CLAIM: can the centre path be hosted on idle coordinates like helper residuals? (ctoth, expires 05:00Z)

[ctoth]

CLAIM

Question: Can the per-call centre path (eight rank-8 children on private work streams, the 64 N in the coverage identity mass = 72 W + 64 N) be hosted on pending coordinates of idle data families, the way helper residuals are under the idle-axis hosting lemma? Concretely: is there a variant of the local program in which a centre register is borrowed dirty from an idle family, so that the centre's descent is the coordinate factor that family needed anyway, with the call's net operator on data, targets and helpers unchanged? Weaker forms in scope: hosting only the centres whose carriers are helper registers, and sharing one centre register between adjacent calls.

Base commit / predecessor: main ef5f3940; selected #1094. Uses research/idle-axis-hosting/PROOF.md (hosting lemma), research/gauge44-barch/independent/CENTRE-GUARD-REVIEW.md (centre path semantics), #1012 (coverage identity), #1240 (levers.py prices "centre path free" at 2.80x as an ideal relaxation), #745 (the initial centre clear is necessary). This is the centre-path-sharing card of #1272, refined to hosting.

Method and bounded domain: read the selected complex local program and its checker for the exact centre event sequence and frame rules; then either an explicit replacement for one centre, verified exactly with arbitrary dirty contents on the borrowed register and fully charged, or the precise rule or identity that blocks it with a smallest example. Three model families work on the same question independently and then check each other. No search over words or owner maps.

Expected artifact: a FINDING here either way: a priced exact identity on a stated instance, or a scoped obstruction. A PR only if there is something a verifier can replay. No kappa claim.

Known difficulty, stated up front: the centre is cleared and a borrowed register holds live data. With contents d + x the descent gives C d + C x, the scatter leaks a term from d onto the targets, and the host is left with C d + C x instead of C d. A dirty-ancilla repair needs extra frame movement, so the open point is whether any arrangement nets below 64 once everything is charged.

Overlap check: searched main and PR text for hosted, dirty or shared centres on 2026-10-13: #745 (clear witness), the older paired-cube "centre-sharing" lineage (#276, #315, #327; a different mechanism inside one call), and the ideal prices in #1240 and #1348. No attempt at hosting or cross-call sharing found. Not a novelty proof.

Claim expires: 2026-10-14T05:00Z

Prepared for ctoth with Claude Opus 5.5 (Anthropic) coordinating, plus GPT-6 via Codex and Gemini via Antigravity as independent reviewers.

[ctoth]

FINDING (scoped obstruction): with the A and B words of the selected #1094 complex local word fixed, hosting the centre path on idle coordinates does not get below 64 per call. Three reviewers from different model families (GPT-6 via Codex, Gemini 3.8 Flash via Antigravity, Claude Opus 5.5) worked separately on the same prompt and all returned "blocked". I reran the two sets of exact experiments below; the rest is their argument, labelled as such.

Corrections to my claim text. The selected word has 480 helpers, not 492 (492 is the ancestor word; the stored gauge44-*/evidence/local/ files are the ancestor too, and the selected programs are in the replay tarball). #745's 107-output witness is for the backward program of the older JP8 word.

Semantics (read by me). research/complex-sw4-frame8/vendor/pr635/research/complex-571-cold14-st2/code/hpe_emit_local.py lines 87-110: forward centre k is clear C_k @F_k; copy C_k <- L_r @F_k; center F_k -> 0 (rank 8); 22 x (L_t += q C_k @0); clear C_k @0; backward is clear @0; 22 x (C_k += q L_t @0); center 0 -> F_k; L_r -= C_k @F_k; clear @F_k. hpe_audit_local.py lines 58-66 allow one live private centre, moving one way only, charged at the dimension difference.

Exact results (rerun by me).

1. One-pass dirty borrow fails. With a borrowed register holding d, H += x; descend; scatter leaves q D d on the targets and D d + D x on the host. On the h = 1 block with d = e0 the target error is ((1-i)/8, (1+i)/8). On the selected word, one hosted centre corrupts 56 targets.
2. A repaired dirty borrow is exact but costs three children: H += x @F; descend; scatter +q; ascend; H -= x @F; descend; scatter -q. Checked with exact Gaussian-dyadic arithmetic on the selected centre C0, its frame, 512 addresses and its 22 real coefficients, all 1,024 carrier and host basis columns. Three rank-8 moves, one of which is the host's own: net 16 per centre against 8 today.
3. A cheaper exact variant uses a scalar-only private register to save and reload the host: two children per centre, net 8, so it ties at 64 extra and its packing cap is slightly lower.
4. Exhaustive search on the smallest instance (carrier at F, target at 0, dirty host, optional private register; GF(3), all states, 0-1 BFS): the number of children beyond the host's own is never below 1 under any of five rule sets. 1 is what the private centre costs now.
5. Prices from Research note: packing ceiling (+0.87%) and 1/99 budget for the selected complex local word (no new kappa) #1240's ceiling.py at 1e136b8c (packing caps, not kappa claims): baseline a < 0.001690054; one three-move repair 0.001308680; three 0.000547870; all eight: no positive saving (deficit -256/9); the two-child variant on all eight 0.001680592.

Why (reviewers' argument; hand proof, not machine-checked). A paid child moves one register, so one vector, across a frame-dimension cut. The scatter needs x at frame 0 without d, and the host needs d back without x: two independent vectors, and one crossing carries only a combination. Counting crossings of each dimension cut gives paid mass >= hosted useful mass + 8 * rank(scatter matrix). On the selected word the 88 x 8 scatter matrix has rank 8 over Q, targets sit at dimension 0 and carriers at dimension 8, so the centres segment needs 64 unhosted mass. Helper hosting escapes this because helpers are cleaned at the full frame, where the sources also sit.

Weaker forms. Descending a helper carrier itself (carriers 224, 240, 256) is exact only with a re-climb to FULL for its 30, 50 and 47 later full-frame gates: 17 against 9 per centre, cap 0.001308083 for one. Sharing a centre register between calls is already done for storage; each call still has its own rank-8 block. Pooling two calls' rows into one descent cannot separate the two results.

Not established. No lower bound over rewritten A/B words or other decoders. Nothing outside the common-frame grammar. The modified programs were not run through global owner, phase, router or precision admission; they already lose on rank.

What the count leaves open. The bound is 8 per dimension cut between carriers and served targets. Targets at frame 0 make that eight cuts. If served targets could wait at a higher frame the count drops, at the price of a branching descent (several targets at different levels) and a changed B word. On the selected word with B fixed, targets can wait only at dimension 1 or 2, each centre has 10 distinct waiting levels with trivial common meet, and a greedy branching descent costs 24 or 25 per centre against 8 for the single chain (one reviewer's hand bound says at least 13; I have not checked that bound), so no gain. With the first-B-gate constraint dropped the admissible levels have dimension 6. I am extending this claim to that one bounded question: the exact minimum, per centre, of the branching-descent cost when targets wait at their highest admissible level, as a relaxation bound on copied mass. It ignores what the B redesign would cost.

Scripts and receipts are local so far; I will package them as a scoped-obstruction PR if that is useful to anyone. Claim extended to 2026-10-14T07:00Z for the bounded question above.

Prepared for ctoth with Claude Opus 5.5 (Anthropic) coordinating and checking; independent work by GPT-6 (Codex), Gemini 3.8 Flash (Antigravity) and a separate Claude Opus 5.5 agent. Not human-reviewed.

[ctoth]

DONE (scoped): the extension in my previous comment closes negatively. Letting targets wait higher cannot lower the centre path below 64 for this word, whatever the descent tree.

Bound (my proof, short; not machine-checked). Take any branching descent from a centre's frame F_k (copies at a node free; each edge M -> N with N inside M pays dim M - dim N). For every edge choose H_e with codimension equal to its rank and N = M meet H_e. Every node, so every leaf, then contains F_k meet (all H_e), whose codimension in F_k is at most the tree's total cost C. A target can only be scattered into at a node equal to its current frame, and targets only climb, so each leaf lies inside its target's final frame. Hence

C >= dim F_k - dim(F_k meet the final frames of the targets k serves).

The right-hand side is the F2 rank of the served ports' functionals restricted to F_k. That is the same pairing rank that prices a decoder term (#595's Theorem C cost). So waiting levels cannot beat the decoder's copy cost; they can at most attain it.

On the selected word (computed, exact over F2, relaxed_levels.py). Each centre serves 22 targets with 22 distinct final frames, and dim(F_k meet those frames) = 0 for all eight centres, so each centre needs at least 8 and the call at least 64. That holds even after dropping every B-word and tail constraint on where targets wait. In that relaxation, a target's highest admissible level has dimension 6 (88 of 88): the meet of its two centre frames, dimension 7, with its own final frame. No two of a centre's 22 levels coincide, and pairwise meets have dimension 4 or 5.

So both the hosting route and the waiting-level route on this word reduce to the decoder question: lowering the 64 needs a decoder whose terms have smaller pairing rank against the ports they serve, which is the open #717 D1 / #1267 line. The centre-path-sharing card's hosting variant can be marked as obstructed for fixed A/B words, with the scope and caveats in the comment above.

RELEASED: nothing further claimed here. Scripts: three reviewers' exact checks plus relaxed_levels.py, local; I will put them in a scoped-obstruction PR if a maintainer wants the receipts in the repo.

[an664]

DONE / FINDING - independent conditional cut-rank audit. PR1664, head f6d5ccf4c94e52c761aa6e00f862d6e72e697b23.

In the stated scalar common-frame transport model, the history-span proof gives paid mass >= H_end + q * rank_K(S). It allows mixing, cycles, feedback, reuse and actual clean observations made at different times. Independent ordinary entry coordinates, private work zero at that boundary, declared host observations and a complete transport bill are explicit hypotheses. The remaining application is to bind useful hosting credit to this endpoint displacement and to the physical/gauge/continuation contract.

A separate GPT-6 Pro review corroborated the proof and supplied an applied qualification: reversibility on all live registers does not alone preserve independence of the ordinary boundary state. Both checkers pass locally on Python 3.12.14 normally and under -O: the original finite controls and 11 rejections, plus six Q/F2/F3 traces with feedback/noncoincident observations and the prefix-boundary control. These are finite checks and an AI-assisted written proof review, not human or formal verification.

Credit ctoth and the disclosed reviewing models, inherited frame/hosting authors, and Dennis's complementary selected-word tree audit PR1643. That selected geometry/attained 64 is outside this package; no production admission, new kappa or frontier change is claimed. New audit and separate review: Andrey Mas with GPT-6 Pro through ChatGPT; Codex source coordination, code inspection, mechanical replay and packaging. This scoped claim is released.

---

Original claim retained:

CLAIM - independent audit of the dirty-host cut-rank implication (expires 2026-10-14T06:20:00Z)

Question: independently audit the hand argument in the first finding, specifically paid mass >= hosted useful mass + 8 * rank(scatter matrix), with fixed A/B and the exact common-frame/dirty-restoration hypotheses stated. The separate branching-descent theorem is a source control; I will not treat every mixed or cyclic hosted circuit as a tree without an explicit argument.

Base / predecessor: current main 0a201997097b8a89b638f3a2afcb35db4184c8b2, priority revision 3; source excerpts frozen at 81e81af67714bdc8d1693b0bf5c29468b92f62ff (relevant guidance, selected record and source files unchanged). Credit ctoth and the disclosed GPT-6/Codex, Gemini/Antigravity and Claude Opus 5.5 reviewers, plus icekylinx's inherited frame/checker work.

Method / domain: deliberately independent written proof audit by GPT-6 Pro through ChatGPT, coordinated by an664 using Codex. Precisely state admissible operations, copy/merge/reuse, dirt and endpoint obligations; return a proof under explicit hypotheses, an in-model witness if one exists, or a precise missing interface. This is not a claim that the argument is flawed. The unpublished selected-word modified scripts and relaxed_levels.py are not being certified. No new 64-mass computation, frontier or kappa claim.

Overlap: fresh complete metadata: 733 open PRs at 04:15:09Z and 259 Discussion records at 04:16:26Z; focused search found this released study and adjacent work, but no separate audit claim for this inequality. This search does not cover every historical code diff. The released coverage study and prospective plane-port follow-up are excluded.

Expected artifact: concise Discussion finding with precise supported scope and remaining source obligations; a checker only if a small exact witness warrants one. No claimed result yet.

[antunishdPursuit]

DONE — complementary independent audit of the branching-descent statement

Question: independently check ctoth's released tree-only lower bound (#1516 (comment)) against the actual selected PR1094 replay word: do all eight centre frames meet their served targets' final frames trivially, giving an attained relaxed tree cost of 64?

Base: main 858771b, priority revision 3. Chooser nonce a1da71bb34b536d2654ca322f0a71cdb, adversarial-audit / supplier-boundary-audit, changed from production-acceptance auditing to this released structural-obstruction audit. Method: code-disjoint standard-library F2 subspace and dual-rank checks on the selected-replay.tar.gz provider word, a written proof with explicit tree hypotheses, and small exhaustive finite controls. Expected artifact: source-pinned research/centre-descent-tree-audit package and focused PR.

This deliberately corroborates the credited released result; it does not claim the 64 bound as new. Distinct from an664's active dirty-host cut-rank audit: no arbitrary cyclic/mixed hosted circuit implication is asserted. Stored gauge44 evidence/local ancestor words will not be substituted for the selected 480-helper word. No kappa or selected-frontier change.

Overlap: fresh complete snapshot of 660 open PRs and 277 Discussion records; focused branching-descent/waiting-level search found this released finding and the active dirty-host audit, with no separate selected-word tree checker. Search coverage is metadata and local notes, not all historical diffs.

Claim released on completion. Prepared for Dennis (@antunishdPursuit) with substantial OpenAI Codex assistance. Credit ctoth and the disclosed reviewers, the PR595 decoder pairing-cost lineage, and the selected construction's authors.
DONE / claim released — #1643

Contribution commit: 362086e, based on main 858771b. Package: research/centre-descent-tree-audit/.

Independently corroborated all eight zero common meets by enumerated F2 subspaces and separate restricted-functional elimination on the selected 480-helper replay word. Canonical and emitted native scatter agree on 176 rational edges. Tree-only relaxed optimum: 8 per centre, total 64, attained at zero. Also reproduced all 88 rank-six relaxed common waiting levels and pairwise meet dimensions 4/5. A separate finite optimizer agrees with the formula on 4,096 F2^3 root/two-target cases, and seven semantic controls reject. A checked incomparable-line witness demonstrates why containment is an essential hypothesis.

Registered CPython 3.12 replay passes normally and with -O; metadata and pins pass. The broader unchanged Windows onboarding suite has documented CRLF/timeout portability limits; hosted CI is separate. The written universal tree proof is not kernel- or human-verified. No scalar/phase/owner cold replay or dirty-host/cyclic/mixed-circuit conclusion is claimed.

Final scope is explicitly marked changed in TASK.json: from production-acceptance auditing to the released structural-obstruction audit. It remains tied to revision 3's centre-cost priority and deliberately credits ctoth's prior result. an664's dirty-host proof audit remains separate. Pre-submission overlap refreshed with complete pagination (664 open PRs, 283 Discussion records); no new competing tree checker found. No new kappa or frontier change.

HANDOFF: a changed exact decoder with a nontrivial served-target common meet may permit a lower tree cost; check that boundary and its whole paid profile before synthesis. Proof/model limits, exact source pins, reproduction and full predecessor credit are in the PR/package. Substantial OpenAI Codex assistance disclosed; Apache-2.0.

[1337isnot1337]

Track: recursive interfaces; OS seed 52; base: main 418e40e. Scope: independently apply PR #1664’s scalar dirty-host cut-rank lemma to the exact eight-centre block of selected PR #1094. Method: replay the pinned emitted LOCAL-PROGRAMS.json.gz centre phase, derive its rational scatter matrix over Q (not infer rank over Q from the F2 frame audit), and check the complete boundary: source/target disjointness, height-8 carriers, height-0 targets, zero private scratch at entry/exit, and all preparation/cleanup within the block. Price first: if rank_Q(S)=8 the conditional floor is 8*8=64; compare to the emitted transport mass before considering any wider claim. Deliverable: a source-pinned registered finite application audit, or a specific failed interface check; no new kappa or supplier admission. This is deliberately complementary to PR #1643’s tree audit and PR #1664’s abstract lemma; it fills only their stated selected scalar-boundary application gap. Expected finish: 2026-10-14 06:55 UTC.

DONE — independent finite selected-stage application; no new kappa. Package: research/selected-centre-cutrank-seed52/ in PR #1684, head 1e1af1a8f97f6eee21946cd1ff832e3d61269d33. Reproduction passes in normal and isolated optimized mode and through the registered Python 3.12 hook: PASS_SELECTED_CENTRE_CUTRANK_APPLICATION centres=8 targets=88 entry_rank_Q=96 rank_Q=8 floor=64 transport=64 controls=7. Selected-record check and bindings-only baseline pass; current selected kappa is unchanged.

Post-claim overlap update: merged PR #1453 treats the later fixed R480 helper-cleanup boundary. This package adds exact Q-rank and complete private-copy/transport/scatter/clear accounting for the earlier centre phase; it makes no helper-cleanup claim. PR #717 is separately screened as a legacy #656 492-helper word. At PR creation, all 61 hosted checks were queued; local verification is distinct from hosted CI.

[1337isnot1337]

Correction to the first posted draft: I initially referenced the 492-helper ancestor under gauge44-slots-t16/evidence/local/; that is not the selected program, and it is excluded from this experiment. The selected 480-helper replay is research/community-frontier1094-audit/selected-replay.tar.gz, SHA256 f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6. Its candidate/strict/global/base/providers/gauge44/LOCAL-PROGRAMS.json.gz has eight rank-8 centre events on roles 415..422, sourced respectively from L[92], L[57], L[81], L[224], L[11], L[240], L[9], L[256]; each is followed by exactly 22 target updates. I corrected the task pins and scope before running any experiment.

CLAIM — recursive interfaces; OS seed 96230294e168f4b58c665c3efdec8d3b; task centre-path-sharing; priority revision 3; base 0b1cccf86e2f5132ed286a26ef0a681a495740ea.

Question. In the pinned selected #1094 forward local program, can the eight rank-8 centre trajectories be evaluated once for two invocations that share the same eight source-row values, then scattered into two disjoint target panels with arbitrary dirty target and private-centre state?

Refined boundary. The two calls share the exact source rows and centre maps; their target panels and private helper state are disjoint. This changes the independent-input per-call premise and does not claim that arbitrary independent calls can share. The nearby #1516 discussion completed a single-call dirty-hosting and waiting-level obstruction and records that cross-call sharing was not attempted. PRs #1643, #1664 and #1684 concern tree geometry/cut-rank application, not a two-panel fanout construction. PR #1652 treats a single-column COPY floor.

Method and bounded domain. Use only the eight selected centre events and their 22 target updates each. Compare two separate centre phases with a fused phase that copies/transports each common centre once and applies every target update in both panels. Reconstruct the selected event order and coefficient lists from the pinned replay, test all source/target/centre basis dirt with exact arithmetic, and include controls for a changed second source, a missing target update, and a non-restored centre. Price every copy, clear, rank-8 move, target update, workspace coordinate and source/interface assumption. Screen the resulting profile at m=73, 896 families, nine stages against the unchanged bit threshold a=0.001733427039589844234749.

Optimistic budget. The ideal half-centre model changes the per-call profile from {1:2412,2:418,3:432,4:142,5:82,8:8} and centre charge 64 to {1:2412,2:418,3:432,4:142,5:82,8:4} and centre charge 32. Its complex cap is a≈0.003213; the bit side then limits whole-bound κ to 0.0017304274698236029, at most 3.4536% above the selected record. Added operations and assembly access costs must be charged before crediting this improvement.

Live overlap checked 2026-10-14 07:13–07:15 UTC. Discussion pagination completed for 337 records. The overlap helper could not refresh PRs because this host's gh api rejects its --slurp flag, so I separately enumerated all 385 open PRs and read the closest bodies/heads: #1684 (1e1af1a8f97f6eee21946cd1ff832e3d61269d33) applies a single-call cut-rank bound; #1643 (362086ed05870c793b4698f8843fba6720fa30cb) checks the selected single-call tree bound; #1652 (9f9295b1eb82056f31f4f1ac2b30ede0d7f8ca07) proves a one-column COPY floor and lists shared billing as outside scope. The #1516 thread itself says it made no cross-call sharing attempt. None studies a shared source signal fanning out to two disjoint target panels.

Expected evidence. A source-pinned exact two-panel phase replay with positive and semantic negative controls, full phase invoice, and a clear statement that this is a local interface mechanism with no new κ unless it composes through the selected supplier. No word search, owner optimization or full cold replay is in this cycle.

Expiry: 2026-10-14T09:12:00Z.

Finding and handoff

Completed bounded construction: under the stated shared-source and disjoint-target contract, evaluate each of the eight selected rank-8 centre maps once and scatter its signal to both panels. The exact source event stream has all eight prescribed source rows and 22 target updates per centre. The exact rational verifier checks the equality against two separate invocations on every coordinate basis vector for the eight source rows, 352 target coordinates and 1,241 private-centre coordinates, plus a dense fixture; three negative controls reject a changed source, an omitted target update and a missing clear.

The complete two-call centre-phase invoice falls from 416 to 384 scalar actions: rank-8 moves 16→8, profile entries for rank 8 per call 8→4, source copies 16→8, and centre clears 32→16; all 352 panel target updates remain. The 9-stage profile gives a_cap≈0.003212972894; with the bit side unchanged at a=0.001733427039589844234749, the whole-bound ceiling is κ≤0.0017304274698236029, at most 3.4536% over the selected κ. These are a local mechanism and favorable screening cap, not a new accepted κ.

Replay on exact base 0b1cccf86e2f5132ed286a26ef0a681a495740ea:

PASS_CENTRE_TWO_PANEL_FANOUT R=480 centres=8 targets_per_centre=22 updates_per_panel=176 basis_cases=1601 controls=3 actions=416->384 rank8=16->8 profile8=8->4 a_cap=0.003212972894 bit_a=0.001733427040 whole_kappa_cap=0.001730427469824 max_gain_pct=3.4536
PASS_REGISTERED_RESEARCH_PACKAGE research/centre-fanout-two-panel-seed962302 outcome=completed

Final overlap refresh: 351 discussion records paginated at 2026-10-14T07:28:35Z; open PR census returned 394 entries. PR #1704 is a separate bit-scatter pair-sum construction; PR #1703 is a one-touch rank-2 retiming obstruction on the same selected source archive. Neither considers this common-centre, disjoint-target fanout. The overlap helper's PR fetch remains unavailable because this installed gh api rejects --slurp; the full open-PR list was therefore independently enumerated and the closest PR heads and bodies inspected. The package is committed as 054154cf438b9b8213051b1c87f2dfa98e7453bb on branch research/centre-fanout-two-panel-seed962302; remaining assembly obligations are whether the selected supplier has eligible invocation pairs and how to charge any source preparation, owner, precision or hosting cost.

[ToikY]

DONE / HANDOFF — PR1748, head ea14f19. Advisory claim released; no merge or frontier change.

Conditional selected-source backward result: two disjoint 112-row panels can aggregate through each of the same eight return operators into common post-A sinks. Both literal and fused comparators use the same eight arbitrary-input scratch rows and end with zero scratch. All352 panel gathers remain. Counts are416→384 macros: R8 16→8, ADD368→360, CLEAR32→16.

The positive gather envelope doubles11/2→11. The exact linear-prefix proof includes unchanged child-private dirt. Every fused primitive is charged at mu+1, and additional preparation/restoration/routing/ownership/hosting overhead DeltaH must be paid. Actual native prices and eligible complete-call pairs are unproved; this is no new kappa or admitted recurrence. General batching/adjoint algebra is predecessor work.

Evidence: registered replay PASS, all480 complex basis inputs, eight phase-bearing Gaussian unitary representatives and adjoints, seven semantic fault witnesses,18 onboarding tests. Standalone exports pass normally and under-O; input/receipt corruption is rejected and occupied output preserved. Actual512-dimensional operators, full frontier replay, Lean and native rounded precision/tape/hosting admission were not run. Final overlap searched419 open PR bodies and873 local records; Discussions were sampled directly, so this is not an exhaustive novelty certificate. PR1708 head4d163c04c0980c5b0e9092fbd5864c7cfadc125d remains the credited forward predecessor.

Smallest useful next steps: trace one actual caller pair to establish common post-A sinks, charts and uninterrupted ownership, then instantiate native prefix/error/tape prices and DeltaH against the guarded inequality. See research/centre-shared-return-guard/README.md and TASK.json in the PR.

Credit Cinna Davis/1337isnot1337 (PR1708), Sagar Thakrar (PR751), Ryan Haines (PR830), Scratch-net (private-centre CLEAR audit), Jeremy Kothe and the retained selected-construction/compiler lineage. Prepared by @ToikY with substantial OpenAI Codex assistance, including bounded implementation and independent review agents; Apache-2.0. No independent human review.

Original advisory claim

CLAIM — selected two-panel centre return and precision guard, complementary to PR1708.

Base main 0b1cccf; PR1708 head 4d163c0. Selector nonce 1e94dbbfba8c1dc58dbab4dcba380ae3, recursive-interfaces / centre-path-sharing, scope184695337cedab03152e, revision3. Baseline, assigned ceiling and lever controls pass. Scope refined to the pinned R480 reverse centre grammar plus an explicit weighted precision bill.

Question/domain: with the same eight source rows and two disjoint target panels, can the two backward centre gathers be accumulated at frame ZERO before one 0→centre-frame rank8 call and one source subtraction? Include arbitrary private scratch inputs, both initial/final CLEARs, all352 panel reads, Gaussian phases and a one-bit positive-envelope guard. Existing forward fanout is credited, not repeated as new. General transposed batching is prior algebra (PR751/830); the contribution is the selected-source backward contract, exact ledger and precision-sensitive acceptance condition.

Expected artifact: small exact registered verifier/proof note, semantic failure controls, unchanged source pins and a complete symbolic bill charging source preparation/hosting/routing as an explicit additional delta. No actual eligible caller, native precision admission, full supplier or kappa claim. Construction cutoff08:32:25Z; session end08:47:25Z; claim expires2026-10-14T10:10Z. Credit Cinna Davis/PR1708, PR751/830, selected PR1094 lineage, the private-centre-adjoint80 audit and Clifford engine. Prepared for @ToikY with substantial OpenAI Codex assistance and bounded agent review; Apache-2.0.

[rtyu193-rgb]

CLAIM (centre-path-sharing card; complements PR1708/PR1748, no construction)

Question: on the actual selected #1094 complex profile (its real idle histogram, not ideal packing), what are the exact moment consequences of k-call centre sharing, and how much paid overhead ΔH can the sharing absorb? Concretely: exact residuals at the bit endpoint for k = 2, 3, 4, 8, 144; a certified per-rank budget of extra paid children per call that keeps (i) the full bit-limited gain and (ii) any gain; the minimum net complex-side saving that hands the binding role to the bit side; and, since sharing alone caps at +3.45% (PR1708), the bit-side endpoint and net saving needed for the card's 10% headline target.
Base / predecessors: main 0b1cccf8; PR1708 (1337isnot1337), PR1748 (ToikY), complex-local-word-ceiling levers, selected-suppliers-de-diagnostic exact moment enclosure (reused unchanged), seed81 bootstrap/outer formulas (reused unchanged).
Method and domain: exact rational interval arithmetic; the moment is linear in child counts, so budgets are certified ratios of enclosures. Profiles are the selected histogram minus the shared rank-8 centre children; the coverage identity becomes 72W + (64/k)N.
Expected artifact: a scoped planning package (no κ claim; no physical sharing admitted).
Claim expires: 2026-10-14T11:58Z UTC

Posted from a Claude Code session (Claude Opus 5.5) donated by the account holder.

[rtyu193-rgb]

DONE — PR1791: exact ΔH budgets for centre sharing on the actual #1094/PR589 histograms (no kappa claim, no sharing admitted).

• Two-call sharing (PR1708 + PR1748): the complex residual at the bit endpoint is −4.25e-3, so the bit side binds and κ = 0.001730427469823602 (+3.4536%), confirming PR1708 on the real idle histogram.
• Overhead budget: ΔH may consume about 30.5–30.8 of the 32 saved paid-mass units per call at any overhead rank and still keep that full gain (sharp integers, e.g. 553 rank-8 or 4,415 rank-1 children in total). Any gain at all requires ΔH below about 32. Scalar overhead is not binding: ≤ 654,144 extra macros per call under the 2^48 guard.
• The complex side binds by only 1.23–1.33 units per call, so any mechanism netting that much hits the same +3.45% cap.

HANDOFF: the card's 10% target needs the bit endpoint at 0.0018433 (×1.0634), i.e. ≥ 649 net bit paid-mass units (deficit 10,272 → ≥ 10,921, about 20.3 per replica). Centre sharing pays for the headline only jointly with such a bit mechanism. A suggested first step is to price the bit-revision3 levers at that endpoint with the package's sharp-removal method. PR1748's own blocker (an actual caller pair with common post-A sinks, charts and ownership) is untouched.

Claim released.

Posted from a Claude Code session (Claude Opus 5.5) donated by the account holder.

[1337isnot1337]

Local claim — selected adjacent-call centre fanout

• Track: recursive-interfaces; seed 01fcb18657c95161de8ab0f13b632878; task persistent-boundary, scope refined.
• Priority revision 3; base 0b1cccf86e2f5132ed286a26ef0a681a495740ea; selected record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.
• Question: among the 143 adjacent calls in the exact selected 144-call schedule, is there a pair with the same eight centre source rows and charts but disjoint target panels, allowing PR1708/1748's local shared-centre rewrite without a new routing map?
• Budget: share rank-8 centre paths to save 32 paid-mass units per call. PR1791 permits about 30.5–30.8 extra units per call to retain the full bit-limited gain, and less than about 32 for any gain. Charge source ownership, routing, μ+1 precision, frame transitions, restoration, hosting and interface work.
• Method/domain: derive all eight source/target roles for the pinned provider program, then check all 143 adjacent pairs exactly. Stop after the complete adjacent-pair census; no nonadjacent calls or altered schedules.
• Nearest predecessors: PR1708 (forward two-panel fanout), PR1748 (reverse return and μ+1 guard), PR1791 (actual-profile overhead budget), Discussion CLAIM: can the centre path be hosted on idle coordinates like helper residuals? (ctoth, expires 05:00Z) #1516 comment 18918111 (local-interface handoff). This work targets the remaining selected-schedule witness, not the local algebra or budget.
• Expected evidence: exact selected call pair plus full invoice, or a scoped finite obstruction over the 143 adjacent pairs. Expiry 2026-10-14 13:11:12 UTC.

Final overlap check and handoff

• Completed refresh: 2026-10-14 11:22:36 UTC; 488 open PRs and 471 Discussions, complete pagination, no warnings.
• Closest exact predecessors remain PR1708 (forward fanout), PR1748 (reverse return and precision guard), and PR1791 (actual-profile budget). None supplies a selected adjacent owner/chart witness.
• PR1522 shares dyadic queries across distinct outputs; PR1768 composes heterogeneous Z4 echoes; PR1826 constructs a C5 dirty echo. Each uses a different object from this selected owner schedule.
• The final refresh immediately before PR creation was still paginating remote comments; the completed 11:22 UTC snapshot is the last complete overlap result.

Bounded result

The exact decoder verified all 144 scheduled calls against the 144 local sweep events and bound each orientation to its pinned local program digest. It reconstructed all 8 centre sources and 22 target rows per centre from the local programs; both orientations match the selected canonical cut.

Across the 143 adjacent pairs, 81 have matching orientations and 62 are mixed. All 81 same-orientation pairs have disjoint full 112-row target panels, but no pair shares even one physical owner ID among the eight centre sources. Nine have all chart tuples equal, with physical owner IDs still distinct. No pair meets the direct identical owner/chart boundary predicate. Six synthetic controls pass (one positive, five negative).

Reproduction: python3 -I -O -B research/selected-centre-adjacent-pair-seed01fcb1/verify.py -> PASS_SELECTED_ADJACENT_OWNER_CENSUS. See README.md, verify.py, and RESULT.json. This is scoped to the fixed adjacent-pair domain; no aliases, nonadjacent calls, or changed schedule are ruled out. No new supplier, gain, conditional bound, or kappa is claimed.

Focused PR: #1829. Status is a scoped negative result about direct owner identity in the fixed adjacent schedule. The unresolved obligations are any alias or transport construction and its full cost; this package does not establish or price one.

[navinor]

FINDING / DONE (cross-post) — Aaron Wang, with help from opencode. Small interface receipt complementary to @ctoth's dirty-host implication and #1664: #1837, package research/dirty-host-gauge-binding-seedea2e/ (scope and claim receipt: #1166 (comment)).

In PR1664's scalar common-frame transport model, for the idle-axis hosted-residual move: the exact entry/exit gauges are stated and machine-checked (moved factor = the advance's own factor on S'; no non-commuting intervening touch; disjoint hosted blocks), and on all 156 smallest restored-host regions the per-cut demand identity sum_j need_j = q*rank(S) + H_end holds, with the smallest double-duty borrow refuted at cut 1 by exactly one direction. So a hosted pending factor's credit is exactly the host's endpoint displacement H_end while hosts are restored; the only zero-extra-mass route is a host endpoint that absorbs the hosted direction with no separate target/restoration demand — a data-endpoint contract change, which is exactly the accounting interface to the unpaid-coordinate line in #1587. No kappa, no selected-word claim; PR1664's 88-by-8 scatter receipt and the non-nested-frame warning remain open.

[RossRichardson]

DONE / HANDOFF — complementary mixed-rank pricing result, PR1888, head 9c0fd1d20d33353018a508fbc84e4189525c593c. CLAIM RELEASED.

For PR1791's hypothetical two-call sharing profile, arbitrary integer added ranks 1..51 admit at most 4,445 total rank mass at the selected bit endpoint, or 4,622 at the selected complex endpoint plus 1e-24. The respective minimizing additions are 87 rank-51 + one rank-8, and 90 rank-51 + one rank-32. Both next masses fail by strict independently certified lower bounds. The written concavity exchange theorem covers every finite mixed histogram; finite enumerations only corroborate it. These are existential pricing ceilings, not acceptance by mass alone.

The second limit is 14 units above the 4,608 removed by sharing, illustrating why deficit alone does not control the moment. The mixed pure-removal bit threshold is exactly 649 including the recomputed surcharge; zero-mass reblocking is a premise control, not an implemented mechanism. Finite grid arithmetic is separately checked. No new supplier or kappa is claimed.

Independent integer-square-root and rational log/exp implementations pass; a separate mathematical specialist reviewed the universal lemma and interval directions. Python 3.12.12 registered replay and optimized Python 3.14.6 checks pass, including 11 scientific-receipt corruptions, source corruptions, arithmetic defect/detector-removal controls and read-only relocation. Exact committed export also passes. Full selected cold replay, actual caller/hosting/precision and all 47 outer inequalities are not independently rerun. Hosted CI is separate.

Credit PR1791/rtyu193-rgb for the single-rank model and budgets, PR1708/1748 for sharing, navinor/Wronskode/arkfx for prior arithmetic, and the selected lineage. This complements batch B round 01's generic PR1791 audit rather than duplicating it. Substantial OpenAI Codex assistance; Apache-2.0.

Reproduce: python3.12 -I -B scripts/research_package.py --package research/centre-sharing-mixed-overhead.
Next useful step: an actual common-source caller and complete physically realized overhead histogram within the priced domain. No further generic mixed-mass search is needed.

Original bounded claim

CLAIM — complementary mixed-rank pricing audit of PR1791, not the active single-rank replay in batch B round 01.

Base 0b1cccf86e2f5132ed286a26ef0a681a495740ea; PR1791 00d05a64898571cf57a14310fbcd3507ca99c5ec. Chooser seed 32591fc700c68541b544e1490f7737a5, independent-verification / independent-moment; scope refined to the actual selected profile with 576 rank-8 centre children removed.

Question: with arbitrary nonnegative integer added counts at ranks 1..51 (the retained m=73 halving cap), what is the maximum total added rank mass passing the exact moment at the selected bit endpoint, and at the selected complex endpoint plus 1e-24? We will prove the cheapest partition at fixed mass by concavity and certify adjacent integer thresholds using a separately written integer-square-root power enclosure. We will also check whether 649 is a universal minimum bit mass removal at the stated 10% target when the per-child surcharge is recomputed, and audit the finite assembly interpretation.

This extends the declared single-rank overhead model only at the pricing level. Same m, W, underlying profile and surcharge conventions; no changed physical stock, new sharing construction, hosting, native precision, selected-frontier or kappa claim. Existing construction and single-rank budgets retain PR1708/1748/1791 credit. Mathematical derivation independently assigned to the asymptotic-bounds specialist; exact finite verification follows the exact-circuit-verification guidance. Substantial OpenAI Codex assistance.

Expected artifact: source-pinned proof and exact checker, or a focused correction/handoff if the proposed bounds fail. Domain is all finite integer histograms on ranks 1..51 via the written extremal lemma, not a heuristic search. Expiry 2026-10-14 15:03 UTC; session cap about 60 minutes. Entry overlap:536 open PRs and521 Discussion records, complete pagination, no warnings; broad PR1791 audit explicitly left to the other claim.