Globally classify the proved 31-cell root-pair excess relaxation across every certified rooted skeleton/profile instance, solving only canonical coefficient signatures and transporting every result back to its original labels.

outside-triple root-pair coupling

Canonicalize the induced weighted excess graph on the five root points under S_5, pair it with the five root-intersection counts, and classify each resulting linear/integer system with exact Farkas certificates or integer witnesses.

Hypothesis: The global root-pair relaxation excludes at least one complete rooted skeleton orbit after all necessary profiles are tested.

Test: Canonicalize all 30,845 rooted-orbit/profile systems, solve the resulting 279 signatures, independently expand every certificate or witness, and count rooted orbits whose profiles are all LP-infeasible.

Exact certificate and witness expansion validates useful profile pruning and reusable infrastructure, but the predeclared success condition failed decisively: every rooted orbit retains many checked integer witnesses.

• There are exactly 16 induced weighted five-root graph types and 279 graph/profile coefficient signatures across the certified 30,845-instance frontier.
• Exactly 3,955 mappings are LP-infeasible with checked rational Farkas certificates.
• Exactly 25,278 mappings have checked nonnegative integer witnesses.
• No certified rooted skeleton orbit is excluded by the current root-pair relaxation.
• The maintained range remains 54 <= C(15,5,3) <= 55.

• python3 scripts/root_pair_excess_coupling_global_v2.py --source-manifest artifacts/joint-orbit-census-20260808/manifest.json --protocol protocols/root-pair-excess-coupling-global-v2.json --output artifacts/root-pair-excess-coupling-global-20260808/result.json
• python3 checkers/check_root_pair_excess_coupling_global_v2.py --source-manifest artifacts/joint-orbit-census-20260808/manifest.json --protocol protocols/root-pair-excess-coupling-global-v2.json --result artifacts/root-pair-excess-coupling-global-20260808/result.json --output artifacts/root-pair-excess-coupling-global-20260808/independent-check.json
• sha256sum -c artifacts/root-pair-excess-coupling-global-20260808/manifest.sha256 returned OK for every listed artifact.

• .proof-experiments/20260808-232306-ce846b: producer completed in 64.89 seconds; 16 graph types, 279 signatures, 30,845 mappings, zero excluded rooted orbits.
• .proof-experiments/20260808-232431-7c8abd: independent checker completed in 26.81 seconds and accepted every expansion.
• .proof-experiments/20260808-232511-75bbd7: all five deliberate mutations were rejected.
• .proof-experiments/20260808-232803-f149fd: the v1 7/13 classification was exactly reproduced.

checkers/check_root_pair_excess_coupling_global_v2.py independently reconstructs skeletons, root orbits, profiles, canonical signatures, transported rows, Farkas arithmetic, and witnesses without importing producer code.

not_requested

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

Original model outcome

progress

Public classification

progress

• Certified forced-link/orbit analysis for C(12,6,4) -> predict that compatibility between multiple forced optimal point links is more discriminating than aggregate root-cell totals -> not yet tested here; promoted as the next bounded route.

• The global coefficient-system quotient contains exactly 16 graph types and 279 signatures.
  Independent reconstruction from all 30,845 mappings and 1,920 relabelling checks. · The certified 31-cell root-pair relaxation frontier. · computed
• Exactly 3,955 profile mappings are rationally infeasible.
  Transported coefficient-by-coefficient Farkas checks. · All 30,845 rooted-orbit/profile instances. · proved
• At least 25,278 mappings satisfy the integer root-cell relaxation.
  25,278 transported witnesses with 783,618 checked nonnegative entries. · The root-cell relaxation only; no five-block realization follows. · computed
• Every rooted orbit retains at least eight explicitly witnessed integer-feasible profiles.
  Independent per-orbit aggregation of transported witnesses. · All 2,145 certified rooted skeleton orbits. · computed

• Exclude any complete rooted skeleton orbit using only the current root-cell equalities and ten root-pair penalty inequalities.
  All 2,145 rooted orbits and all 30,845 necessary profiles. · Every orbit retains at least eight independently checked integer witnesses. · artifacts/root-pair-excess-coupling-global-20260808/independent-check.json · Add a strictly stronger proved constraint involving actual outside subsets, multiple point links, or full five-block compatibility.
• Treat rationally feasible/integer-UNSAT Z3 statuses as certified profile exclusions.
  Nine signatures covering 1,612 mappings. · No independently replayable integer-UNSAT certificate was produced. · The checker records these as unresolved_transports=1612. · Supply independently checked cutting-plane, LRAT/DRAT, or exhaustive integer certificates.

• Two-link amalgamation for adjacent points.
  It retains actual link incidence and shared-block compatibility absent from the exhausted root-cell relaxation. · Bound and test the first canonical adjacent-link pairs in the 15-cycle/root-31 case. · high · open
• Proof-producing OPB leaf solving.
  It remains the most direct exclusion route once a pinned RoundingSat/VeriPB/CakePB stack is available. · Replay the saved tiny calibration bounds before attempting a hash-bound rooted leaf. · high · open
• Outside-subset realizability refinement.
  The 31-cell witnesses do not identify subsets of the ten outside points. · Encode one surviving profile using exact outside point/pair degrees and triple coverage, with independent SAT decoding. · normal · open

Objective: Determine whether exact compatibility of two adjacent forced optimal links prunes structures that survive every root-cell profile.

First action: Run jq '.partitions[] | select(.partition==[15]) | {matrix,root:(.root_orbits[]|select(.representative_mask==31))}' artifacts/joint-orbit-census-20260808/manifest.json, then hash-bind the selected adjacent vertex pair in a new two-link protocol.

Stop condition: Redirect if the first bounded canonical pairs are all feasible, a checked link-orbit census cannot be obtained, or SAT decoding/proof replay disagrees.

• Design the bounded two-link amalgamation protocol for an adjacent pair in the partition-[15], root-mask-31 skeleton.
• Enumerate canonical optimal C(14,4,2) links with full pair-multiplicity matrices and a checked orbit census.
• Test exact shared-pair block compatibility; independently decode SAT pairs and replay a proof for each UNSAT link-orbit pair.
• Keep the global 279-signature table only as a sound prefilter for stronger encodings.

• 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 ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?k=4&t=2&v=14 ↗
• https://arxiv.org/abs/2607.23766 ↗

GPT-5.6 Sol principal designed, audited, implemented, and interpreted the epoch. Pre-existing GPT-5.6 Terra delegate memos supplied advisory experiment-design and challenger leads only; their claims were independently recomputed and they were not counted as validation. Deterministic tools: Python 3.12.3, Z3 4.13.0, exact Fraction arithmetic, jq, sha256sum, and the project run_experiment wrapper. No proof assistant or external solver certificate checker was used for the nine integer-UNSAT solver statuses, which remain unresolved.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1171.4s

Review state

not a result claim

Attempt ID

covering-c1553-20260808-233239-3a9c96

No human review recorded.