Incremental integer-feasibility screening of the first 100 safely quotiented seven-zero triple-excess headers for the 15-cycle pair-excess skeleton

joint-header triple-excess-zero gate

Couple each canonical pair-excess skeleton/root header to seven forced-zero triple-excess coordinates, then solve the shared nonnegative integer system incrementally.

Hypothesis: The first 100 canonical [15]-skeleton joint headers all admit nonnegative integral triple-excess vectors, and incremental throughput is at least two headers per second.

Test: Solve the pinned first-100 header prefix using one shared 455-variable, 105-equation Z3 system with seven activation assumptions per header, then independently reconstruct and check every witness.

Explicit witnesses prove feasibility for exactly the tested prefix, and the independent checker validates their arithmetic. Nothing supports extrapolation to the remaining headers. Because no header was excluded and no cover was found, the field-progress gate is unmet.

• The first 100 headers in the pinned canonical [15]-partition ordering are feasible in the seven-zero triple-excess integer projection.
• Those 100 headers use 100 distinct global zero-coordinate sets.
• The independent checker validated 100 marked witnesses and one unmarked positive control, totaling 45,955 entries and 10,605 pair equations.
• All six specified result and coverage mutations were rejected.

• python3 scripts/cycle15_seven_zero_triple_excess_gate_v1.py ... --limit 100 produced 100 SAT, 0 UNSAT, 0 UNKNOWN at 4.756511 headers/second
• python3 checkers/check_cycle15_seven_zero_triple_excess_gate_v1.py ... --allow-prefix returned valid=true
• python3 checkers/test_cycle15_seven_zero_triple_excess_mutations_v1.py rejected six of six mutations
• sha256sum -c artifacts/cycle15-seven-zero-triple-excess-gate-20260810/manifest.sha256 passed

• .proof-experiments/20260810-143203-f19edb: producer classified the first 100 headers as SAT at 4.756511 headers/second
• .proof-experiments/20260810-143240-19d2d7: independent checker reconstructed and accepted all 100 witnesses
• .proof-experiments/20260810-143248-78c624: all six mutations were rejected

checkers/check_cycle15_seven_zero_triple_excess_gate_v1.py independently enumerates triples and pairs with nested loops, reconstructs the canonical headers, and scatter-adds every witness coefficient without importing Z3 or producer code.

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

• Marked-system robustness screening -> forcing seven unique-triple coordinates should expose incompatibility hidden by the unmarked projection -> no incompatibility appeared in the first 100 headers, so only a complete partition run can justify scale-up.

• All first 100 canonical [15]-partition headers are feasible in the marked integer projection.
  pilot-prefix100-result.json plus independent checker SHA-256 730d68c9124f597860d91e58c0658441ae14c5e44a2671390feafa7013ff38e2 · First 100 of 12,096 canonical headers only · computed
• The first-100 prefix contains no duplicate exact global seven-zero set.
  distinct_zero_sets=100 and cache_hits=0 · Same prefix only · computed

• Exclude any of the first 100 canonical headers using only the seven-zero triple-excess integer projection.
  Deterministic first-100 [15]-partition prefix · Every header has a directly and independently checked feasible integer vector. · artifacts/cycle15-seven-zero-triple-excess-gate-20260810/pilot-prefix100-independent-check.json · Add a genuinely stronger necessary constraint, such as literal block realizability; repeating the same projection cannot exclude these headers.
• Obtain prefix savings from exact zero-set memoization.
  First 100 headers · All 100 exact keys were distinct. · pilot result cache_hits=0 · Observe duplicate exact keys outside the tested prefix; unsafe relabeling is not sufficient.

• Complete [15]-partition seven-zero gate
  It is the smallest complete skeleton-partition discriminator and determines whether the marked relaxation merits global scale-up. · bash scripts/submit_cycle15_seven_zero_triple_excess_lab_v1.sh · high · open
• Constructive defect-10 repair
  A verified degree-18 seed with only ten uncovered triples remains the closest constructive state and is the predeclared redirect route. · Design a bounded trade/ejection-chain tranche targeted at the exact defect set, with direct cover checking. · normal · open

Objective: Complete and independently validate the full 12,096-header [15]-partition gate.

First action: bash scripts/submit_cycle15_seven_zero_triple_excess_lab_v1.sh

Stop condition: Redirect if all headers survive, fewer than 1,210 are infeasible, maps disagree, any mutation passes, or negative statuses cannot be converted to replayable proofs.

• From a lab-enabled epoch, run: bash scripts/submit_cycle15_seven_zero_triple_excess_lab_v1.sh
• After completion, run the independent checker without --allow-prefix against the content-addressed result.
• If at least 1,210 headers are infeasible, convert each negative status to deterministic PB/SAT with replayable proof logs before claiming exclusion.
• If fewer than 1,210 are infeasible, redirect to the constructive defect-10 repair route and do not scale this relaxation to 124,988 headers.

• https://www.coveringrepository.com/systems.aspx?k=5&t=3&m=-1 ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?k=5&t=3&v=15 ↗

GPT-5.6 Sol served as principal investigator. GPT-5.6 Terra delegates supplied advisory reconnaissance; their exact memos were promoted under sources/advisory and were not treated as independent mathematical validation. Python 3.12.3, Z3 4.13.0, standard-library exact checking, SHA-256, and the computational-researcher experiment harness were used. The checkpointed lab submitter was invoked but failed before queueing because its service-state directory was read-only. No CAS, proof assistant, external write, or publication was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1095.3s

Review state

not a result claim

Attempt ID

covering-c1553-20260810-143846-ec0419

No human review recorded.