Build the complete root-free [13,2] exact pair-excess CNF, quotient it by all 52 D13 x C2 automorphisms with sequential lex leaders, and run a matched proof-capable two-seed discriminator.

complete exact-pair branch with full automorphism lex quotient

Pair caps and coverage encode one globally complete outer skeleton branch; all-group lex leaders select one primary assignment per branch-automorphism orbit, while matched CaDiCaL runs measure whether the quotient improves proof search.

Hypothesis: On the complete unrooted [13,2] pair-excess branch, the exact D13 x C2 lex quotient either decides the formula or reduces both decisions and wall time by at least 20 percent at 2000 conflicts for seeds 0 and 1553.

Test: Generate base and all-group-lex CNFs with a common exact prefix, independently reconstruct both, reject four semantic mutations, and compare two matched CaDiCaL runs before allowing scale-up.

The formula and quotient claims are supported by exact independent reconstruction, mutation tests, regeneration, and proof-stack smoke replay. The only solver outcomes were UNKNOWN, so they cannot support a mathematical exclusion; matched telemetry decisively fails the predeclared scale gate.

• The base CNF exactly represents the complete unrooted [13,2] pair-excess branch: every model is a 54-block degree-18 covering with pair multiplicities 5^91,6^13,7, and conversely every such branch cover has a model.
• The candidate CNF retains exactly one primary assignment from every D13 x C2 orbit of base models.
• At the fixed two-seed 2000-conflict protocol, both formulas were UNKNOWN and the quotient increased decisions by 24.5215782984x; no branch was excluded.
• The maintained range remains 54 <= C(15,5,3) <= 55.

• independent-check.json valid=true: 379507 base clauses and 451830 lex clauses exactly reconstructed; all cap sums 72; 52 automorphisms; 4282 toy lex cases.
• mutation-controls.json: four of four coverage/cap/action/lex mutations rejected.
• result-check.json valid=true: four UNKNOWN logs reparsed, decision ratio 24.521578298397042, process-time ratios 2.983050847457627 and 1.9634146341463417.
• proof-smoke.lrat replayed against the smoke CNF and was rejected against the candidate CNF without the contradictory units.
• regeneration-check.json: base and candidate CNFs and manifests byte-identical across reruns.

• .proof-experiments/20260812-055129-d70d6c: generated the 109998-variable, 379507-clause base CNF.
• .proof-experiments/20260812-055146-a4b0b3: generated the 260591-variable, 831337-clause all-group quotient.
• .proof-experiments/20260812-055208-6ed2fa: independent exact reconstruction PASS.
• .proof-experiments/20260812-055229-1d70ab: four mutations rejected.
• .proof-experiments/20260812-055758-9bd8ee: final matched two-seed pilot UNKNOWN; telemetry gate failed; LRAT smoke passed.
• .proof-experiments/20260812-055814-751c9b: independent raw-log and LRAT result replay PASS.
• .proof-experiments/20260812-055635-d12c08: byte-identical regeneration PASS.

check_partition132_full_branch_lex_v1.py reconstructs the CNF with a separate counter implementation and group action; check_partition132_full_branch_lex_result_v1.py reparses raw logs and independently replays LRAT.

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

• Graph canonical labelling -> predict that full orbit minimization will reduce CDCL search -> exact quotient succeeded semantically but caused a 24.52x decision explosion, so transfer should use unit orbital branching rather than a monolithic existential lex network.

• Coverage plus [13,2] pair caps forces degree 18 and exactly 54 blocks.
  Independent exact CNF reconstruction and the incident-cap-sum argument in independent-check.json. · Every model of base.cnf. · proved
• The saved 51-lex suffix selects exactly one assignment from each D13 x C2 orbit of base primary models.
  All group elements/actions and clauses reconstructed; group closure/preservation and 4282 small semantic cases pass. · The complete [13,2] branch primary-model set. · proved
• The full lex encoding fails the fixed two-seed advancement gate.
  Independent raw-log parsing gives decision ratio 24.521578298397042 and process-time ratios 2.983050847457627 and 1.9634146341463417. · CaDiCaL 1.7.3, seeds 0 and 1553, 2000 conflicts on the saved formulas. · computed

• Scale the saved all-52-element sequential lex compiler on the [13,2] branch.
  This exact CNF compiler and matched 2000-conflict CaDiCaL protocol. · It missed both 20 percent gates and increased decisions by 24.52x while leaving both runs UNKNOWN. · result.json and independently checked raw logs. · A materially different symmetry encoding or solver that independently demonstrates decision ratio <=0.8 on the same hash-bound base, or a complete checked branch proof.
• Treat 90 saved labelled families and at least 91 local plateau classes as a corpus discrepancy.
  The two cited immutable prior packets. · They use different universes and units: 90 labelled families in 16 classes versus a later lower bound of 40+51 point-isomorphism classes. · sources/advisory/terra-epoch110-injected-audit-20260812.md with four prior packet hashes. · A hash-level mismatch within either packet or an explicit claim that both counts refer to the same universe and unit.

• Disjoint first-selected-block orbit cubes for the complete [13,2] base CNF.
  Unit clauses may deliver the same certified branch symmetry directly to CDCL without 150593 lex auxiliaries. · Extract the 106 root orbits, define the first-selected-orbit no-earlier-selection condition, and run one smallest-orbit cube at 2000 conflicts. · high · open
• Native pseudo-Boolean complete [13,2] branch control.
  It removes totalizer and lex auxiliary variables, but would need a proof-producing translation before scale. · Build-only exact PB instance and compare primary propagation on one fixed seed; stop if it cannot emit independently replayable proof semantics. · normal · open

Objective: Test whether disjoint unit-propagating root-orbit cubes outperform the harmful monolithic lex quotient on the complete [13,2] branch.

First action: jq '.partitions[] | select(.partition==[13,2]) | {automorphism_order,root_orbits:(.root_orbits|length),smallest:(.root_orbits|min_by(.orbit_size_within_skeleton))}' artifacts/joint-orbit-census-20260808/manifest.json

Stop condition: Redirect if union/disjointness cannot be independently proved or the first 2000-conflict cube does not reduce decisions by at least 20 percent relative to base.cnf.

• Extract the 106 existing [13,2] root-block orbits from the certified joint-orbit manifest and define a disjoint first-selected-orbit partition, rather than overlapping rooted leaves.
• Generate one unit-propagating orbit cube over the saved base CNF and compare it with the root-free base at 2000 conflicts; stop on less than 20 percent decision improvement.
• If the unit cube passes, independently verify union coverage and only then prepare segmented proof leaves; otherwise redirect to a native-PB [13,2] branch or constructive route.

• 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://arxiv.org/abs/math/9502238 ↗

GPT-5.6 Sol principal designed, implemented, ran, audited, and interpreted the epoch. Two injected GPT-5.6 Terra delegate memos supplied advisory reconnaissance only; Sol rejected their 90-versus-91 discrepancy, confirmed the zero-delta fixed-link warning from deterministic artifacts, and did not count model agreement as validation. Python 3.12.3 generated and independently reconstructed CNF; CaDiCaL 1.7.3 ran four bounded searches and proof smoke; pinned drat-trim and lrat-check converted/replayed LRAT; SHA-256, mutation testing, byte regeneration, and official-source web search were used. No subagents, lab job, package installation, system change, CAS, proof assistant, or external write was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1722.3s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260812-060454-790033

No human review recorded.