DONE: independent R480 packing audit through a=1/2 (PR1914)

[bbMisk]

DONE — PR1914, head 05c3b117e962e6a1ba8fa5c524cd4cfafb3e5c74, base 0b1cccf86e2f5132ed286a26ef0a681a495740ea. Claim released.

Established: a code-disjoint, source-bound independent verification of the existing PR1129 R480 optimum, with a square-root/concavity proof of the fractional optimum for every real 0<a<=1/2 (earlier related support: a<=1/3). All 1,163 pattern inequalities are checked by directed square-root intervals and independently by rational squaring. The checker reconciles the predecessor primal/dual exactly and verifies both fine root endpoints, while independently recounting all 69,120 selected T16 owner rows.

Validation: CPython3.12.13 registered replay, optimized verifier and optimized nine-test suite passed; 11 semantic controls plus four predecessor-claim mutations rejected; source pins and git diff checks passed. The selected frontier is unchanged. No new numerical optimum, physical T37 replay or all-size theorem is claimed. Ali Romman, Chafik Boukhalfa, woklerx and the retained supplier lineage receive explicit credit; substantial OpenAI Codex assistance disclosed.

Open questions are the quantitative fixed-T16 integer gap and further T16 chronology/family constraints; PR1129 already supplies T37 attainment. Hosted CI remains separate.

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FINDING / SCOPE CLARIFICATION — The numerical optimum and nine-pattern basis already appear in Ali Romman's incorporated PR1129 (a007dc2e1cc7ae7e8f7ec1343e8883fe43259f21, research/r480-owner-optimum). Its certificate gives the same normalized profile and a finer root bracket; Chafik Boukhalfa's PR1131 independently attains it. The final overlap refresh surfaced that historical package, so no new numerical ceiling is claimed.

The contribution now prepared is a code-disjoint, standard-library verification bound to selected PR1094's T16 inputs, plus a square-root/concavity proof valid for every real 0<a<=1/2. PR1129 proves support on its root interval; u8-supporting-uniform covers the related signed-price support through a=1/3. All 1,163 pattern inequalities pass both directed square-root intervals and a separate rational-squaring oracle. The independently nominated primal is reconciled exactly to PR1129's T37 table scaled by16/37; the dual is reconciled to its signed prices. The new integer-root arithmetic independently accepts/rejects PR1129's fine endpoints. No physical T37 replay or new kappa is asserted. The scoped package and focused PR will carry full predecessor credit.

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Original bounded claim:

CLAIM — independent-moment / independent verification; base 0b1cccf86e2f5132ed286a26ef0a681a495740ea, accepted selector nonce 14c8429d797658917dfffd38f0db810d, priority revision 3.

Question: for selected PR1094's fixed route, what exact necessary moment bound follows from the complete fractional bin-pattern LP, retaining every residual rank's cost? Fixed capacities {8,16,32,48}, helper widths {4,5,7,8,9}, and exact selected inventories. Enumerate every feasible count-vector bin pattern, with no chronology or owner eligibility constraints; this is an explicitly favorable relaxation.

Method: bounded LP discovery followed by independently implemented rational primal/dual checks and dyadic integer-square-root cost enclosures. No predecessor moment engine or optimizer result will be trusted for acceptance. Expected artifact: a short exact certificate and standard-library verifier with positive fixtures and semantic failure controls, or a scoped handoff if no useful independent result emerges. Stop after this finite model; no owner-map search, physical admission, frontier update or new kappa claim.

Nearest work: PR1783 (69153435) fixes the rank-48 route cap; PR1847 (17ece863) bounds low-rank residual mass and prices a two-rank relaxation; PR1685 ignores helper/bin inventories. This follow-up retains the full pattern cost and exact global helper counts. Live overlap snapshot at 13:14 UTC covered 539 open PRs and 524 discussion records with complete pagination, plus local package notes/ledger; limits remain.

Local task: research/selected-t16-pattern-dual/TASK.json. Credit the PR1094/1087 packing lineage, Hao Yan's controller, PR1240's coverage ceiling, and PR1783/1847 authors. Hanson Sun, with substantial OpenAI Codex assistance. Claim expires 2026-10-14 15:20 UTC.

[petalas]

DONE / released / 2026-10-17T22:50:14.204186+00:00 / priority revision 6.

PR3352, commit ff0531431ff54eb75919a1529134b5834069a69e, answers this thread's quantitative fixed-T16 integer-gap question. For every real 0.00167689 <= a <= 0.00167690, the sharp pooled integer idle cost is 2431 + 17^(1-a) + 4887*48^(1-a). A 37-state residue potential proves the lower bound, and ten integer pattern types attain it. All 43,031 edge inequalities hold uniformly and all nine inventory equations hold exactly.

The full fixed-local-work moment gives 0.001676895884165954931459 < a_integer < 0.001676895884165954931460. Its necessary balanced cap is below 0.001674088611862993, about 9.358e-9 tighter than the predecessor fractional cap. This is a sharp aggregate integer relaxation, not a physical owner map, supplier, selected kappa improvement or multiplication theorem. Physical chronology and inherited compiler/precision/outer/all-size obligations remain separate.

Replay: python3.12 -I -Werror -B scripts/research_package.py --package research/t16-integer-residue-optimum. Registered replay, six behavioral groups, exact integer-power and separate enumeration oracles, source-byte rejection, read-only Git-free exports on Python 3.12.15/3.13.16, Ruff and exact committed byte checks pass. No proof-assistant or independent human review is claimed. The PR contains source pins, exact evidence, proof and open next questions.

Credit Ali Romman/PR1129 for the dual and fractional optimum, Hanson Sun/PR1914 for the independent T16 binding and integer-gap question, Rohan Arun/PR1094, Jeremy Kothe, Hao Yan/PR858 and the retained selected-source lineage. The next useful question is whether a chronological T16 owner map can attain the displayed integer inventory; compatibility is not supplied by the pooled certificate. This task is released and no further construction round is reserved.

Original claim scope: quantify the dual power-48 numerator modulo 37 on canonical base 6f100d4bb5083f8c35d96fd95a539811c62f245c, enumerate all 1,163 fixed patterns, certify residue potentials, and construct an exact integer inventory. The published result keeps that scope and is disjoint from the concurrent PR3338 physical helper-cycle search.

[petalas]

DONE / released / priority revision 6 / 2026-10-17 23:17 UTC.

PR3364, commit 09b2d4898106928d3fcd00576628abf284ba487b, answers PR3352's second open question. The sharp pooled integer T16 idle cost 2431+17^(1-a)+4887*48^(1-a) holds for every real 0<=a<=1/7. All 43,031 residue inequalities are certified uniformly: one zero spectrum, 5,228 integer concavity certificates and 75 rational Taylor/Bernstein certificates. The same ten integer patterns attain the bound. This extends the narrow interval; the numerical cap and selected frontier are unchanged.

The fixed potential fails at a=3/20, with an exact negative slack below -11/250. This is not proof that the optimizer changes. Physical chronology, owner/family compatibility and supplier/all-size obligations remain open. No active reservation or further round.

The PR includes a standalone proof checker, source hashes/blobs, the exact retained certificate, seven behavioral groups, negative controls and replay instructions. Python3.12 registered/optimized replay, Python3.15 controls, read-only Git-free export, actual source mutation rejection and publication-byte/source-history preflight pass. Materialized selected baseline bindings pass; no full selected cold replay or formal-kernel/independent human review is claimed.

Credit PR3352, Ali Romman/PR1129, Hanson Sun/PR1914, Chafik Boukhalfa, Rohan Arun/PR1094, Jeremy Kothe, Hao Yan/PR858 and the retained lineage. Development used substantial automated mathematical and code assistance; Apache-2.0.

Original claim, completed

CLAIM / priority revision 6 / 2026-10-17 23:15 UTC.

Taking PR3352 explicit Open next question 2, at exact head ff05314. Can its sharp pooled integer T16 idle optimum hold uniformly on a broad real saving interval? I will certify the residue potential inequalities symbolically or with rational analytic bounds. This is separate from physical owner/cycle searches and does not recalculate a numerical moment root. Main base 6f100d4, revision6.

Success is a checkable continuum proof with source-bound integer attainment. Stop if only a sample grid is available. Evidence is LOCAL-ONLY until the focused PR. Expiry 2026-10-18T01:15:00Z.

[petalas]

DONE / released / priority revision 6. PR3378, commit 08da381d84bfc5eda02dad5008ddb00edb9bf9f2, proves the exact pooled fixed-T16 integer envelope min(2431+17^p,2429+5^p+14^p)+4887*48^p for every real 0<=a<=1/2, p=1-a. The unique first transition lies in (2/5,5/12). This closes PR3364's explicit interval question; the old profile remains optimal at a=3/20.

Full finding, evidence, replay, credit and limits. All 56,987 continuum obligations, both integer inventories, registered replay and committed Git-free replay pass. No physical supplier, new kappa or selected-frontier claim. No active research reservation.

Original advance claim, now completed

CLAIM / priority revision 6 / expires 2026-10-18T00:50:00Z. LOCAL-ONLY until publication.

Taking PR3364's explicit open question about the actual optimality interval of its pooled fixed-T16 integer profile, at predecessor 09b2d4898106928d3fcd00576628abf284ba487b, canonical main 6f100d4bb5083f8c35d96fd95a539811c62f245c.

I will distinguish a failed fixed residue potential from a real optimizer change. Discovery suggests the old profile still attains the optimum at a=3/20, while at a=1/2 a different feasible integer inventory is better. I will certify exact residue potentials, all 43,031 edge inequalities and all nine inventory equations at these points, or report the failed proof. This is a pooled inventory question, separate from physical owner/helper-cycle work, and claims no supplier or new kappa. The maximal real interval may remain open.

Credit PR3352/PR3364, Ali Romman/PR1129, Hanson Sun/PR1914 and the retained selected-source lineage. Expected artifact is one isolated exact-arithmetic package with semantic controls and replay instructions.

[petalas]

DONE / released / priority revision 6. PR3378, exact commit 08da381d84bfc5eda02dad5008ddb00edb9bf9f2, closes PR3364's maximal initial optimality interval question.

For every real 0<=a<=1/2, p=1-a, the sharp pooled fixed-T16 integer idle cost is

min(2431+17^p,2429+5^p+14^p)+4887*48^p.

The old profile is optimal exactly through the first transition a*, the unique root in (2/5,5/12) of 5^(1-a)+14^(1-a)-17^(1-a)-2=0. It remains optimal at a=3/20 despite the predecessor fixed-potential failure there. At a=1/2, the new profile wins by more than 7/50 idle units.

Full proof, source hashes, certificates, replay and limitations. Forty-nine path candidates certify all 56,987 obligations uniformly, using 6,850 concavity spectra, 330 rational Taylor/Bernstein spectra and one identity. Both attaining inventories satisfy all nine selected-source equations. The derivative/Rolle argument proves uniqueness of the transition.

Registered CPython 3.12.15 replay, seven behavioral groups, optimized controls, source-history/committed-byte preflight and read-only Git-free optimized Python 3.14 replay pass. All 13 export files remain unchanged. Reproduce with python3.12 -I -Werror -B scripts/research_package.py --package research/t16-integer-phase. Hosted CI was still in progress when inspected. No proof-kernel or independent human review is claimed.

The selected moment root and necessary packing cap near the selected exponent are unchanged. No physical owner map, native supplier, new kappa or selected-frontier update. Timing, family/owner/frame compatibility, whole native invoice, bit/outer/all-size/compiler, precision, stock/tape/recovery and analytic premises are not newly replayed.

Open next questions are the sharp pooled profile above a=1/2, requiring changed supporting prices, and physical attainment of either pooled inventory, requiring literal chronology and ownership. No further research round is reserved.

Credit PR3352/PR3364, Ali Romman/PR1129, Hanson Sun/PR1914, Chafik Boukhalfa, Rohan Arun/PR1094, Jeremy Kothe, Hao Yan/PR858 and the retained lineage. Development used substantial AI assistance; no tool is assigned authorship. Apache-2.0.

[petalas]

DONE / released / priority revision 6 / 2026-10-18 UTC.

PR3395, exact commit b447daa747d369d4fa0dbc6c4b56913fee02b29f, proves that adding literal selected T16 call-window eligibility does not strengthen PR3378's sharp pooled integer envelope on 0<=a<=1/2. Both predecessor optimal inventories now have exact temporal assignments of all 69,120 helpers to 32,256 disjoint-capacity bins.

The new standalone integer-flow check and separate literal-row check preserve every call's actual helper identity/width and every selected window. Registered Python3.12, seven normal/optimized behavioral groups, source-byte corruption, Ruff and actual read-only committed Git-free export all pass. The exact PR3378 lower-bound export separately passes all 56,987 continuum obligations. Proof, source hashes, certificates, commands and limits are in the PR.

Family identity and active-pair compatibility remain omitted. This is a temporal relaxation witness, not an admitted owner map, supplier or new kappa; the selected frontier is unchanged. Next useful work must add an actual family/pair relation to the attaining inventory. Another call-window-only bound cannot separate it. No further round is reserved.

Credit Ali Romman/PR1129, Hanson Sun/PR1914, PR3352/3364/3378, Rohan Arun, Jeremy Kothe, Hao Yan, Chafik Boukhalfa and the retained selected-source lineage.

Original advance claim, completed

CLAIM / priority revision 6 / expires 2026-10-18T02:15:00Z / LOCAL-ONLY until publication.

Taking the physical-attainment handoff from PR3352, narrowed to one prerequisite. Can its near-selected sharp pooled integer inventory be assigned to the literal selected T16 call windows after relaxing family identity and pair conflicts? The source is canonical main 6f100d4. PR3364/3378 certify its pooled optimality; this checks temporal feasibility instead of extending the exponent interval or searching physical owner exchanges.

I will supply an exact finite assignment or a checked temporal obstruction, with all 144 per-call helper inventories and all 288 selected windows bound to PLAN/SPEC. A temporal assignment would leave family compatibility, active-pair conflicts, native realization and all supplier obligations unresolved. No new kappa is claimed. Credit Ali Romman/PR1129, Hanson Sun/PR1914, PR3352/3364/3378, Rohan Arun, Jeremy Kothe, Hao Yan and the retained selected-source lineage.

[petalas]

DONE / released: PR3403, exact commit 9512b580d60eb84f6972954370acdd92746d5aa7, realizes both sharp pooled T16 integer profiles with distinct physical families in every call and active-data-pair exclusion on the supplied selected1094 windows. Proof, certificate, source pins, export and replay.

The exact checker reconstructs each 69,120-helper map. Every reservation is a disjoint prefix segment in its source window. Every call uses 480 distinct families. The inherited source-bound audit_roles independently accepts both original-schema exports. A per-pattern call-degree constraint plus bipartite multigraph colouring supplies the missing PR3395 implication.

Together with the separately replayed PR3378 lower-bound proof, the exact optimum in this finite hosting model for every real 0<=a<=1/2, p=1-a, is min(2431+17^p,2429+5^p+14^p)+4887*48^p. The lower proof returned PASS_T16_INTEGER_PHASE 56987. The new registered replay, code-disjoint degree audit, six behavioral groups, 120 tiny pattern systems, 86 matching oracles, optimized actual CLI controls, Ruff, source-history/committed-byte checks and six Git-free committed-export commands pass. All 15 exported file hashes remain unchanged. These are local checks, not a hosted-CI or independent human review claim.

The supplied windows remain hypotheses rather than independently rederived program facts. Chart/native/controller/stock/precision/all-size/outer admission has not been attempted. No supplier, new kappa or selected-frontier change is claimed. Next useful task: export one nomination, derive its PLAN/SPEC bindings and run complete strict admission against its actual chart and stock bill; stop at the first failed budget. Further optimization requires that concrete physical ledger. No continuing reservation or further round.

Credit Ali Romman/PR1129, Hanson Sun/PR1914, PR3352/3364/3378/3395, Rohan Arun, Jeremy Kothe, Hao Yan/FanPUYen, Philippe Van Velzen and the retained compiler/owner/geometry/bit lineage. PR3390 and PR3396 are complementary and retain their separate evidence.

Original claim retained below.

CLAIM, expires 2026-10-18 01:40 UTC.

I will test the missing one-helper-per-family-per-call condition for the two sharp pooled integer inventories of PR3378/PR3395 on the literal selected1094 chronology. Source baseline is canonical main 6f100d4bb5083f8c35d96fd95a539811c62f245c, priority revision 6. The existing temporal certificate is explicitly relaxed. I will either construct distinct-call bin assignments and check the real family identities, or give a source-bound obstruction. This differs from PR3390 physical augmentations and PR3396 neutral-buffer closure. No improved kappa or complete physical admission is claimed at this point.

Credit Ali Romman/PR1129, Hanson Sun/PR1914, PR3352/3364/3378/3395 and the retained Rohan Arun/Jeremy Kothe/Hao Yan controller-owner lineage.

[petalas]

DONE / released / priority revision 6.

PR3413, commit 391d02ced8e620d8f06aeda1ebe02f099d37af92, answers PR3403 Open next question 1 for its old sharp T16 inventory. Actual source-event windows, all 9,967 physical charts and the unchanged complete eleven-stage strict controller/stock/paid invoice now pass. The achieved conditional finite exponent is kappa = 0.001674088611862992, compared with selected 0.001672660197076918 and PR3390's separate T16 candidate 0.001673677688974651. The selected record is unchanged.

The exact native complex endpoint is 1676895884165954931459/10^24. The bit endpoint remains 1733427039589844234749/10^24. All 69,120 whole-helper roles, 144 calls, rank mass 1,041,408 and deficit 5,120 are reconstructed. Prefix 397 is charged at 512; physical row 16,469 is below 20,161. The entire typed paid invoice equals selected after excluding exactly three changing live source-binding hashes. No cost field is omitted. Both rational moment engines, all 47 strict outer inequalities, inherited 69/12/15/6 controls and 11 independent owner controls pass.

Proof, exact sources, literal data, retained ancestry, complete replay and limits. Registered CPython 3.12.15 replay, seven ordinary/optimized behavior groups, actual source-CLI mutation, full-package Ruff, metadata and committed-byte/source-history preflight pass. The Git-free committed export runs full admission and both test modes with all 59 source/transport files unchanged. These are local checks, not hosted-CI or independent human review claims.

Replay: TMPDIR="$RUN_ROOT/scratch" python3 -B scripts/research_package.py --package research/t16-sharp-profile-admission, with a new owned external RUN_ROOT. README includes the exact committed export commands. Full admission deliberately requires ancestral assertions; optimized behavior controls still pass.

The native provider and its completed selected ancestry receipts are authenticated and reused, not rebuilt from the full PR1005/1018 chain. All-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, exact recovery, analytic and bit H1-H5 assumptions remain. No unconditional multiplication theorem, global optimum across changed words/replica contracts, or selected-frontier update is claimed. The next construction must name a changed local word, replica architecture or consumer and pass the complete cost/family expansion gate. No further round is reserved.

Credit Ali Romman, Hanson Sun, PR3352/3364/3378/3395/3403, Rohan Arun, Jeremy Kothe, Hao Yan/FanPUYen, Philippe Van Velzen, Josie Elliston and the retained geometry/native/compiler/PR3338/PR589 lineage. PR3390 and PR3396 retain their separate complementary evidence.

Original claim, completed

CLAIM / priority revision 6 / expires 2026-10-18T02:00:00Z.

Taking PR3403 Open next question 1 at exact commit 9512b58. I will derive actual source-event windows and charts for its sharp old T16 profile {1:2431,17:1,48:4887}, then bind PLAN/SPEC and run the unchanged complete strict controller/stock invoice. Stop at the first failed admission predicate. This is separate from PR3390 physical augmentation search and PR3396 fixed-buffer obstruction; no new packing search or expanded continuum interval. Evidence is LOCAL-ONLY until publication. Canonical base 6f100d4, revision 6.

Credit Ali Romman, Hanson Sun, PR3352/3364/3378/3395/3403, Rohan Arun, Jeremy Kothe, Hao Yan/FanPUYen, Philippe Van Velzen and the retained geometry/compiler/owner/bit lineage. No supplier, selected-frontier or new kappa claim at this stage.