Exact count-only qualification of a high-three-bit FNV-1a owner for the oversized depth-four internal-orbit-1 canonical frontier, using separate C++17 and Python enumerations, raw-ordinal restart reconstruction, key digests, and mutation controls.

checkpointed canonical pair-surplus augmentation

Compress orbit-1 residual tables by the retained S4 stabilizer quotient, serialize each canonical table as 70 bytes, assign it to (FNV1a64(table) >> 61) & 7, and compare exact key ledgers from materially different implementations.

Hypothesis: The high three FNV-1a bits partition all 21182 canonical orbit-1 profiles exactly once into eight nonempty buckets containing at most 5000 profiles each.

Test: Enumerate all 78278 raw orbit-1 tables independently in C++17 and Python, require exact agreement on all 21182 canonical keys, owners, bucket counts, and SHA-256 digests, and reconstruct the clean ledger from two fixed raw-ordinal segments.

The predeclared observable was completely reproduced by a materially different implementation, including every canonical key rather than aggregates alone. The largest bucket is below the frozen cap, so the owner-function uncertainty is resolved. Because no parent ledger or SAT certificate was produced, the outcome is scoped progress rather than a candidate covering result.

• For all 21182 canonical depth-four profiles in internal orbit 1, the owner (FNV1a64(canonical_70_bytes) >> 61) & 7 has exact bucket counts [2664,2679,2637,2561,2655,2636,2706,2644].
• The maximum qualified bucket contains 2706 profiles, so every bucket satisfies the frozen 5000-record cap.
• The sorted union of raw-table ranges [0,39139) and [39139,78278) is byte-identical to the clean ledger.
• The maintained range 30 <= C(15,6,3) <= 31 is unchanged.

• C++ full enumeration: .proof-experiments/20260812-075042-b0ab7c, return code 0, 0.287 seconds, 17920 KiB peak child memory.
• Restart binding: .proof-experiments/20260812-075137-5a6e1f, PASS_CPP_HIGHBITS_PREFLIGHT and clean/resumed SHA-256 310fd5c90f8cc6ce2a0c66a3f575565805c409345573aabb00f097ea2a662f36.
• Independent enumeration: .proof-experiments/20260812-075149-f234ec, PASS_INDEPENDENT_HIGHBITS_PREFLIGHT after 78278 raw tables and 21182 canonical keys.
• Independent rerun: .proof-experiments/20260812-075226-83fddf produced a byte-identical receipt.
• Receipt hash bindings were checked against every decisive artifact; git diff --check and JSON parsing passed.

• .proof-experiments/20260812-075042-b0ab7c: C++ clean enumeration emitted 21182 keys with high-bit loads [2664,2679,2637,2561,2655,2636,2706,2644].
• .proof-experiments/20260812-075056-60deae and 20260812-075057-070119: fixed raw ranges emitted 15156 and 6026 canonical keys.
• .proof-experiments/20260812-075110-55af81: mathematical union completed but receipt writing failed on unresolved relative-path normalization; retained as a failed provenance control.
• .proof-experiments/20260812-075137-5a6e1f: corrected binder proved byte-identical clean/restart output.
• .proof-experiments/20260812-075149-f234ec: independent Python checker matched every key and rejected all mutations.
• .proof-experiments/20260812-075226-83fddf: independent receipt reran byte-identically.

checkers/check_pair_surplus_depth4_orbit1_highbits_v1.py uses retained pure-Python residual-table recursion and minimum-image canonicalization rather than the new C++ implementation. It compares all keys and digests, reproduces the low-bit vector, checks restart bytes, and rejects delete, duplicate, owner, byte, shift, and total mutations.

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

• Hash-partition engineering -> low rolling-hash bits can preserve input parity while high bits should mix fixed-sum tables -> low bits produced four empty buckets, whereas high bits produced eight balanced buckets with maximum 2706.

• The exact high-bit bucket vector is [2664,2679,2637,2561,2655,2636,2706,2644].
  C++ producer receipt plus independent Python receipt with identical key digests · All canonical residual multiplicity tables of depth-four internal orbit index 1 · computed
• The high-bit partition's maximum bucket has 2706 profiles and therefore passes the 5000-record cap.
  Exact eight-bucket vector totaling 21182 · The frozen high-bit owner and orbit-1 profile universe only · computed
• The two fixed raw-ordinal segments reconstruct the clean ledger byte-for-byte.
  Both ledgers have SHA-256 310fd5c90f8cc6ce2a0c66a3f575565805c409345573aabb00f097ea2a662f36 · The frozen C++ enumeration order and split at raw ordinal 39139 · computed

• Use the low three FNV-1a bits as eight orbit-1 subchunks under the 5000-record cap.
  All 21182 canonical internal-orbit-1 profiles · The exact vector [5204,0,5558,0,5246,0,5174,0] has four empty buckets and maximum 5558. · artifacts/epoch110-20260812/orbit1-fnv8-count-control.json, reproduced again by the epoch-112 independent checker · None for the frozen low-bit owner; use a different owner such as the now-qualified high-bit function.
• Treat the high-bit decomposition as excluding any 30-cover.
  Internal orbit 1 and the global covering problem · A total owner function only partitions profiles; it proves none infeasible. · No parent, CNF, witness, or UNSAT proof was generated. · Terminal, independently replayed SAT/UNSAT evidence for every exactly owned case.

• Parent-rich high-bit orbit-1 stress pilot
  The count gate passed with substantial margin, and the existing optimized producer already contains parent reconstruction code. · Emit the eight qualified buckets and independently compare every deletion parent with the frozen depth-three ledger. · high · open
• Constructive 30-cover search with a materially new generator or neighborhood
  A directly checked 30-block witness remains the smallest terminal certificate, but previous incidence seeds and local neighborhoods should not be repeated. · Specify a new structural generator and a short falsifiable pilot before allocating solver time. · normal · open
• Native pseudo-Boolean proof toolchain qualification
  Exact degree equations are naturally PB, but the current route label lacks a pinned emitter and two replay paths. · On a retained known-UNSAT control, hash-pin RoundingSat, VeriPB, and CakePB and require terminal proof acceptance plus truncation and input mutations. · low · open

Objective: Qualify parent-rich orbit-1 materialization under the new owner without starting SAT work.

First action: Modify scripts/materialize_pair_surplus_depth4_orbit1_bucket_v1.cpp to assign (hash >> 61) & 7, then run all eight buckets through the computational-researcher harness and the independent parent checker.

Stop condition: Any incorrect or foreign deletion parent, key gap or overlap, bucket above 5000, restart drift, mutation acceptance, or projection beyond 900 seconds or 1 GiB ends or redirects the route.

• Change the retained parent-rich orbit-1 C++ producer to use the qualified high-bit owner and emit all eight buckets.
• Independently reconstruct all four deletion parents per record and require membership in the frozen 1775-key depth-three ledger.
• Require exact 21182-key union, clean/resume identity, mutation rejection, and the existing time, memory, and record caps.
• After that pass, obtain human approval for the exact full 61-orbit ledger scope before any lab submission.
• Keep native PB held until a pinned emitter, VeriPB, and independently elaborated CakePB path qualify on a known UNSAT control.

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

GPT-5.6 Sol acted as principal investigator. Two GPT-5.6 Terra delegates supplied advisory route-selection and verification memos; their agreement was not evidence. Deterministic computation used g++ 13.3.0, C++17, Python 3.12.3, SHA-256, and the computational-researcher experiment harness. No SAT solver, CAS, proof assistant, or external proof checker was used this epoch. Web checks consulted the maintained LJCR entry and arXiv. All accepted computed claims were reproduced by separate C++17 and Python implementations.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

947.7s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260812-075712-5bd90b

No human review recorded.