Parent-rich materialization and independent exhaustive validation of the qualified high-bit subpartition for depth-four pair-surplus internal orbit 1.

checkpointed canonical pair-surplus augmentation

Compress four processed vertices against eleven exchangeable external vertices to canonical 70-entry multiplicity tables, partition the largest internal-edge orbit by high FNV bits, and reconstruct every depth-three deletion parent before any SAT compilation.

Hypothesis: The eight preflight-qualified high-FNV-bit buckets materialize all 21182 canonical profiles of depth-four internal orbit 1 exactly once, with every S3-canonical deletion parent present in the frozen 1775-key depth-three ledger.

Test: Run clean and interrupted/resumed C++17 materializations, then use a materially different Python/Burnside encoding to reconstruct all keys, orbit weights, and deletion parents and reject seven corruption classes.

The producer is bound to exact canonical tables and frozen parent data, while an independent Burnside/profile implementation proves the aggregate count and validates each record. Exact union, parent closure, restart determinism, rerun identity, and mutation rejection justify a scoped progress result. They do not meet the positive or negative verification contract for the covering number.

• Depth-four pair-surplus internal orbit 1 has exactly 21182 canonical profiles, partitioned by high FNV bits into exact parent-rich bucket sizes [2664,2679,2637,2561,2655,2636,2706,2644].
• For those 21182 profiles, all 80851 reconstructed deletion-parent incidences lie in the frozen 1775-key depth-three ledger; there are 1236 distinct deletion parents and 634 distinct owner parents.
• The clean and interrupted/resumed materializations are byte-identical, and the independent validation receipt is byte-identical across fresh processes.
• This result eliminates no depth-four profile and does not change the maintained range 30 <= C(15,6,3) <= 31.

• python3 scripts/pair_surplus_depth4_orbit1_highbits_v2.py ... -> PASS_ORBIT1_COMPLETE, 21182 profiles, maximum bucket 2706.
• python3 checkers/check_pair_surplus_depth4_orbit1_highbits_v2.py ... -> PASS_INDEPENDENT_ORBIT1_UNION; receipt SHA-256 b693a6b6346d079d196a881946dac305c7f7503867567578048999937797ff6c.
• cmp clean/final.json resumed/final.json and all eight corresponding chunk files -> identical.
• Independent checker rerun receipt SHA-256 b693a6b6346d079d196a881946dac305c7f7503867567578048999937797ff6c.

• .proof-experiments/20260812-083508-07c614: C++17 compile passed in 3.939 s.
• .proof-experiments/20260812-083528-c6c1be: clean eight-chunk producer passed in 3.240 s, peak child memory 33132 KiB.
• .proof-experiments/20260812-083554-db0c51 plus 20260812-083606-0dbedf: declared three-chunk stop returned 2, then resume passed; output matched clean bytes.
• .proof-experiments/20260812-084034-9622d1: independent checker passed in 134.921 s, peak child memory 195732 KiB.
• .proof-experiments/20260812-084310-3ec740: fresh checker rerun passed in 128.023 s and emitted the identical receipt.

checkers/check_pair_surplus_depth4_orbit1_highbits_v2.py is a materially different Python/Burnside encoding from the C++ producer. It returned PASS_INDEPENDENT_ORBIT1_UNION, reconstructed every record and parent, rejected seven mutations, and reran byte-identically.

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

• Certified C(12,6,4) stabilizer-orbit decomposition -> predict that exact canonical ownership plus parent closure can make a proof frontier auditable -> orbit-1 ownership became bounded and independently checkable, but no SAT/UNSAT covering leaf was decided.

• The high-bit owner partitions all 21182 canonical profiles of depth-four internal orbit 1 into bucket counts [2664,2679,2637,2561,2655,2636,2706,2644].
  Clean and resumed producer manifests plus independent Burnside/profile receipt b693a6b6346d079d196a881946dac305c7f7503867567578048999937797ff6c. · Internal weighted-edge orbit 1, residual target (4,4,3,3), under the retained S4 x S11 quotient. · computed
• Every reconstructed deletion parent of those profiles belongs to the frozen 1775-key depth-three ledger.
  Independent recomputation of 80851 record-parent incidences, seven mutation controls, and byte-identical rerun. · The same 21182 orbit-1 profiles and the epoch-102 parent-key universe. · computed

• Repeat the five-profile coloured canonical root-link discriminator as proposed by Terra.
  The unchanged degree-profile split and coloured first-block canonicalization. · The retained epoch-19 enumerator already implements the same five target profiles and degree colours; its type-0 frontier grew [1,2,14,128,2258,7598] and breached the 10000-node gate. · scripts/canonical_root_link_pilot_v1.py and artifacts/epoch19-20260809/root_link_canonical_primary_receipt.json. · A new sound bulk completion filter, ownership condition, or stronger invariant that is absent from epoch 19 and independently proves safe elimination.

• Complete the 62437-profile depth-four parent-rich ownership ledger.
  The largest stress orbit now passes exact subchunk and parent gates; only 38705 profiles remain without validated parent records. · After human approval, generalize the C++ producer and run a clean/resume full-union materialization with qualified splits for orbits 0 and 5. · high · open
• Direct constructive 30-cover search with immediate double validation.
  Any 30-block witness settles the exact value without exhaustive negative certificates. · Use a materially new degree-12 generator and send any candidate to both retained direct 455-triple checkers. · normal · open
• Proof-producing PB incidence decomposition.
  A complete PB proof chain could avoid large CNF proof transport. · Only after pinned RoundingSat, VeriPB, and CakePB are available, replay the 450-variable 87-equation transparent overdegree UNSAT calibration with mutations. · low · open

Objective: Obtain approval and then finish the exact depth-four parent-rich ownership prerequisite without compiling SAT leaves.

First action: Present the hash-bound remaining scope of 38705 profiles across 60 internal orbits, including qualified subchunk designs for oversized orbits 0 and 5, and request human approval before running or submitting it.

Stop condition: Stop on any scope refusal, count/parent/hash mismatch, owner gap or overlap, restart drift, checker disagreement, projected segment above 900 seconds or 1 GiB, or an attempt to interpret ownership as cover exclusion.

• Request human approval for the exact full parent-rich depth-four scope: the remaining 38705 profiles across 60 internal orbits, with qualified subchunks for oversized orbits 0 and 5.
• After approval, generalize the C++ producer without changing canonical serialization, run clean/resume materialization, and require the existing full-union checker to reconcile all 62437 profiles and every parent.
• Compile no SAT leaves until the complete hash-bound ownership union passes; then forecast CNF and proof volume on the smallest owned leaf before any lab submission.
• Keep the native PB route held until a pinned RoundingSat-to-VeriPB-to-CakePB chain passes the retained transparent UNSAT calibration.

• https://www.coveringrepository.com/systems.aspx?k=6&t=3&m=-1 ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?k=6&t=3&v=15 ↗
• https://arxiv.org/abs/math/9502238 ↗
• https://arxiv.org/html/2607.23766v1 ↗

GPT-5.6 Sol was principal investigator. Two GPT-5.6 Terra delegates supplied advisory prior-art and verification memos; Sol independently audited their claims, rejected the duplicate root-link suggestion, and did not treat agreement as evidence. Deterministic tools were Python 3.12.3, g++ 13.3.0 with C++17, exact integer enumeration, Burnside counting, SHA-256, cmp, and the computational-researcher experiment harness. CaDiCaL 1.7.3 was present but unused; RoundingSat, VeriPB, CakePB, CAS, proof assistants, cloud lab, and external proof services were not used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1733.3s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260812-085435-5eb761

No human review recorded.