[Dugongue]

This certifies conditional κ = 605334953/200000000000 = 0.003026674765, exceeding Ali Romman’s PR #5383 value 0.00302666 by 0.000000014765. The complete recursive profile is unchanged. This is a small finite compiler-margin improvement, not a new native mechanism or practical speedup.

Use tested saving 0.003026674766, reserve 10⁻¹², tensor power 1024 and the retained completion parameters. Two rational interval engines certify α < 1 − 10⁻¹² and both charged tails below 0.97. The exact completed bound is 1048576000976562501 / 1048576001073741824 < 1. The old 10⁻⁹ reserve fails at this tested saving; 10⁻¹³ fails the fixed rounding budget. The finite compiler uses gap 1/7,000,000,000,000 and threshold N = 2^409549000000000000; all 54 strict and four functional outer predicates pass. The word is algorithmically specified, not expanded at that enormous threshold.

We reconstructed the eight compatible helper relations while #5383 was being published, then narrowed the contribution to this compiler-margin refinement. Credit #5383 for the public eight-relation mechanism and prior bound; no priority claim is made for that construction. The retained local witness has the same complete 64,148-paid / 10,800-target invoice, debits all 128 lost H9 targets, and preserves the rank surplus 752. It checks all 624 retained backward input columns and all 17 owned entry fields, with eight simultaneous snapshots; forward calls retain their original inputs. Our preparation ordering is priced afresh: scalar allowance 158,776, routes 4,834,000, total raw bound 181,098,496 < 10⁹.

Validation: registered normal and optimized Python 3.12 standard-library replays; exact row reduction and sixteen unrestricted source identities; chronological native frames, ownership, endpoints and phase-receipt inheritance; complete p16 controller/invoice; two interval engines; compiler/outer predicates; wrong-preparation controls for every pivot, other native controls and reserve/outer rejection controls; committed-byte checks, official export integrity and optimized read-only Git-free replay. The interpreter and pricing are adapted from #5377, not independently authored engines. No hosted CI, Lean/kernel check or human acceptance is claimed; full-history ancestry checking is not claimed in the shallow checkout.

python3 -B scripts/research_package.py --package research/eight-owned-relations
python3 -B scripts/check_research_commit.py --package research/eight-owned-relations

The result retains the selected source’s native/all-size, owned-erasure, precision/tape, analytic, prime and recovery contracts. Physical precision/storage execution, source phase lowering and ordinary BIT construction are authenticated/reused rather than freshly executed. The #4610/#5241 admission and #5384 single-relation audit do not automatically admit this eight-relation endpoint. Selected-result metadata is unchanged. Larger draft #5270 is not used; #5349 documents its physical-reference/controller mismatch.

Credit Ali Romman #5377/#5383; Cao Yifan #4610; Chris R #5241/#5384; Cinna Davis #4470; zxv #5283 and completion/compiler work; Jacob Alan Sussman’s mixed-target recursion; Dugongue’s transported-frame lineage; ToikY and all retained native, Clifford, BIT, precision and analytic contributors. Smaller-reserve tightening already appears in #4610/#5241; the new result is its exact application to this eight-relation bill. Full source pins and frozen predecessor hashes are included.

One scoped package, based on canonical main 1ec1119, refreshed before release. Overlap checks covered 100 recently updated PRs, all 214 open search results containing “kappa”, and targeted bodies through #5384; Discussion coverage is incomplete. Prepared by Dugongue with substantial OpenAI Codex assistance, solo. Apache-2.0. Open review questions are in README.md and TASK.json.

[Clear1nsight]

HANDOFF

Research discussion / PR / artifact: Completed and released the three supporting publications: independent validation #5395, six-plane oracle #5391, and scoped ceilings #5393. This updates the original publication claim in place. Each package includes its own source pins, evidence and handoff; no construction search is reserved by this DONE.

Exact commit: Validation 275dc377246f91ef30dc9e05241b0f637aa807fb; oracle 96f193143a7a2ff8a4e6b9d574d7f551d68a7da3; ceilings 5744cc24d89df28d8c889615f7e667003d5fdf25. Canonical base 1ec1119972c9aefe42525172d07b332fcff81cb4. Consumed scientific heads: Ali Romman #5383 4bd6efa51a495a7c7b7754915cf0244e7e60969e and Dugongue #5387 b1ab650d36f59e5be682a813145b7c67e219e341.

What is established: Independent physical, complete literal census, fresh finite-template precision/stock/tape and directed rational compiler/outer validation support conditional κ=.003026674765, gain .000004324765 over validated #5377 and .000004898965 over selected #4610. The complete invoice is 64148 paid /10800 productive, surplus752, with all128 lost H9 targets debited. #5387's changed pivot L261, retained L288 and L256 snapshot/zero site received a fresh physical proof. The strict fixed-profile crossing is (.00302667476807,.00302667476808), with a full stated-domain ceiling proof. It is not an attained endpoint or a global construction ceiling.

One actual source-package registered normal/optimized pair passed in140.030862s, peak223576KiB,44 author-path controls and20535 unchanged scientific/provenance/Git files. The independent validation package then freshly reran both physical engines, full census/chronology, precision checks and exact funding in128.740804s, peak224952KiB,352 unchanged guarded inputs. It authenticates the complete frozen source-cold evidence; its CI reruns the independent engines rather than that source-cold pair. No own #5383 author cold pair is claimed.

The oracle preserves six cost planes and rejects missing costs, stale evidence, enlarged compiler domains and unearned credit; its labels consume separately trusted hash-bound receipts. The ceiling package proves all3282 remaining frozen-#5383 paid rows nonzero at every positive width, with a carefully scoped single-row surjectivity corollary, and tests all562 controller allocations within two FULL/QUERY changes at exactly three target prices. These are independent scoped support, not new κ mechanisms. All three packages passed separate publication-byte/source/export audit and local registered checks. All first hosted runs now pass on the exact publication heads: oracle40026894699, ceilings40027085617 and validation40027726348. The validation run freshly executes the independent engines and authenticates the frozen source-cold receipt; it does not rerun that source-cold pair. Parallel independent audit #5396 corroborates the same fixed point through separate engines; it supplies no additional κ gain. The two contribution chats are coordinating successor work to avoid further duplication.

What remains uncertain: The five assumptions native_all_columns, owned_erasure, compiler, precision_tape, analytic_recovery remain. Native phase foundations and ordinary BIT are authenticated inherited evidence; no astronomical compiler word, Lean/kernel theorem, unconditional result, human acceptance or selected transition is claimed. Later #5390's changed compiler tuple and #5392's owned transposition are outside this certificate. The latter is now receiving its own separate exact-head review. Matching histograms and numerical superiority never transfer physical or closure coverage.

Smallest useful next task: Review one independently reproduced obligation against the literal source; for a stronger construction, bind its actual endpoint, target census and complete cost before using a new oracle policy. Ali Romman's active paid-history, forward-transpose and all-backward-wrapper streams retain their scope. The separate bounded pair7 idle experiment has its own claim. No duplication is reserved here.

Reproduction command and expected runtime: Standard-library CPython3.12; use python3 -B scripts/research_package.py --package research/price-plane-independent-validation (~130s pair), --package research/source-bound-price-oracle (~1s pair), or --package research/frozen5383-scoped-ceilings (~40s pair). Canonical committed-byte/source-history preflight and Git-free integrity commands are in each README. Frozen assertion-based child checks deliberately remain unoptimized inside both wrapper modes. Hosted CI and scientific admission are distinct.

Predecessor credit: Ali Romman #5377/#5383 owns the native relation mechanism; Dugongue #5387 owns the changed literal implementation and funded compiler refinement; Cao Yifan #4610, Cinna Davis /1337isnot1337, zxv, Jacob Alan Sussman, Chris R /Clear1nsight #5241/#5384, ToikY, Tekalign, Douglas Colkitt and all retained native, Clifford, BIT, precision, compiler and analytic notices preserve credit. New independent work by Chris R /Clear1nsight with substantial OpenAI Codex assistance; Apache-2.0.

{"schema":"integer-mult-coordination/v1","kind":"DONE","task":"complete-price-plane-independent-validation","scope":"Published independent eight-relation validation, reusable six-plane oracle and frozen-source scoped ceilings; construction discovery and later successor admission excluded","base":"1ec1119972c9aefe42525172d07b332fcff81cb4","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/5395"}

[Clear1nsight]

HANDOFF

Research discussion / PR / artifact: Bounded pair7 IDLE44/100 investigation complete and released. This public comment records the exact symbolic failure and cost constraint; full producer/reviewer scripts and receipts are local-only, not a publicly replayable package. No new PR, controller witness or κ is claimed for this experiment.

Exact commit: Canonical base 1ec1119972c9aefe42525172d07b332fcff81cb4; source #5383 4bd6efa51a495a7c7b7754915cf0244e7e60969e; controller SHA256 1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f. Only cuts44/50/56/99/100 were tested, with the same33 LOCAL/QUERY choices, both forward calls and source boundaries.

What is established: Two independent exact Laurent engines agree. Write the actual segment B*C*A, with A equal to a=D0*D1*D3*D5*D7*D9*D11*D13 on rows14/15, and B the disjoint stage product on17/19/21/23/25/27/29/31/32. Coalescing requires Cprime=A^-1*C*A; entrywise the correction is (a^(1[j in {14,15}]-1[i in {14,15}])-1)*C[i,j]. It has11 nonzero cells. At cut100, naïve fusion leaves normalized full-endpoint residue *(row14,column15)=(1-a)Q^-1. All five naïve cuts fail in five endpoint cells each. The formal corrected recipes restore the complete32×32 endpoint, but each requires eight non-scalar ADD coefficients involving a±1 or b±1. These are outside the declared rational scalar alphabet; no literal implementation was produced.

At tested C=.00303001 the independently enclosed optimistic gain 224*(H64+H72-H136) is [62.945416730174373612,62.945416730174373613]. Adding the source moment gives about62.12222538839760, or62.12198922003937 after its10^-9 productive reserve, before correction/ordinary costs. One added H64, or63 added H1 requests, fails this optimistic tariff. This is not a proof that a correction requires either charge. Unknown correction costs are not set to zero.

What remains uncertain: There is no literal existing-alphabet correction, priced paid-reuse adapter, correction cost bound, physical endpoint/phase/owned-return proof, complete new invoice or funded point. A nonzero Laurent coefficient or matrix rank is not a native-query lower bound. Rational boundary retiming and broader controller grammars were not searched; no universal ceiling follows.

Smallest useful next task: Stop this round. Any continuation first needs one explicit legal and completely priced realization of a named a±1/b±1 coefficient, preserving all source targets. Recheck live overlap before claiming that separate construction. Ali's paid-value reuse, forward transpose, signed-swap caller and coded-helper streams remain untouched.

Reproduction command and expected runtime: Local-only workspace scripts outputs/price-plane-idle-corridor-20261024/producer/reproduce.py (~0.3s) and outputs/price-plane-idle-corridor-20261024/review/check.py (~0.224s/18660KiB), standard-library Python3.12. Exact public formula above is directly checkable against the pinned controller. No native build, author cold replay, Lean or physical compiler was run.

Predecessor credit: Ali Romman #5383/#5377; Cao Yifan #4610; Cinna Davis /1337isnot1337 controller/helper lineage; zxv; Dugongue; Jacob Alan Sussman; Chris R /Clear1nsight; ToikY and retained source notices. New bounded test by Chris R /Clear1nsight with substantial OpenAI Codex assistance; Apache-2.0.

{"schema":"integer-mult-coordination/v1","kind":"DONE","task":"pair7-idle-corridor-fusion","scope":"Five exact pair7 cut counterexamples and unpriced formal corrections; no literal controller, query lower bound or funded kappa; scope released","base":"1ec1119972c9aefe42525172d07b332fcff81cb4","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/5387#issuecomment-6375128760"}