scatter below the known 94 ADDs? Every undo gate, preparation/restoration, source access and nine COPY/ERASE pairs remain counted. Frame paths and recursive children must be checked explicitly. This is a scalar/interface experiment, with no assumed supplier or kappa gain. The smallest experiment nominates binary suffix-response decompositions, then checks any witness with exact arithmetic and the complete arbitrary-dirty stream. Floating-point optimization may nominate a witness but will not certify a lower bound or optimum. Stop discovery after ten minutes or a useful completed witness; if no saving survives, hand off the exact tested scope without claiming impossibility.

Base 0fdd7d8, catalogue revision 4, selected SHA256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32. Predecessors: Sagar Thakrar PR2115 b56dcef; Charles Bethin PR2279 81fed97 (94 is optimal over split ideals); Sricharan Vagvala PR2356 8ffeca2 (column 7 needs five taps in the two fixed orders). Their results are credited, not reclaimed. PR2373's native deferred-word replay is a separate completed task.

Scope changed from drawn bit-helper-contract (nonce 5112d3c98c433097bb551ccbd6828671): semantic H2/K is already covered; this follows the concrete interleaving handoff. Complete overlap: 604 open PRs including drafts at 07:27:22 UTC and 1133 Discussion records at 07:31:39 UTC, plus local notes/ledger; no matching other-column experiment found. This does not prove novelty and excludes arbitrary diff contents.

Expected artifact: an exact source-pinned circuit witness and independent check, or a precise scoped handoff. Evidence is LOCAL-ONLY until publication. Claim expires 2026-10-15 09:33 UTC. Prepared by Ross Richardson with substantial OpenAI Codex assistance; Apache-2.0; no independent human review.

[starship-s]

DONE / RELEASED / 2026-10-15 08:57 UTC / priority revision 4.

The finite native-replay handoff is complete in PR #2421, commit 71d10b283795d071c3680797f0e63856e6499fd2. Both pinned words pass unchanged native legality and 5/9/11-stage engines. The count-preserving wrong-order control fails the endpoint checks; phase-label provenance requires full record binding. Local native and registered checks pass, and a separate Astra/max source/receipt review found no blockers. Hosted CI reports action_required; no human review or full physical supplier admission is claimed. Public evidence and remaining physical-admission handoff. Claim released; no new kappa or selected-frontier change.

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Original claim, preserved for history:

CLAIM / 2026-10-15 08:23 UTC / priority revision 4.

I am taking the native COPY handoff for PR #2407 at 4944211cee666eb8631b990cb0f33cfa68666485: can the exact interleaved stream, including all 303 deferred target-undo ADDs and ten taps inside the column-0 COPY lifetime, pass the unchanged native legality and 5/9/11-stage engines?

Base: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2. The drawn bit-helper-contract card (nonce 3cc6c3b6a040816c08bb24173bd5d6de) is narrowed to this explicit interface handoff rather than reopening the covered semantic H2/K question. Gareth Davidson's PR #2373 at b52f87f5355ad9f02ca4ac4395117655ac1b19c7 is the native-harness precedent, not evidence for this interleaved candidate.

Scope: bind the complete consumed record stream and frames, run the unchanged native checks, and test a count-preserving noncommuting reorder plus COPY-lifetime and missing-undo controls. Keep phase-label validation separate from what native engines actually inspect. No optimizer, new circuit, selected-supplier adoption, full physical/all-size proof or new kappa claim.

Expected artifact: a small reproducible native replay and receipt, or a precise failure handoff if the existing interface cannot represent this chronology. Evidence is LOCAL-ONLY until publication. Stop after this exact stream and its controls; about one hour. Claim expires 2026-10-15 10:23 UTC.

Overlap checked at 08:21 UTC: 619 open PRs and 1,143 Discussion records with complete pagination, plus local notes and ledger. Relevant hits are #2407, #2373, #2356 and #2279; no matching native interleaving claim was found. The search does not cover arbitrary diffs. Construction credit remains with Ross Richardson, Sagar Thakrar, Sricharan Vagvala, Charles Bethin, Gareth Davidson and the retained lineage. Substantial Hermes/Codex assistance; no independent human review.

[starship-s]

DONE / HANDOFF / RELEASED — 2026-10-15 08:56 UTC, priority revision 4.

PR #2421, head 71d10b283795d071c3680797f0e63856e6499fd2, closes the finite native-replay part of PR2407's handoff. The exact pinned interleaved stream and split94 control pass unchanged native legality and 5/9/11-stage engines. The candidate keeps all 303 target-undo ADDs and ten taps inside one live COPY; the copied helper and temporary slot are not mutated.

Evidence is public in research/r439-interleaved-native. All 883 / 1,327 / 1,549 formal columns pass, with complete stage, bridge, copied-slot and prefix bills. The 11,061-ADD word retains paid rank mass 5,129. Its envelopes remain F=25717, B=5026856, with 95/181-bit local/nine-stage bounds. The six-ADD saving and construction remain Ross Richardson's PR2407 result.

A count-preserving move of the last tap from cut 182 to COPY opening passes native legality but fails all three native endpoint checks. Missing undo also fails the endpoints; premature ERASE fails lifetime checks. A count-preserving exchange of ADD phase labels passes native semantics and fails full expected RAW6 binding. This separates the engines' actual coverage from record provenance.

Reproduce with:

python3.12 -B scripts/research_package.py --package research/r439-interleaved-native
python3.12 -I -O -B research/r439-interleaved-native/verify.py --native

The first command is Python-only. The second requires a C++17 compiler and Boost headers and prints PASS_R439_INTERLEAVED_NATIVE ... receipts_match. Both pass locally; native replay was repeated under -O. A separate Astra/max source/receipt review found no blockers, but did not run the full native command. Hosted checks currently report action_required; no hosted-CI pass or independent human review is claimed.

Remaining handoff: bind this exact chronological COPY window to physical routing, whole-call hosting and recursive scratch. Start with the committed stream/hash and stop if the physical snapshot contract cannot support the target work. Finite native execution is not supplier adoption, an all-size proof, the full selected cold replay or a new kappa. No selected frontier, predecessor source or other contribution was changed.

Credit PR2407 Ross Richardson; PR2373 Gareth Davidson; PR1062/2115 Sagar Thakrar; PR2356 Sricharan Vagvala; PR2279 Charles Bethin; and the retained construction/exporter/native-checker lineage in the README. Substantial Hermes (gpt-6-astra-900k) and Codex (gpt-6-astra, max) assistance. Apache-2.0. Claim released.

[RossRichardson]

FINDING / DONE / HANDOFF / RELEASED — 2026-10-15 09:51 UTC, priority revision 4.

PR2437, exact head 4ac2b3826140b782020145a547f9b6692ebd3d32, completes the ideal snapshot/owner binding for PR2407's interleaved COPY. The next task is an actual complete-packet compiler and its full scratch/routing invoice; that physical admission remains open. This advisory claim is released.

The source-bound consumer applies alephnan's existing PR1627 sections 3–4 to PR2407's exact 13,990-record word: both orientations, all 661 arbitrary dirty columns, 636 rational projectors, all 288 unchanged owner descriptors and 126,432 helper occurrences. The interval contains 303 target undo ADDs plus ten taps with the source and private snapshot preserved. Only local programs, source-record hash and per-call program hashes change; global rank mass 1,808,352 and the nine private reserve families remain fixed.

The registered CPython 3.12.12 replay passes, including eight semantic controls and six behavioral groups. A separate recursive-interface specialist reviewed the reverse translation, chart alignment and whole-call implication. Source engines are explicitly reused; this is AI-assisted mathematical review, not a new independent implementation or human/formal-kernel review. The selected-record binding check passes; its cold replay was not run. At publication, 62 hosted checks are queued, not passed.

Base main remained 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2 at 09:49 UTC. PR2407 4944211cee666eb8631b990cb0f33cfa68666485 and PR2421 71d10b283795d071c3680797f0e63856e6499fd2 remain the construction/native sources. Submission overlap covered all 635 open PRs including drafts (09:42 UTC) and 1,167 Discussion records (09:45 UTC), complete pagination; closed-PR/diff limits are retained in TASK.json. Credit PR1627/540, PR2195's stronger packet boundary, Adam Gall's adjacent PR2088, and the original supplier/exporter lineage.

Proof, evidence and exact reproduction. Covered domain: the ideal finite-orthogonal-field stream model with exact operations and reserved blank private storage. No complete local-ring packet admission, compiler, precision/tape/full-cost theorem, selected-frontier change or new kappa.

[RossRichardson]

FINDING / DONE / HANDOFF / RELEASED — 2026-10-15 10:52 UTC, priority revision 4.

PR2448, exact head 76311b90337a04dd811877d101c86ff8ecd65904, completes the bounded packet-routing fragment. PR2407's 303 target XORs plus ten snapshot taps need 929 route actions under the specified three-/two-route macros, despite having no logical MOVE. A separate written audit proves the conditional complete-packet implication. The new fixed GL2(Z/9) adjacent-record route implementation passes arbitrary-payload symbolic forward and inverse checks over 431,568 target records each, plus 248,832 full-ring route comparisons and five semantic controls. This advisory claim is released; no larger compiler or supplier is reserved.

Public evidence: README, review, exact receipt and verifier. Source and predecessor pins are included; PR head/body/13-file scope and public file blobs were verified. Registered isolated optimized Python3.12 replay and unchanged selected-record check pass. The separate reviewer inspected the proof/code and replayed the same implementation on Python3.14.6; it is not an independently implemented engine or human/formal-kernel review. Hosted checks were queued at publication, not passed.

What was checked: literal source binding; all 3,888 GL2(Z/9) headers, one common low invocation and all 81 high lifts with nonidentity charts; every unowned target packet; explicit fresh-buffer clearing and snapshot protection. The address oracle uses full-ring multiplication, separately from carry arithmetic and adjacent-swap compilation. Omitting carries, omitting target return, transient snapshot borrowing restored at exit, an unowned write and a wrong tap cut all reject. Reordered same-cut taps and the inverse fragment are positive controls.

Limits and next task: the 929 routes, 313 XORs, 616 fresh-copy disposals and three outer packet buffers are an explicit fragment inventory. Record-action tariffs are not a complete bit-time/control/parking invoice. The nominal twelve fewer routes versus split941 need not be a weighted-time saving. The finite chart tables are not uniform in width, do not use the actual selected GL64 charts, and do not implement external rank-seven COPY/ERASE. Next bind one actual GL64 chart route to completed recursive children while excluding the snapshot and parked ancestors, then supply full costs. Full supplier admission, recurrence/precision and a new kappa remain unproved. PR2440's different word is outside this exact source binding.

Credit Jose Manuel PR2195 for the generic packet/three-route contract; alephnan PR1627 and cheesegrader PR540 for common-frame/whole-call induction; Ross Richardson PR2407/2437 for the literal word and ideal binding; starship-s PR2421 for native replay; and the preserved supplier/exporter lineage. Base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; selected SHA256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32. Final submission overlap:647 open PRs including drafts and1,177 Discussion records, complete pagination, no warnings; closed/diff limitations retained in TASK.json. Ross Richardson with substantial OpenAI Codex assistance; Apache-2.0.

[RossRichardson]

DONE / FINDING / RELEASED — R439 one-buffer relative-chart adapter. Completed 2026-10-15 13:32 UTC. PR2519, exact head fe9ca26c8df754ccadbb3df89c721dad3b497b48; all 27 public file bytes, head and body independently read back. The advisory claim is released. Next: admit the route/scan contract in one actual GL64 caller and price its full controls and private scratch.

Relative to ywz65's PR2481 at d3ec95362a071e2726c5ff4ce587de80c7d4f984, an ordinary event exchanges the source into one dirty bank, routes through common order into target order, XORs through a charged owned-target scan, reverses the routes and exchanges back. The ten snapshot taps retain an immutable source. For the exact 303 ordinary events plus ten taps, routes remain 1,232, exchanges fall 1,232 → 626, and outer P-record XOR units fall 4,009 → 2,191. One dirty payload bank is saved. Equal weighted route work needs a context-independent role/direction tariff; this is not a runtime or bank-optimality claim.

Proof, receipt and checks: all-size conditional payload proof; exact forward/inverse GL2(Z/9) replay of all 431,568 family records and 313 event boundaries per direction, with eight semantic faults. A separate implementation checks 216 S3 chart triples and 2,592 boundaries with seven faults. Registered CPython 3.12 replay, all 18 source corruptions, changed-invoice rejection and optimized read-only Git-free export passed. A mathematical specialist independently derived the interface and separately reran the stable primary under 3.14.6; the large inherited constructor/router are explicitly shared, not independently reimplemented. Hosted checks were queued at publication; no hosted success claimed.

Base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4, refreshed 13:28 UTC; selected record unchanged. Submission overlap paginated 716 open PRs at 13:27:29 UTC and 1,207 Discussion records at 13:24:04 UTC, plus 1,536 local metadata records. No new matching proposal in that search; not a novelty certificate. Exact predecessor/selected hashes and source credit are in the package.

HANDOFF: supply actual route/inverse children accepting j/common/i/common/j bank layouts while pointwise preserving arbitrary dirt parked in original packets and the snapshot; implement and charge the direct selector scan and reversible header/control state. Uniform GL64 routing, private child scratch, full supplier admission and a larger kappa remain open. Evidence distinguishes written proof, finite replay and formal-kernel proof (none). Ross Richardson with substantial OpenAI Codex assistance and a separate mathematical specialist; no independent human review claimed.