Apply exact per-block intersection moments to lift-test two frozen pair-surplus/triple-excess controls, and certify unsupported required triples by exhaustive local enumeration.

local block-intersection moment lift obstruction

For each possible block, compute its pair-surplus and triple-excess sums, retain it only when a six-bin other-block intersection histogram realizes all four exact moments, then detect positive-multiplicity triples with zero eligible support.

Hypothesis: Each of the two named epoch-114 stored (H,e) controls has a triple of required multiplicity at least one that belongs to no locally intersection-moment-feasible 6-set.

Test: Enumerate all six-bin histograms for one block, scan all 5005 candidate blocks for each frozen control, and independently reconstruct any required triple with zero eligible support.

The obstruction is a finite exact contradiction: a required triple must lie in a block, while exhaustive enumeration shows none of its 220 possible containing blocks can satisfy the necessary local intersection moments. Independent reconstruction validates the computation, but the quantifier is over two fixed e vectors only.

• Every block in a hypothetical 30-cover satisfies the four local intersection-moment equations stated in the technical report.
• The exact epoch-114 stored control-3K5 excess vector is not induced by any 30-block cover; triple {1,5,11} has required multiplicity 1 and zero locally admissible containing blocks.
• The exact epoch-114 stored control-2C15 excess vector is not induced by any 30-block cover; triple {1,10,12} has required multiplicity 1 and zero locally admissible containing blocks.
• No complete H is excluded and the maintained range remains 30 <= C(15,6,3) <= 31.

• Producer experiment 20260812-121714-97d407 returned PASS_TWO_SCOPED_OBSTRUCTIONS in 0.525 s.
• Fresh producer experiment 20260812-121806-574bbf reproduced the receipt byte-for-byte at SHA-256 53a39960d135da9296659f54f4ed57010125f734ad709a65670cf66ff8e53678.
• Independent experiment 20260812-121815-73fd3c returned PASS_INDEPENDENT_DP in 1.729 s, accepted 30/30 actual cyclic blocks, and rejected four mutations.
• Exact scope is two named stored H/e profiles; no symmetry quotient, random-sample extrapolation, H exclusion, or global result is claimed.

• .proof-experiments/20260812-121714-97d407: producer, 169 and 167 eligible blocks, 9 and 2 unsupported required triples.
• .proof-experiments/20260812-121806-574bbf: fresh byte-identical producer rerun.
• .proof-experiments/20260812-121815-73fd3c: independent DP/check, cyclic boundary control, four rejected mutations.

checkers/check_local_moment_lift_obstruction_v1.py constructs the reachable moment set by a 29-step DP rather than the producer's six-bin enumeration, rebuilds both H/e maps from the pinned source, scans all 5005 blocks, validates a separately constructed cyclic exact-degree-12 family, and rejects four 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

• Aggregate moment methods -> prediction that retaining moments per candidate block will expose lift obstructions hidden by global sums -> both named marginally feasible e controls were rejected by zero-support required triples.

• Every block B in a hypothetical 30-cover has a nonnegative integer intersection histogram satisfying the four exact local moments.
  Direct double count plus independent cyclic exact-degree boundary check. · All hypothetical 30-block C(15,6,3) covers. · proved
• The two named stored epoch-114 e vectors fail the local lift condition.
  Producer receipt SHA-256 53a39960d135da9296659f54f4ed57010125f734ad709a65670cf66ff8e53678 and independent PASS_INDEPENDENT_DP receipt. · Exactly control-3K5 and control-2C15 with their stored e vectors. · computed

• Lift the exact epoch-114 control-3K5 marginal witness to 30 blocks.
  Only that stored e vector over the stored 3K5 H. · Required triple {1,5,11} has zero locally moment-feasible containing blocks. · Exact producer and independent DP/check receipts. · A different exact e vector over the same H that passes local admissibility.
• Lift the exact epoch-114 control-2C15 marginal witness to 30 blocks.
  Only that stored e vector over the stored 2C15 H. · Required triple {1,10,12} has zero locally moment-feasible containing blocks. · Exact producer and independent DP/check receipts. · A different exact e vector over the same H that passes local admissibility.
• Treat aggregate block-intersection moments as equivalent to local per-block lift feasibility.
  The two named stored H/e controls. · Aggregate moments pass while the independently checked local test rejects both exact e vectors. · Current receipts and the audited current challenger aggregate-moment control. · A proof that the aggregate system plus additional stated constraints implies every local block condition.

• Joint local-admissibility and triple-marginal model for one complete H.
  It quantifies over e instead of rejecting arbitrary witnesses and is the smallest route that could exclude a whole H or produce a liftable e. · Encode one named H with e pair marginals and sufficient locally admissible support, with a predeclared size/time/proof cap. · high · open
• Constructive exact-degree incidence search with a materially new decomposition.
  A direct 30-cover remains the shortest terminal certificate, but unchanged flat incidence runs are closed. · Only after a new structural restriction, run a matched short comparison against the frozen baseline. · normal · open

Objective: Determine whether local admissibility can constrain all e over one complete H without recreating the full incidence search.

First action: Write an efficiency design for one fixed-H joint model, including exact variable/constraint counts, sound conditional-admissibility encoding, and certificate format.

Stop condition: Redirect if the model is comparable to the 33178-variable incidence CNF, cannot produce replayable negative evidence, or exceeds the first bounded cap without a feasible e.

• Design one bounded joint model coupling e pair marginals to local block admissibility for control-3K5 or control-2C15.
• Predeclare model-size, time, and certificate caps; do not enumerate another arbitrary batch of standalone e witnesses.
• If the joint model yields e, attempt exact block lifting and directly check any 30-block witness; if infeasible, claim only with a replayable proof.
• Keep native PB held until pinned RoundingSat, VeriPB, and CakePB pass the retained dual-replay 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/abs/2607.23766 ↗

GPT-5.6 Sol principal investigator. Two GPT-5.6 Terra delegates supplied advisory prior-art and verification memos; Sol audited them, confirmed that the local CakeLPR binary is not the missing CakePB verifier and does not unblock the absent PB chain, and did not treat model agreement as validation. Deterministic work used CPython 3.12.3 standard-library exact integer/set arithmetic, SHA-256, cmp, and the computational-researcher experiment harness. An exploratory SciPy 1.11.4/HiGHS MILP status check motivated replacing solver output with the exact unsupported-triple certificate and is not claimed as evidence. Web access was attempted for the maintained sources; retained primary-source audits supplied the status baseline. No SAT/PB solver proof, CAS, proof assistant, cloud lab, external proof service, human validator, or publication action was used for the result.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1131.1s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260812-122653-ea6c8b

No human review recorded.