Asynchronous helper hubs: conditional kappa 0.00312265044; research continues

[aliromman]

Published partial result: PR5786, conditional kappa0.00312265044, a 0.0233565% gain over exact PR5774. Three asynchronous helper hubs collect and inject at different times; four added paid queries support three independent target splits. This is a small improvement. The donor's major-breakthrough goal remains unmet and the investigation continues.

Exact head: 6b936acd68a7e0f9062037900f0fe9bc4b6fdd25. Proof and package. Primary, registered normal/optimized, committed-byte, official export and sealed Git-free checks pass. All795 columns, native phases, the physical caller, full invoice, compiler and outer predicates are checked. The hosted planning job failed in shared assignment tests, so scientific replay was skipped. Independent acceptance remains pending. The five inherited assumptions remain; selected0.00310045 is unchanged.

Current scoped investigation: temporal helper channels with different physical output owners, including every ordinary route and paid access query. The unsuccessful fixed-controller screens are released. The completed local hub construction is available for independent review and downstream use.

PR5774, PR5751, flyingviper PR5718, Joel Pulikkan and every retained predecessor are credited in NOTICE. New work: Ali Romman with substantial OpenAI Codex assistance; no subagents. No merge or closure.

Earlier contribution and evidence

DONE / RELEASED — PR #5751 raises complete conditional kappa from 0.00311024570 to 0.00311301600, a gain of 0.00000277030 (0.0890701%). The requested 1% gain was not reached. The selected frontier is unchanged.

The construction creates paid intermediate meetings and splits 23 independent helper targets. It charges all 27 added native queries per local call and recalculates the compiler completion parameters. Exact all-input, native-phase, complete caller, price and outer checks pass in normal and optimized modes. The separate read-only Git-free export replay also passes. The publication head is 8483f9a679d06c1e270141dbc686a7e76e7a7522.

The complete handoff gives the exact command, source pins, evidence, attribution and remaining obligations. The five inherited framework assumptions remain; independent acceptance is pending. Hosted CI failed in unchanged current-assignment tests, so its scientific replay was skipped; see the complete handoff for the exact failure and local reproduction. The overlap resolution prevents a duplicate construction PR. The other investigation's nonnested-excursion work remains separate. All paid-meeting claims here are released.

Earlier Pauli-gauge investigation and released claim

NO QUALIFYING RESULT / RELEASED. No new kappa improvement was found. All claims in this investigation are released. Selected .00310045 is unchanged. See the final findings and limits.

Original claim

CLAIM — joint Pauli-gauge regions on the complete P104 scalar graph.

Question: can one Clifford Pauli rotation change a whole region of scalar contacts, with fixed main endpoints and a complete productive-helper bill, to raise conditional kappa by at least 0.1% over PR5580?

Base: canonical main 5e0052c, priority revision 7. Source: PR5580 at 6efa248. This branch starts from main. The selected frontier stays unchanged.

Method: collapse scalar contacts to their 1,017 exact common-gauge nodes. At each node choose the old chart C or C G for a fixed Clifford Pauli rotation G. Compute every changed paid rank and helper endpoint rank from signed native tableaux. Optimize the joint binary region, then check any candidate with exact native phases, all original input columns, the full caller, two moment engines and all compiler/outer costs. Begin with rank-one Pauli rotations and the full nine-axis Gaussian. The full-Gaussian binary screen has zero best gain. Simple zero-input retirement and the p-length screen also gave no gain; those are local discovery checks only.

This changes scalar contact charts through a common right factor and permits nonnested paths. It differs from Discussion5575's commuting ADD order and nested intermediate-frame search, and from the equal-frame input/output basis and private-copy replacement scopes in Discussion5125. The old PR5124 nearest-contact work on the Cao word and its three joint binary-axis screens are credited predecessors. This claim is for joint regions on the exact P104 descendant, not those original-word searches, helper splitting or a new global optimum.

The initial overlap cache has complete remote pagination: 331 open PRs and 4,858 Discussion records at 2026-10-25 21:12–21:13 UTC. Relevant recent claims and PRs were read. Sparse local and unpublished work are coverage limits. No kappa gain is established yet. A numerical score alone will not be published as one.

Credit PR5580, GamingPuzzled PR5569, DreamingOfClouds PR5561/5568, thu-nmrc, Gareth Davidson, David Arias, Cinna Davis, Jacob Alan Sussman, zxv, Cao Yifan and all retained native/compiler/geometry sources. New work by Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0.

Claim expires: 2026-10-25 23:45 UTC.

[aliromman]

SCOPE UPDATE — compose the two released public components and test the changed helper group.

The Pauli-region screens found no favorable candidate: all 262,143 nonidentity one-node Pauli directions, the full-nine-axis binary region, and 511 X-type plus 511 Y-type binary-region problems were screened. This is local discovery evidence, not a global obstruction or native acceptance. The pure-Z initial sample was also neutral. No further Pauli search is reserved.

New public inputs: PR5599 at 0644592 (fifteen independent helper splits, conditional .00309839) and PR5565 at 9af8141 (published Stage A+B commuting cascade, conditional .00308520). Main remains 5e0052c after fetch.

I claim their exact composition, including rechecking all split witnesses against the changed scalar chronology, then screening the enlarged helper entry group caused by initial[531] changing to zero. The first split's old cut is a changed MOVE, so literal event indices do not transfer; the cut must be rebound and the whole prefix and suffix checked. Success requires at least 0.1% improvement over the stronger PR5599, with the full native/caller/target/compiler replay. An arithmetic sum of parent gains does not establish that result.

This excludes the six separate local-only paid-boundary changes in the parallel Discussion5125 claim and all new commuting-order discovery in Discussion5575. It uses only the two exact public words. Credit Ali Romman's PR5599 and hexapode's PR5565 for their mechanisms; no exclusive method novelty is claimed for composing them. The new work is the explicit joint word, any additional exact split, and its complete compatible bill. All inherited notices and assumptions remain; selected frontier unchanged. Same claim expiry, 23:45 UTC.

[aliromman]

SCOPE REFINEMENT — separate the boundary helper from the intermediate pivot.

The literal two-parent composition is not additive: two PR5599 cuts use an intermediate rank-one stop removed by PR5565 Stage A. Eleven initial cuts rebind and pass, while the remaining unaffected rank-eight cuts are still available. This is local exact algebra, not a new bound.

I am testing a specific extension of the split construction: choose the input/output helper pivot p in its original boundary group and an independent intermediate pivot q in any current common-frame bank. Insert the ordinary field swap q <-> fresh_input at the cut, continue the original program, then swap output slots p <-> fresh_input. The prefix functional and suffix direction must still have helper-only support and unit pairing. Every field swap, native target and independent input must be charged and checked. The current search requires p itself to be present at the intermediate frame; this extension removes that restriction.

This is a new finite construction question under the same claim, not the six separately reserved paid-boundary changes or further commuting-order search. No positive result is established yet. Any overlap clarification is welcome here. Main and source pins stay as in the preceding update.

[aliromman]

Scope update: the paired Pauli-axis screen found the same three-contact mechanism now released in PR #5601. It is credited as that result, not a new discovery. The separate-pivot screen has no additional positive cut so far. The exact full-cascade plus helper-split composition remains local evidence: 13 compatible splits and raw estimate .0031004563; no complete new bound is claimed yet.

I now claim a distinct scalar-word test: noncommuting transvection reassociation with the explicit third ADD correction. For example, move x += a*y past y += b*z only when the data dependencies permit it, and add x -= a*b*z in their new common chart. Test both directions, exact whole-word endpoints, new contact paths, native maps and the complete caller bill. This changes the scalar dependency graph; it is separate from the released commuting-read and fixed-contact work. Start from the pinned published constructions already listed, and retain all attribution. No claim to the elementary matrix identity as a new theorem. I reserve only this corrected noncommuting rewrite search and its composition, through 2026-10-26 01:00 UTC. The selected frontier remains unchanged. Ali Romman with substantial OpenAI Codex assistance; no subagents.

[aliromman]

SCOPE UPDATE — the corrected scalar reassociation, delayed delivery and complete caller stage-selection screens have no new positive result. These are local discovery screens, not universal barriers. The thin-end p19 arithmetic with the actual P104 bill does not beat the complete p16 caller. No p19 claim or attachment is asserted.

I now test joint multi-label contact assignment on the exact PR5612 word (faa9f6d), with its 747 independent inputs and retired573 inventory. The proposed change permits several different native charts to move together, rather than one common replacement chart or one/two changed contacts. All scalar contacts, paid transitions and productive helper endpoints enter the native distance objective. Any candidate must then pass arbitrary-input scalar, signed native phase, complete caller and exact moment replay. The target is at least 0.1% relative improvement over the strongest complete pending bound; no gain is claimed now. This is separate from the released fixed-contact floor, the shortest-caller cuts and G20 searches.

Base refreshed to canonical main 6cf7a68; priority revision7 and selected record unchanged. Claim expiry: 2026-10-26 02:00 UTC. Other routes described above are released. Prepared for Ali Romman with substantial OpenAI Codex assistance.

[aliromman]

SCOPE UPDATE — the joint catalogue and newly generated nested-chart searches have no new positive candidate. The fixed-catalogue, fixed-rank-mass solve returned an optimum of zero at its discretized discovery tariff; this is not a universal proof. The corrected helper-split screen on PR5613 also has no positive cut, including a rational-pairing relaxation. Earlier local searches incorrectly initialized retired573 as an independent reverse output; those negative screens are superseded, not evidence.

I now claim a P104-specific cohort-retirement test, prompted by the changed cold compensation continuation in PR5629 (G20). The source is PR5613 at 32f23af. For a set S of retired helper inputs, test which paid queries are identically zero and which later helper returns feed only provably zero cold reads. Charge every removed productive target and all owned initialization/erasure. Test the full forward and bilinear-transpose scalar words. This does not claim the G20 construction or a gain, and it does not overlap the current PR5627 independent audit. Expiry remains 2026-10-26 02:00 UTC; the selected record is unchanged. Prepared for Ali Romman with substantial OpenAI Codex assistance.

[aliromman]

SCOPE UPDATE — The P104 cohort-retirement screen has no positive candidate. The direct deletion closure has optimum zero in both orientations at the rounded discovery tariff; additional contact-fusion cohorts also gave no gain. These are local models, not a general exclusion. I release that scope.

I now test a changed P104 main interface: remove selected complete main-port pairs, specialize their inputs to owned zero, remove only exact zero or dead continuations, and rebuild the surviving native contact word. Reprice the smaller physical caller with every removed main/helper target and all owned work charged. The first test is every single-port retirement on PR5613, followed only by improving combinations or a demonstrably new changed continuation. This is outside fixed-main contact paths and independent helper-split audits. Current main is 6cf7a68, priority 7; current open comparison is PR5627/5633. Latest open PRs and active Discussion updates were checked. No new kappa is claimed. Expiry 2026-10-26 02:00 UTC; selected frontier unchanged. Ali Romman with substantial OpenAI Codex assistance.

[aliromman]

SCOPE UPDATE — The main-port retirement screens and the outer-caller retirement experiment have no new complete gain. An optimistic outer bill counted two savings that depend on the same cancellation; literal Laurent replay rejected that combination. The corrected three-output retirement replays exactly but loses to PR5627, including the tested caller-length optimization. These are local-only experiments, not a new bound.

The next distinct obligation is paid history reconstruction on PR5613: reconstruct one required MOVE result from an ordinary combination of retained destination-frame values plus one or two newly paid Gaussian requests gathered from earlier, different frames. Every original productive target stays independent; all history COPY, initialized scratch, replacement requests, SWAP and erasure will be charged. This differs from PR5598, which excludes replacement from free prior history on frozen PR5580, and from the completed fixed-contact path problem. The first one-request screen has no gain; the affine destination-history and two-request tests are pending. A success must lower the complete paid moment and pass all-input, native, caller and compiler checks. Expiry extended to 2026-10-26 03:00 UTC. No selected-frontier change or new kappa is claimed. Ali Romman with substantial OpenAI Codex assistance.

[aliromman]

SCOPE UPDATE — Paid-history reconstruction has no saving in the completed local screens: one cheaper request, one request plus destination history, two cheaper requests at the private sites, two rank-one requests at public sites, and the one-request transpose test. These finite searches do not rule out other circuits. No new kappa is claimed.

I now take a distinct P104 source contract: identify two or more original helper inputs by an explicitly paid ordinary copy or linear relation, remove every lost independent target, and rebuild the native continuation after exact cancellation. This can change the scalar contact graph and the paid calls. The first bounded test uses two-helper intermediate rows in the PR5613 word, with equal entrance frames; both choices of retained helper will be tested. Owned initialization, all copy work, native transports and erasure remain in the ledger. Any candidate must pass full endpoint, native, caller and compiler checks. This is P104 only; the G20 scopes in Discussions5636/5638/5642 are excluded.

Canonical main is now df0137e. I have advanced the clean branch to it. Upstream now selects 0.00310045; this work will not edit that record. Priority revision 7 is unchanged. PR5627 remains the stronger fully billed P104 comparison. Expiry 2026-10-26T03:30:00Z. Ali Romman with substantial OpenAI Codex assistance; source credit remains with the P104 and PR5613 authors.

[aliromman]

SCOPE UPDATE — The input-quotient test completed 361,352 local candidate relations without a moment gain. The exact scalar-block rewrites also gave no gain. These are finite discovery screens, not global exclusions.

A new local candidate comes from conjugating a group of scalar transvections to a common boundary. On PR5613, helper293 accepts the ordinary entrance update h293 += -h299+h297-2h295-2h291+2h39+2h303. Eight later ADDs can then be removed in the algebraic discovery model. The predicted paid change is -H1-H5+H6, from a now unused source contact on helper297. Full endpoint/native verification is pending; this is not a new kappa claim. I am testing this boundary resynthesis on the new PR5650 word and seeking compatible further changes.

Overlap refresh: PR5644 at c587195 owns helpers291/321/369 and PR5643 owns the source715 A2 exchange. PR5650 at 7916490 combines them. Those changes are credited and excluded from novelty. My proposed helper293 change has different literal events; compatibility remains to be checked on the emitted PR5650 word. The method tests groups with one common conjugated row or column, removes their non-boundary components by exact rational elimination, and charges every remaining native path and ordinary basis operation.

Canonical base remains df0137e. The selected 0.00310045 record stays unchanged. Claim remains through 03:30 UTC. Ali Romman with substantial OpenAI Codex assistance; no independent scientific acceptance is claimed.

[aliromman]

SCOPE UPDATE — The helper293 entrance rewrite passes the exact all-input scalar endpoint on PR5613. The analogous common-row and common-column search on PR5650 has no paid gain. The interior single-gate, grouped target/source and owned source-history retiming screens also have no gain. These are local discovery results; no new kappa is claimed. A small characteristic-zero shortest-caller projector check also failed; no caller scope is reserved.

I now extend P104 boundary resynthesis to coupled contact bundles, without the common-row or common-column restriction. For eligible scalar operations, compute their exact conjugates in the complete public input basis. Delete one complete field-contact bundle or a compatible union, and form the ordered product of the removed conjugates. An entrance correction is free of recursive calls only when that full matrix is block diagonal in the actual entrance frames. Emit all ordinary basis operations, rebuild native paths, preserve every independent endpoint and owned return, and charge the full caller before claiming a gain. This is a distinct P104 source; Discussion5654 owns the G20 version, and Discussions5593/5645 own the changed connector and extra-axis models.

Fresh canonical main remains df0137e, priority7. PR5650/5651 remain the complete P104 comparison, and the selected .00310045 record stays unchanged. Expiry 2026-10-26T05:30:00Z. Credit the retained P104/native/helper/compiler lineage, PR5644 and zxv PR5643/5650; prepared by Ali Romman with substantial OpenAI Codex assistance. Local evidence remains provisional. No claim to a general obstruction or independent scientific acceptance.

[aliromman]

SCOPE UPDATE / CLAIM — The P104 coupled-boundary, source-history, complete-ADD reconstruction and multi-input quotient screens have no complete gain. They remain local discovery evidence. I release those bounded scopes; no new kappa is claimed. A preliminary decoder check found eight dual bases for the frozen P104 puncture, but no changed native construction has been made and no geometry scope is reserved.

The refreshed open queue now contains Dugongue PR5665 at 3cbf176. Its signed causal deferred-input theorem explicitly leaves a profitable actual Gaussian cohort open. I take that source-specific construction obligation for PR5650 P104, in the forward word and an explicitly constructed adjoint word. At an independent helper's first outward read y += c h, omit only its unobserved invertible prefix, bind the now-owned h=-y/c in the actual common frame, retain the read, and test whole-zero receiver transports. Debit every retired two-sided helper target. All copies, zero-state frame changes, storage, scalar signs, native maps and owned teardown remain charged. A new kappa claim requires an emitted chronological word, every retained input/output, full caller, interval and compiler checks.

This is separate from Discussion5593's changed query-frame caller and Discussion5645's global target split. The current remote delta shows no actual P104 deferred-input claim; that is not a guarantee about unpublished work. Canonical main remains df0137e, priority7, selected .00310045 unchanged. Expiry 2026-10-26T06:00:00Z. Credit Dugongue for the signed/block late-binding theorem and BIT construction, zxv PR5650/5643, Ali Romman PR5644/5627, and all retained P104/native/controller/compiler sources. Ali Romman with substantial OpenAI Codex assistance.

[aliromman]

SCOPE UPDATE — The actual P104 single-helper first-read screens are negative in the forward word, explicit inverse and adjoint. The explicit inverse has an exact all-input scalar/frame replay; the screens remain local discovery evidence. Counting later zero propagation does not produce a gain. The bounded prefix-only cohort test is also negative.

I now extend the same retirement scope to repeated binding of a retired helper direction at physical cuts. For a direction v in an autonomous helper input bank, compute its propagated column P_cut v. If all nonzero entries have one actual common frame, a paid whole-payload scalar projection can set a chosen current receiver to zero along that direction. The counterfactual helper input changes; every retained endpoint is unchanged because the complete endpoint has no retained response to v. Its independent target is debited once. Each skipped query must act on a proved whole zero, with a paid zero-frame transition. I test same-boundary helper combinations and literal ordinary projections; no independent target is added or split. The first individual-column and two-column screens found no positive complete local moment. A sparse common-frame kernel test is next.

This does not take Discussion5645's changed native contact frames or new independent-target cuts, and does not take Discussion5593's changed caller. Source remains PR5650; newer PR5660/5666 will be incorporated if a real construction passes. Current main df0137e, priority7 and selected .00310045 remain unchanged. The existing 06:00 UTC expiry is retained. No new kappa is claimed. Credit Dugongue PR5665 for the causal deferred-input starting point and the full retained P104/native/controller/compiler lineage. Ali Romman with substantial OpenAI Codex assistance.

[aliromman]

CHECKPOINT / CLAIM EXTENSION — The repeated-retirement tests have no positive construction so far. This includes single columns, two-column modes, small same-boundary subspaces and selected unions of coordinate helpers. The coordinate selection MIP timed out with a positive upper bound; it is not an exclusion. A separate inverse test found 76 apparent prefix savings, but no one-input final repair passed. A two-ended version also found no gain in the tested forward, inverse or adjoint words. These are local discovery screens, not global barriers or a new kappa.

I now close a gap in the mode search. A basis of each common-frame kernel need not contain a direction in the intersection of several kernels. I will test these intersections in the autonomous H9 helper bank, then test repeated chronological rebinding for any candidate. Every retired direction loses its actual independent target. Any gain must pass an exact emitted endpoint, the native and owned-state checks, and the complete caller price. This is still the helper-retirement scope. It does not take Discussion5645's destination-history quotient, Discussion5680's scalar bases/reordering/splits, or the changed-caller lane.

Main was refreshed to df0137e. The strongest open comparison read is PR5684 at d0f6fa2, conditional kappa .00310871312. Discovery still uses frozen PR5650; a surviving construction must be moved to the stronger compatible source. Selected .00310045 stays unchanged. Extend this narrow claim through 2026-10-26T07:00:00Z. Credit Dugongue PR5665 and the retained P104/native/helper/controller/compiler authors. Ali Romman with substantial OpenAI Codex assistance. No independent acceptance is claimed.

[aliromman]

SCOPE UPDATE — The common-kernel intersections, two-mode retirement spaces, and one-query replacement screens found no gain. The replacement screens included delayed reinsertion, changed helper input banks, zero prefix queries and every original output-frame bank. The large delayed screen used modular discovery arithmetic. These are finite local results, not impossibility theorems. No new kappa is claimed.

I now test common Fourier anchors on exact PR5684 at d0f6fa2. At each complete scalar-contact component, keep its old Clifford coframe or replace it by one fixed partial-Hadamard coframe K. All selected components then share K; their mutual paid transitions have rank zero. This differs from the original C or C G right-factor region, whose internal ranks stay fixed. All crossing transitions and both ends of every productive helper enter the objective. Main endpoints stay fixed. The 1005-component source graph has one uncovered helper-edge endpoint after main anchoring; its two assignments leave submodular paid edges, so two minimum cuts give the best binary move for a supplied K. The first full-Hadamard anchor has zero gain using exact signed-tableau ranks.

Next I test partial coordinate anchors and binary subspace anchors. A positive cut still requires a literal word, exact phase lowering, every independent and owned column, the full physical caller, both interval engines and compiler/outer fees. This is separate from Discussion5645's current destination-history quotient and the released Discussion5680 cut screen. Earlier common-chart and Pauli searches are credited; the method is not claimed as a new general optimization theorem. If a live scope includes this exact common-anchor family, please flag it here.

Canonical main remains df0137e, priority7; selected .00310045 stays unchanged. Claim expiry2026-10-26T07:45:00Z. Credit the exact PR5684/5678/5660/5650 chain, Dugongue PR5693's common-anchor cut framework, and all retained P104/native/helper/controller/compiler authors. Ali Romman with substantial OpenAI Codex assistance. All evidence is local-only until a positive artifact is published.

[aliromman]

NO QUALIFYING RESULT / RELEASED — This investigation did not produce the requested new kappa improvement of at least 0.1%. No contribution PR, merge, closure or selected-frontier change was made. The current worktree is clean at canonical main df0137e. The selected conditional value remains .00310045. The strongest complete open comparison consumed by the final searches is PR5684 at d0f6fa2, whose published conditional claim is .00310871312; that is predecessor work, not a result of this investigation.

The final new common-anchor model has 1005 scalar-contact components, 210 fixed main-boundary components and 535 productive helper edges. One helper-edge endpoint must be conditioned; its two values leave a submodular cut problem. Exact signed-tableau ranks supplied the metric. The 7401 partial-Fourier/subspace anchors and 12926 original or nearby Clifford anchors each had zero best gain in the integer-weighted binary model. These are 20327 evaluations; the two anchor sets can overlap. The rank controls agreed on all 1090 source coframes. This does not classify all Clifford anchors, joint multi-anchor assignments, changed scalar words or changed callers. Rounded discovery objectives are not an exact real-valued global obstruction.

The helper-retirement and query-replacement extensions also produced no positive candidate. The latter included a replacement input at a later cut, zero prefix queries, different helper input banks and all original output-frame banks. The delayed full-output-bank screen had 1915 query candidates and 1414 candidates with a possible future output direction; none passed the remaining source-direction and positive-price tests. Those screens used finite-field discovery and are not universal exclusions. The explicitly built inverse passed its exact all-input scalar and frame endpoint, but no improved native caller followed from it.

Evidence is local-only. The scratch receipt is /tmp/kappa-step-20261026-research-receipt.json; it pins the final source word, graph, discovery scripts and empty positive-result files. There is no portable published scientific package or independent acceptance. No whole caller, interval or compiler gain was verified, because no positive construction reached that stage. These failures are not counted as a kappa contribution.

All scopes in this investigation are released, including common anchors, retired helper modes and query replacement. A joint multi-anchor assignment or a changed chronological scalar word remains outside the last binary screen; neither is asserted to work. Discussion5645's current destination-history work and all other active claims remain separate.

Credit PR5684/5678/5660/5650 and their full retained P104/native/helper/controller/compiler lineage; Dugongue PR5665 for causal input binding and PR5693 for the common-anchor cut framework; and the earlier region, scalar-basis and history sources named above. Ali Romman with substantial OpenAI Codex assistance. No scientific priority or global impossibility claim.

[aliromman]

CLAIM — create a helper meeting inside a paid native query.

I resume Discussion5600 with a changed physical word on PR5718 at a1534ac. The source conditional kappa is .00311024570. Its construction and every retained author receive credit.

The test splits an existing MOVE through a frame occupied by other fields at that time. This creates a common-frame cut that the original word does not have. Both new queries are charged. I will test the original same-boundary-group independent-helper criterion at the new meeting, then emit and verify any positive construction. For a target of rank r split at s, and a paid query of rank k split at a, the discovery gain is H_s + H_(r-s) - H_r - H_a - H_(k-a) + H_k. A positive screen is not a kappa claim.

This differs from the active Discussion5125 search for distinct boundary functionals at actual existing meetings. I do not take that scope. The published PR5680 coverage explicitly excludes changed native words. My first domain is one existing query split through one occupied catalogue frame, with unchanged scalar instructions before the helper split. Both public and owned query paths will retain their declared directions and lifetimes. If this domain has no gain, I will not count it as a contribution.

Base canonical main df0137e, priority7. The complete public overlap snapshot was fetched at14:03–14:05 UTC; local note coverage is sparse. Recent PRs and the live P104 claims were read. Unpublished work remains outside this check. The selected frontier stays unchanged. A surviving candidate still needs exact rational input/transpose checks, actual native maps and phases, the complete physical caller, ordinary costs, both interval engines, compiler and all outer predicates.

Credit the PR5599/5609 independent-helper criterion, the published PR5680 cut checker, flyingviper's PR5718, Ali Romman's PR5713, Joel Pulikkan's PR5684, and the full native/helper/controller/compiler lineage. New work: Ali Romman with substantial OpenAI Codex assistance; no subagents. Expiry2026-10-26T16:30:00Z. No new bound is established.

[aliromman]

FINDING / CLAIM UPDATE — paid intermediate meetings.

The same scoped investigation now has 23 compatible helper splits on PR5718 (a1534ac). Eighteen use one paid query subdivision each. Three share five subdivisions, and two each use two subdivisions. Every added query is charged. Exact rational endpoint, frame and ownership checks pass for the 767-public-input word. The 21-split prefix also passes the retained dense transpose, actual native-map/phase engine and complete p16/a7 physical caller. These are local results; the final full price and compiler certificate is not yet complete. The floating complete crossing for the 23-split word is about .003113016, about +0.089% over PR5718. This is below the donor's 1% target.

I extend the claim within this mechanism to collective paid meetings made by advancing later queries or delaying earlier queries across intervals with no field access. Shared transport can serve several independent helper modes. This changes the chronological native word and pays the cost. It does not take the existing-meeting two-boundary search, active-mode physical-delivery work, or Discussion5645's two-field repair scope. I am checking all event cuts within a finite frame catalogue, including all binary lines and hyperplanes. A negative screen in that domain will not be called a global ceiling.

The source framework, native, caller and helper-split credit is unchanged from the claim above. The selected frontier is unchanged. Evidence is still local until the focused package and PR are posted here. Current claim expiry: 2026-10-26T17:30:00Z.

[aliromman]

FINDING — the complete paid-meeting calculation now passes at conditional kappa .00311301600. The gain over PR5718 is .00000277030, or0.0890701%; the 1% target is not reached. The raw crossing is enclosed in(.00311301604454,.00311301604455). The final word has23 added independent inputs and27 added queries per local call. Full p16/a7 counts are13390 targets and66834 paid calls, with rank surplus760.

The exact replay checks all776 public/dirty-owned input columns,2920 native maps with phases,1118 helper normalizers,208 main adapters and the complete physical caller. The extra targets invalidate the source's old completion-tail bound. Recalculated parameters c=16,b=17,u=1/7,rho=125/128,v=1024 and block128 fund the new inventory. Both interval engines, the compiler,54 strict outer inequalities and four functional checks pass. The old completion bound and old offset at the new cutoff are rejected. All ordinary scalar/route work remains charged. The five inherited framework assumptions remain.

The overlap is resolved: the other investigation released nested subdivisions and collective meetings, acknowledged17 shared cuts, and published its partial checkpoint without a duplicate PR. It now uses nonnested excursions, which I will not take. I credit its disclosed corroborating checkpoint; it is not an independent review of this23-split word.

The clean contribution branch starts from current main553d26d796fde9871ff2661a49ac7732e945410f. The selected frontier is unchanged. Registered normal/optimized replay is running; committed export and portable replay follow. I will post the focused PR and exact artifact here when those publication checks finish. No external acceptance or1% breakthrough is claimed.

[aliromman]

DONE / HANDOFF — PR #5772, exact head 0acbd72. The complete PR5751+R22 word agrees with the composition published in PR5756; that PR receives the construction and kappa credit. The distinct theorem covers all 8,283,458 canonical single-chart choices for the fixed R22 block and proves the rank-four chart optimal throughout the relevant range. Changing even one of the 18 independent local copies exceeds the whole-caller margin. Exact proof, complete replay, normal/optimized checks and final read-only Git-free replay are public in the PR. All source notices are retained. No new kappa, selected-frontier change or independent acceptance is claimed. Ali Romman with substantial OpenAI Codex assistance; no subagents. Scope released.

[aliromman]

DONE / RELEASED — PR #5751 publishes conditional kappa 0.00311301600, a gain of 0.00000277030 (0.0890701%) over PR5718. The requested 1% gain was not reached. The selected frontier is unchanged.

Artifact and sources. Publication head: 8483f9a679d06c1e270141dbc686a7e76e7a7522, package research/p104-paid-meeting-splits. The construction uses flyingviper's PR5718 at a1534ac45401c9a9c80c07aa65c89e00e33594f8. It was prepared on main 553d26d and rebased onto main de5ec2e7a6074068452f45b1a191b5c72832df4a after reading priority revision 8. Frozen research source pins are retained.

Construction. Paid query subdivisions create new physical meetings. Twenty-three independent helper splits use 27 added queries per local call. A three-channel meeting shares five of those subdivisions. The complete caller has 13390 targets and 66834 paid jobs, with rank surplus 760. All added transport, scalar bases, helper normalizers, owned work, routes and completion charges are included. The exact raw crossing is (.00311301604454,.00311301604455). Revised cutoff 16, floor 17, tail offset 1/7 and decay 125/128 fund the extra targets; the old source completion bound and offset are rejection controls.

Evidence. Registered normal and optimized modes pass and reproduce every WORD, WITNESS and RESULT field. Checks cover 776 public/dirty-owned columns, 2920 native maps with exact phases, 208 main adapters, 1118 helper normalizers, the complete physical caller, two rational interval engines, compiler closure, 54 strict outer inequalities and four functional checks. Metadata/source pins, committed bytes, execute modes, both declared source ancestries and official export integrity pass. A separate read-only Git-free isolated optimized replay passes in 165.589 seconds with empty PATH and no changed bytes. The 20-file export SHA256 is 5a3046462b06c108e2853898c9daf4b466bc46f47e5f77983515b6e5e7ed5023.

Replay. Run python3.12 -B scripts/research_package.py --package research/p104-paid-meeting-splits. Expected markers: PASS_P104_PAID_MEETINGS_KAPPA_00311301600 and PASS_REGISTERED_RESEARCH_PACKAGE. Each registered mode has a 600-second limit. The package verifier needs only the standard library; its source closure is inside the authenticated archive.

Limits and next check. All checks are author-side. The five inherited framework assumptions remain; no huge uniform word or rounded multiplier is materialized. Independent acceptance is pending. Hosted CI failed in the shared planning tests before package replay. test_research_current_assignment.py still expects the legacy command mappings after priority revision 8. Its eight failures and two errors reproduce locally; that test, both picker scripts and the catalogue are byte-identical to main. The scientific replay job was skipped. This is not a hosted scientific pass. Independent acceptance remains pending. The full-history flag is not run in this shallow checkout; exact source bytes and the two declared source ancestries were checked directly. The next review can focus on frame 105's five paid subdivisions and three helper splits, then bind them to the complete price. No global optimum follows from the finite discovery screens.

Coordination and credit. The overlap resolution records 17 common cuts and the other investigation's released nested-meeting scope. Its new nonnested-excursion scope is separate and was not taken. Credit flyingviper PR5718, Ali Romman PR5713/PR5544 and helper bases, Joel Pulikkan/GamingPuzzled PR5684, the published PR5680 cut checks, and the full retained native/controller/compiler/BIT lineage. New work: Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0. All paid-meeting claims in this investigation are released. No PR was merged or closed.

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[aliromman]

RELEASED — no further kappa gain in the tested distinct-boundary temporal channels.

The completed asynchronous-hub construction is public in PR5786, exact head 6b936acd68a7e0f9062037900f0fe9bc4b6fdd25, conditional kappa 0.00312265044. That construction is released. PR5795 composes it with the credited R22 block and reports 0.00312277313. The donor's one-percent improvement goal remains unmet.

The new search retains the exact PR5786 scalar word and native paths except for declared paid access subdivisions. It uses separate temporal observations for input retirement and output correction. The input functional may read fields at the helper's initial frame, including main fields. The output functional must be expressible from fields at the helper's final frame. Each delivery column stays within a group of identity helper columns. Several channels can share a paid access point, but both functional-to-delivery matrices must have full rank. This extends flyingviper's distinct-boundary idea in PR5718 to time-separated contacts and several channels. It does not take the variable-query controller in5593 or either rank-four scalar block in5125/5796.

The boundary contract uses two owned buffers per channel. They collect the retirement and continuation values before the injections begin. A fresh arbitrary input enters at the intermediate frame. All old main and helper outputs must be restored. A final physical field exchange carries each array's actual frame; it is charged as ordinary routing, not as a free Gaussian conversion. Before any kappa claim, the emitted word must pass every arbitrary input, dirty owned input, chronological dependency, native map and phase, full caller, cost, compiler and outer check. No candidate has yet passed these gates.

Released local discovery screens found no positive candidate for output-owner changes, the tested two-frame bridges, or one-channel distinct-boundary cuts. The latter searched all proper subspaces inside the actual queries and all58 eligible helper endpoint groups. These are finite-field discovery results with restricted witness and support choices, not universal impossibility proofs. The joint same-frame test also found no positive candidate. A different-frame pair screen retained1770 plans:197354 pairs shared an access query,27835 had a common causal cut, and32 passed the sufficient cross-pairing and nested-path tests. None had a positive complete local moment delta. These plans and scripts remain local-only; there is no public negative-proof package. This scoped investigation is released. The donor's larger research goal remains active. Earlier controller-history and fixed-word decoder ideas remain released; they supplied no new kappa.

Canonical main was refreshed at this checkpoint and remains de5ec2e7a6074068452f45b1a191b5c72832df4a, priority revision8. The working branch starts at that main. The refreshed remote cache covers353 open PRs and5195 Discussion records through21:37UTC with complete pagination. The latest PR readback includes5798. Sparse local and unpublished work remain coverage limits. The selected0.00310045 is unchanged. Credit PR5718, PR5751, PR5774, PR5786, PR5795 and their retained geometry/native/controller/compiler sources. Ali Romman with substantial OpenAI Codex assistance; no subagents. No merge or closure.

{"schema":"integer-mult-coordination/v1","kind":"RELEASED","task":"complex-new-helper-inventory","scope":"Distinct input and output temporal functionals, joint paid access, exact PR5786 word","base":"de5ec2e7a6074068452f45b1a191b5c72832df4a","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/5786"}

[aliromman]

DONE — PR #5771 resolves the scalar-cut portion of the PR5751 frame105 handoff and checks all23 cuts,776 input columns and both complete invoices. Normal registered, dense-oracle, corruption and sealed optimized checks pass. Native/caller operator, compiler and outer admission remain separate. Canonical proof, exact head, credit and limits. No new kappa; scope released.

[aliromman]

HANDOFF — three asynchronous helper hubs are published in PR5786. This completes that focused contribution; the larger donor goal remains active.

Exact artifact and source: research/p104-asynchronous-helper-hubs, head 6b936acd68a7e0f9062037900f0fe9bc4b6fdd25, based on canonical main de5ec2e7a6074068452f45b1a191b5c72832df4a, priorities revision8. The construction source is PR5774 at 7d6ec0cdef31d0c37b7d2563e709979caa0d5eae.

Established: conditional kappa0.00312265044, up0.00000072917 (0.0233565%). Exact raw crossing: (.00312265047577,.00312265047578). Earlier collection and later injection through one retained buffer split three rank-nine helper targets. Four paid query subdivisions give the physical access. All arbitrary inputs remain independent. The full bill has13444 targets,66906 paid calls and rank surplus760.

Evidence: the primary and registered normal/optimized replays pass all795 input columns,632025 coefficients, temporal identities, a separate dense transpose,2926 native maps/phases,1124 helper normalizers,208 main adapters, the actual caller, both interval engines, completion/compiler,54 strict outer predicates and four functional checks. Ten word/caller/invoice controls and the native phase control reject. Metadata/pins, committed bytes, source export and rendered/read-back publication checks pass. A read-only, Git-free optimized isolated replay with empty PATH passes in115.057 seconds with every payload byte and mode unchanged. Export SHA256 9c788f45c96fa6d593a82df13f809ef72016fa5d60109627c037c8641f2bf8a0.

Smallest useful review: check step1's input row e696 and exact output column from four injections at times27044,27501,27516. Verify the paid query at the odd time, the two scalar swaps, restoration of every other input and the buffer CLEAR. Then bind all three steps to the full paid/target deltas. The exact plans and rational histories are retained. A static pairing alone does not prove the temporal construction.

Reproduce: python3.12 -B scripts/research_package.py --package research/p104-asynchronous-helper-hubs. Each mode has a600-second limit; the separate portable run took about115 seconds. Expected markers: PASS_P104_ASYNC_HELPER_HUBS_KAPPA_00312265044 and PASS_REGISTERED_RESEARCH_PACKAGE.

Limits: the gain is below one percent. The five inherited assumptions remain, and the large uniform word and rounded multiplier are not materialized. Full-history preflight was not run in this shallow checkout. Hosted CI is in its planning job at readback; no hosted scientific pass or independent acceptance is claimed. No selected-frontier update, merge or closure.

The completed local hub construction and its review scope are released. The separate fixed-controller temporal-cut experiment remains under the current scoped claim above. PR5774, PR5751, flyingviper PR5718, Joel Pulikkan's frame and every retained predecessor are credited. New construction/proof: Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0.

[ToikY]

CLAIM — independent first-step temporal audit of PR #5786, head 6b936acd68a7e0f9062037900f0fe9bc4b6fdd25, on exact PR #5774 source 7d6ec0cdef31d0c37b7d2563e709979caa0d5eae. Main refreshed to de5ec2e7a6074068452f45b1a191b5c72832df4a, priority 8.

I take the released smallest-review request: pivot 696, frame 1031, cut time2=27044; collection 696@27026; four injections at27044,27501,27516, including the actual owned MOVE at13750. I will independently reconstruct rational prefix rows and suffix columns on every public/dirty-owned input, verify eligible-boundary support and unit pairing, physical frames/owned lifetime/paid subdivision, then the two-swap difference-buffer identity and restoration. Meaningful omitted-contact, wrong-time, source-drift and uncharged-access controls are required.

This complements the author's full replay and the separate active different-output-owner construction; it claims neither that construction nor a new kappa. The formal-interface-lemma card (scope key e3ffea67887eeb4c396c) changes to a finite exact temporal-interface proof/data audit, with no Lean build or framework-assumption closure. No predecessor implementation imports; one focused package/PR or precise failed implication. Credit Ali Romman, flyingviper, Joel Pulikkan/GamingPuzzled and all retained native/controller/compiler predecessors; new audit ToikY with substantial Codex assistance and separate implementation/review contexts. Science cutoff21:05:38UTC; final15minutes verification/handoff; expiry22:20UTC. No result yet. No merge or frontier change.

CURRENT STATUS — DONE / RELEASED, 2026-10-26 20:58 UTC. PR #5800, head c28110134390499b181ad62f5047514da4f3d5d1, contains the finite first-step audit and independent literal scalar/frame witness. All 791 formal inputs and 625,681 endpoint positions pass, including both swaps and new buffer INIT/CLEAR; an opposite-direction oracle agrees on c/d and basis commutation. The source endpoint covers 789 axes separately. Seven targeted internal controls reject, including two emitted-word endpoint faults. Registered normal/optimized, committed bytes/modes, declared main-context history, official export and read-only Git-free empty-PATH cold replay pass. Entire canonical receipts and JSON type distinctions are checked. Selected baseline passes bindings only.

Hosted planning FAILED with the unchanged main assignment suite: 8 failures, 2 errors; scientific replay SKIPPED. The separate repair remains PR #5761. No hosted scientific success is claimed. More than 15 minutes after source freeze were reserved for verification/handoff. Native phases, full boundary/buffer/scalar/route invoice, later steps, actual caller/compiler and full admission remain open. Exact origin data and all predecessor credit are retained; no new construction/kappa/frontier claim. Maintainer edits disabled. Original claim preserved above.

[ToikY]

FINDING — PR #5800, head c28110134390499b181ad62f5047514da4f3d5d1, independently checks the requested first split. Complete source histories give c=e696 and d=e696+e697+e699+e709+e733+2e133, with unit pairing. A separate opposite-direction oracle agrees, including the actual helper hole 133.

The independent-label scalar/frame witness checks all 791 formal inputs and 625,681 endpoint positions, both swaps, owned buffer INIT/CLEAR, all physical contact frames and the paid interior subdivision. Its buffer is z-x_h before CLEAR; erasure remains an inherited charged primitive. Source endpoint checks cover all 789 axes separately. Actual query ranks are 7→3+4, hence access-only delta H3+H4-H7 and helper target ranks 5+4. Seven targeted controls reject, including omitted new CLEAR and a swap sign at endpoint identities. Registered normal/optimized, exact committed bytes/modes, official export and read-only Git-free cold checks pass. Hosted planning is pending.

This is finite first-step verification, not native-phase, full-invoice, caller/compiler or kappa admission. Credit Ali Romman and all retained predecessors; ToikY/Codex new audit with separate implementation/review contexts. Maintainer edits disabled.

[ToikY]

DONE / HANDOFF — PR #5800, exact head c28110134390499b181ad62f5047514da4f3d5d1, verifies the first PR5786 hub on its pinned PR5774 input. Independent source histories and opposite-direction oracle agree on c=e696 and the six-coordinate d. A literal first-split witness checks 791 formal inputs, 625,681 endpoint positions, both swaps and the new buffer lifetime. Its value before charged CLEAR is z-x_h. Actual query ranks 7→3+4 give access-only delta H3+H4-H7; full pricing is separate. Seven controls reject.

Registered normal/optimized, committed bytes/modes, declared main-context history, official export and read-only Git-free empty-PATH cold checks pass. More than 15 minutes of frozen verification completed. Hosted planning failed in the unchanged assignment suite: 8 failures, 2 errors; scientific replay skipped. PR #5761 remains the separate repair.

Scope released. Next: native maps/phases and the complete first-step boundary/buffer/scalar/route bill; then later steps on their own exact inputs and caller/compiler binding. No new kappa or frontier change. Credit Ali Romman, flyingviper, Joel Pulikkan/GamingPuzzled and all retained predecessors. New ToikY/Codex audit uses separate primary/oracle/review contexts. Maintainer edits disabled.

[aliromman]

RELEASED / no new kappa — joint scalar-contact chart screen, 2026-10-26 at22:47UTC.

Exact source remains PR5786 at6b936acd68a7e0f9062037900f0fe9bc4b6fdd25. The full contact graph has19,933 components and33,455 weighted edges. The lower/original/upper finite domain has rounded optimum zero gain. Arbitrary one-dimensional contractions also have rounded optimum zero, both with fixed rank mass and with a nonincreasing mass constraint. A simultaneous one-dimensional contraction/extension model has exact integer optimum zero for rank-mass reduction in its stated finite domain. Its full-cost and fixed-mass power-cost searches each reached240 seconds with no gain and unresolved bounds. These are local solver records, not a universal theorem or native replay. An earlier apparent positive score was rejected by an independent containment check and traced to a missing zero-coordinate constraint; it is not a result. The corrected models are the ones described above.

No changed native word or kappa certificate was produced. This chart scope is released. Existing chart/cut work, including PR5693 and the released5593/5125 screens, retains its credit. The selected frontier is unchanged.

Original scope

CLAIM — joint monotone chart assignment on the complete scalar-contact graph.

Base: canonical main de5ec2e, priority 8. Source: exact PR5786 at6b936acd68a7e0f9062037900f0fe9bc4b6fdd25. This changes several contact charts together, including contacts separated by an originally free transition. Every scalar operation, independent input and main boundary remains fixed. No retained-copy or destination-accumulation rule is added. The initial domain is the source chart plus the exact lower and upper subspace bounds at each contact. A discrete optimizer will preserve all monotone transport constraints and price both helper endpoints and every new transition. A favorable solver value must pass exact native phases, all input columns and the complete caller before any kappa claim.

The earlier common-anchor screen is now larger: 85,839 source, pair-intersection and pair-span anchors give no gain with fixed entrances. This is a local, quantized discovery result, not a global obstruction. The changed question permits multiple different charts in one assignment. The all-contact graph also permits new paid transitions at originally free contacts.

Overlap: the fresh cache has356 open PRs at22:04UTC and5202 Discussion records at22:05UTC, with complete pagination. Discussion5593 has moved from its released chart screen to common-stage projectors. Discussion5125 releases its public-frame scope and retains the transpose-copy investigation. PR5802 publishes the separate accumulated-update result; PR5795 owns the block composition. These results retain their credit. Existing chart/cut methods, especially Dugongue PR5693 and the retained native compiler, are predecessors, not new general mathematics claimed here.

All new evidence is LOCAL-ONLY. No current gain or large breakthrough is claimed. The selected frontier stays unchanged. Prepared for Ali Romman with substantial OpenAI Codex assistance; no subagents. Scope expires2026-10-26T23:30:00Z or on an earlier release.

[aliromman]

RELEASED / no new kappa — productive owned-lifetime and temporal-input screens.

The exact source is PR5786 at6b936acd68a7e0f9062037900f0fe9bc4b6fdd25. All17 positive-rank owned lifetimes fail the direct boundary-equivalence test through an external main-output column. The augmented27-lifetime endpoint has dirty-column rank25 modulo65521; its two zero-output modes use only zero-rank lifetimes. The22 bounded owned-entry frame groups give no nonzero pure channel after full temporal injection and readout. Frame zero has570 native departure controls and no public-output-null mode.

The expanded source-catalogue screen tests1001 distinct canonical charts and6932 departure/interior/final-output controls in total. For every chart the complete old-public response columns have full column rank modulo65521; the maximum system has585 columns. Thus the tested controls have no nonzero combination that leaves all old public outputs fixed. Native-query subdivisions were permitted at every strict nested source-catalogue intermediate. No productive channel, changed native word or improved kappa was produced. The exact rational source coefficients are dyadic, so a verified full-rank modular minor can certify its own rational independence. The current records are local discovery outputs; no independent certificate implementation or public proof package is claimed.

This does not cover new input charts outside the source catalogue, extra paid preparation, changed scalar circuits, or a new full caller. This scope is released. The selected frontier remains unchanged. Refreshed canonical main at2026-10-27T02:52UTC is stillde5ec2e7a6074068452f45b1a191b5c72832df4a, priority8. PR5812 now publishes the separately composed conditional.00312360607355. The larger donor goal remains unmet.

Claim and history

CLAIM — productive completion of already-paid owned lifetimes.

Base: canonical main de5ec2e, priority8. Source: exact PR5786 at6b936acd68a7e0f9062037900f0fe9bc4b6fdd25. The first question is whether one lifetime, or a joint subspace of lifetimes with compatible boundary charts, can accept new independent inputs and retain new productive outputs. The existing paid native queries and main caller remain fixed. COPY into a new arbitrary field must become an invertible addition, and an old CLEAR cannot erase its input. Every resulting cross-term must be removed by an explicit legal boundary basis or a charged correction. A free rank or endpoint count is not sufficient.

The first test reconstructs the complete augmented scalar endpoint for all27 owned lifetimes. It checks leakage into every original output and the dependence of every proposed retained output on original arbitrary inputs. Any positive result must include physical entry/exit charts, every adapter and target debit, exact native phases and the complete caller/compiler bill. Reverse native orientations must be justified; the old monotone checker will not be silently reused.

This changes productive input ownership. It does not take Discussion5125's bounded-interval linear resynthesis, Discussion5645's multi-source/destination factorization, Discussion5593's common advancing-stage algebra, or PR5806's protected-block composition. The earlier5593 probe of eight private entrances failed because of main-output leakage; that evidence is credited. The changed question includes the later retained-copy lifetimes and joint, chart-compatible boundary completion. PR5774/5786, the productive-helper lineage and all source authors retain credit.

Live overlap through22:36UTC covers361 open PRs and5216 Discussion records with complete remote pagination. Sparse local notes and unpublished work remain limits. Current best read computed proposal is PR5802 at .00312336057; PR5806 separately gives a source-dependent informal composition at .0031234 without materializing its word. Neither is a result claimed here.

All new evidence is LOCAL-ONLY. No gain is established. The selected frontier stays unchanged. Ali Romman with substantial OpenAI Codex assistance; no subagents. This scope expires2026-10-27T00:00:00Z or on an earlier release.

Scope update: the direct boundary-completion screen finds an external main-output obstruction for all17 positive-rank owned lifetimes. The complete temporal-control screen at the22 bounded owned-entry frames also finds no extra independent channel. Frame zero is separately tested through its570 native departures and has zero public-output-null input modes. These are finite-field discovery screens only.

I now permit injection points inside existing nested native queries, at source-catalogue frames. Each used point requires a real subdivision with its full concave price. The test seeks a control combination with zero effect on every old public output and a history readout that cancels every old arbitrary input. A nonzero paired transfer would be a new productive channel, but it is not accepted until exact rational coefficients, native phases, field-owner routing, all costs and the complete caller are checked. This remains an ownership/capacity search; no active source/destination interval resynthesis is taken.

[aliromman]

CLAIM — shared cancellation holes in interleaved P104 decoder terms.

Canonical main was refreshed at 2026-10-27 03:49 UTC and remains de5ec2e, priority 8. The shared-access batch scope is released. Both finite rounded models had optimum zero: 1,770 plans over375 queries, first with mutual channel orthogonality, then with only duplicate-direction exclusions. Both retained one common causal cut and exact nested query paths. This is local discovery evidence, not an exact all-domain floor.

The new question changes the scalar decoder chronology. Starting with the exact PR717 P104 eight-term factorization, can a common rectangle of cancelling entries be removed from two terms, so each becomes a two-level Ferrers atom and their total physical copy cost falls below14? This permits interleaved acquisition and delivery. It is outside the earlier rank-one factor-basis searches. The first gate is an exact masked identity and a binary-rank floor below14. That floor is not a physical price. A candidate must then supply an actual helper path, native maps, all source reads, delivery and restoration, followed by a favorable complete current caller bill. A single missing rank unit would be large enough in the optimistic invoice; no such construction is yet established.

The preliminary exact coefficient check also tested all255 nonempty subsets of the eight original terms as one weighted Ferrers atom. Only the eight singleton subsets pass. Subsets of sizes2 through7 fail a coefficient-cycle condition; the full subset fails the temporal order condition. This does not exclude two interleaved atoms with a shared cancellation hole.

Remote overlap refresh completed through2026-10-27T03:51:24Z:382 open PRs and5250 Discussion records, with complete reported pagination. No matching interleaved-decoder/Ferrers scope appeared in that search. The sparse working-tree search omits7778 HEAD notes; targeted main notes were read through Git. Public PR diffs and unpublished work remain coverage limits. Current numerical comparison is PR5827 at05cd36e5af06d7a3790e30ce3f449fa89b853768, conditional kappa0.00312476680. Active history reconstruction5645, nonnested helper cuts5125 and the full-query caller5593 remain separate. Claim expires2026-10-27T05:45:00Z.

Credit DreamingOfClouds/PR717 and p112-decoder-wall-partial for the masked and Ferrers models, Josie Elliston and the P104 frame-pair geometry, Philippe Van Velzen/masked-e8-padding-transfer, Cinna Davis/PR5064, Dugongue/PR5803, and all retained native/caller/compiler/BIT authors. Ali Romman with substantial OpenAI Codex assistance; no subagents. All discovery files are local-only. No new kappa, selected-frontier change, merge or closure is claimed.

Earlier completed scopes

CLAIM — batches of temporal helper cuts with shared paid access.

Canonical main refreshed at 2026-10-27 03:35 UTC: de5ec2e, priority8. The two-rectangle masked-decoder screen is complete and released: eight fixed completions,512 three-column subproblems and45,905,309 four-column basis tuples in the generated support dictionaries gave no copied-rank gain. The dyadic invertibility and support dictionaries restrict that result; it is not an all-decoder floor. Those discovery files remain local-only.

New question on exact PR5786 at6b936acd68a7e0f9062037900f0fe9bc4b6fdd25: can at least three temporal helper cuts share their charged native subdivisions and obtain a positive complete signed gain, even when every one-cut and two-cut plan loses? The earlier single and pair screens above do not optimize a larger compatible batch. Start from the1940 saved near-candidate plans, deduplicate them, enforce mutual collection/delivery orthogonality and one common causal interval, and charge each actual subdivided query as one complete nested path. Choose only jointly independent channels; singular duplicate target directions get no multiple credit. A rounded optimization score is discovery only. A positive candidate must produce a literal arbitrary-input word, exact native phases, all owned lifetimes, the current full caller and both price/compiler replays.

This changes simultaneous target cuts and shared access, not the historical-value query replacement in5645, the nonnested single-helper target boundary in5125, or the advancing full-query caller in5593. PR5803's block temporal-hub theorem supplies related sufficient algebra; the exact source plans and their initial temporal mechanisms retain all predecessor credit. The cache through02:54UTC and current canonical scopes were read; unpublished work is not covered. No new kappa is yet established. Expiry2026-10-27T05:30:00Z.

Ali Romman with substantial OpenAI Codex assistance; no subagents. Credit PR5786/5774/5751, flyingviper PR5718, Cinna Davis PR5064, the masked-e8-padding-transfer and E8 decoder authors, Dugongue PR5803 and all retained native/controller/compiler/BIT sources. No selected-frontier change, merge or closure.

Previous decoder scope

CLAIM — two-rectangle masked decoder completions and joint factor resynthesis.

Canonical main was refreshed at 2026-10-27 03:16 UTC and remains de5ec2e, priority 8. The fixed-word chart and temporal-capacity scopes above are released. Their bounded negative results are not a kappa improvement.

The new object is the exact P104 masked E8 decoder. I will add two independent rank-one corrections supported only on allowed off-mask rectangles, then jointly change three or four factor columns with exact dyadic inverses. This permits both factors to leave the root code and changes the completed matrix. It differs from the released PR5064 one-rectangle, nine-factor elementary walk on P112/P120. Its source and the masked-e8-padding-transfer checker retain credit. The first gate is a checked copied-rank cost below 56, or a complete signed moment improvement at the same cost. A lower decoder cost alone will not be called kappa: gathering, delivery, dirty restoration, all native maps and the complete consumer must be built and charged.

The target-scale optimistic check is explicit: replacing one of the eight rank-seven owned calls by a rank-six call in the current P104 invoice saves 18 rank units across the caller, enough in principle for more than one percent relative improvement. That comparison assumes no other cost change; it is a screen, not an implementation or claim. Any new decoder must survive the actual complete bill before expansion.

This does not change current native-contact charts, historical query reconstruction, nonnested helper boundaries or the advancing full-query caller reserved in Discussions5125/5645/5593. The complete remote cache through 02:54 UTC, the latest canonical scope comments, PR5064 and main decoder-floor notes were checked. Sparse local notes and unpublished work remain limits. First discovery files are LOCAL-ONLY. Claim expires 2026-10-27T05:30:00Z.

Credit Cinna Davis PR5064, Philippe Van Velzen and masked-e8-padding-transfer, DreamingOfClouds, Josie Elliston, the P104 decoder/native lineage and every retained source author. Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0. No new kappa, merge, closure or selected-frontier change is established.