2026-08-12 17:16 UTCgpt-5.6-sol · high

derive global block-pair intersection moments and squeeze the square mass Q of pair surplus against the collision mass R of triple excess

No Progress

Global block-pair intersection moments give two exact identities and the necessary interval 15+ceil(Q/3)<=R<=floor(115+7Q/6). Independent reconstruction and four mutation controls passed. All 50 saved marginal witnesses pass with wide margins, so the lemma is retained but unstructured sampling is redirected. The covering range remains 30 through 31.

Research-policy redirect

Evidence receipt creation failed; durable progress is withheld.

Strategy and discriminator

global intersection-moment inequalities

Compress all 435 unordered block pairs into six intersection bins and use two nonnegative pointwise binomial-polynomial slacks to derive exact Q-R identities.

Hypothesis: Every putative 30-block cover satisfies 15+ceil(Q/3) <= R <= floor(115+7Q/6), and at least one of the 50 saved marginally feasible epoch-114 (H,e) witnesses may violate this necessary condition.

Test: Derive both inequalities from the six possible block-pair intersection sizes, compute Q and R for all 50 hash-pinned controls, and require a separate implementation to rebuild every H degree, every e marginal, every histogram moment, and four mutation rejections.

Rationale

The mathematical claim follows from exact double counts and pointwise nonnegative polynomials on the complete intersection domain 0..5, while a materially separate checker reconstructs every tested marginal. Progress is limited to a reusable lemma because no H/e witness, cover case, or global family was eliminated.

Claims requiring scrutiny

For every putative 30-block C(15,6,3) cover, 3R-Q-45=n_1+4n_4+15n_5.
For every putative 30-block C(15,6,3) cover, 345+7Q/2-3R=15n_0+4n_1+n_4.
Consequently 15+ceil(Q/3)<=R<=floor(115+7Q/6).
All 50 hash-pinned epoch-114 marginal witnesses pass this interval and admit an abstract six-bin histogram satisfying the four counted moments.

Evidence and scope

python3 scripts/global_intersection_moment_squeeze_v1.py --out artifacts/epoch125-20260812/global-intersection-moment-result.json
python3 checkers/check_global_intersection_moment_squeeze_v1.py --result artifacts/epoch125-20260812/global-intersection-moment-result.json --out artifacts/epoch125-20260812/global-intersection-moment-independent-check.json
producer rerun byte-identical at SHA-256 0a229ce36ad1a227d88742b82bd1d0a0d752a70ee27163d2d2cb555536ff16fe
independent checker PASS on 50 cases and four rejected mutations

Computational experiments

.proof-experiments/20260812-170947-0b40b1: 50 controls, 0 rejected, minimum margins 37 and 55
.proof-experiments/20260812-170954-d4553a: independent PASS on 50 controls and four mutation rejections

Independent checker

checkers/check_global_intersection_moment_squeeze_v1.py independently rebuilds sparse H/e tensors, validates all marginals and histogram moments, derives both pointwise slack arrays, and rejects four mutations without importing producer code.

Contribution gate

not_requested

No structured gate reasons were recorded in this legacy attempt; see the adjudication ledger.

Original model outcome: no_progress
Public classification: no_progress

Cross-domain transfers tested

block-intersection polynomials -> linear inequalities on six intersection bins -> exact Q-R squeeze; observed result: sound theorem but 0/50 marginal pruning
certified covering case splits -> require complete ownership before leaf solving -> observed result: full depth-four union remains held at the explicit approval gate

Established facts

3R-Q-45=n_1+4n_4+15n_5 and 345+7Q/2-3R=15n_0+4n_1+n_4 for every putative 30-block cover.
global-intersection-moment-lemma.md plus independent pointwise slack and marginal reconstruction · simple 30-block (15,6,3) covers with the established exact degree-12 pinning · proved
All 50 saved epoch-114 marginal witnesses satisfy the derived interval and admit abstract compatible intersection histograms.
producer SHA-256 0a229ce36ad1a227d88742b82bd1d0a0d752a70ee27163d2d2cb555536ff16fe; independent checker PASS · exactly the 50 hash-pinned epoch-114 witnesses · computed

Ruled out in this epoch

Scale unstructured sampling of the unchanged epoch-114 marginal relaxation using only the Q-R moment squeeze.
the retained relaxation and its 50 deterministic controls · 0 of 50 controls were rejected; minimum lower and upper margins were 37 and 55. · artifacts/epoch125-20260812/global-intersection-moment-result.json · A complete owned H/e catalogue, a source-motivated extremal family near either bound, or a stronger coupled inequality with a measured pruning signal.
Repeat scripts/canonical_root_link_pilot_v1.py unchanged.
the five degree-coloured root-link profiles under the 10000-node cap · Epoch 19 already ran the same enumerator and independently recorded a 10001-node cap breach. · artifacts/epoch19-20260809/root_link_canonical_primary_receipt.json and epoch-113 audit · A new independently proved sound bulk completion filter or materially different ownership decomposition.

Open leads

Complete depth-four pair-surplus parent ownership union
Count and 82-chunk geometry are already independently qualified; exact ownership is the missing prerequisite before proof leaves. · After explicit approval, parent-materialize the remaining 38705 profiles and reconcile exactly 62437 records against the frozen 1775-parent ledger. · high · open
All-root link-lift relaxation sharing one e tensor
It couples the marginal e equations to actual 12-block root links and is materially stronger than the moment squeeze without yet enforcing global block identity. · Compile one named 3K5 control with a known-link positive control and a 20-second fail-closed solver cap. · normal · open

Continuation checkpoint

Objective: Build an exact once-only depth-four ownership union after the human scope gate, or otherwise test one genuinely coupled link-lift relaxation.

First action: Request approval for parent-materializing 38705 remaining profiles across the qualified 82-chunk geometry.

Stop condition: Stop on approval refusal, any count/hash/owner/parent/restart disagreement, or an attempt to promote ownership alone as a covering result.

Next moves

Request explicit approval for the exact remaining 38705-profile parent-materialization scope, then reconcile the full 62437-profile ownership union.
Reuse the Q-R interval only on complete owned H/e candidates; do not sample more unchanged marginal witnesses.
If ownership approval remains unavailable, formulate one bounded all-root link-lift relaxation with an independently checked positive control and stop on timeout or no pruning signal.

Citations

Tool disclosure

GPT-5.6 Sol principal; two GPT-5.6 Terra delegates for advisory reconnaissance only. Python 3.12.3 exact integer/JSON/SHA-256 code and the computational-researcher experiment harness generated evidence. Web search checked status and prior art. No CAS, SAT/PB solver, proof assistant, cloud lab, external proof service, or human validator produced evidence.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 1080.7s
Review state: evidence receipt failure; not durable progress
Attempt ID: covering-c1563-20260812-171654-a17042

Human review ledger

No human review recorded.