Degree-capacity dominance audit of the proposed root-link residual-budget pruning filter.

root-link degree-capacity dominance audit

Rewrite forced link degrees as a_y=r_y-4 with nonnegative excess sum four, then maximize the filter expression using only fixed degree capacities.

Hypothesis: The residual-budget filter rejects at least one child legal under a fixed root-link target degree vector.

Test: Determine whether max(0,ell_yz-4) can exceed the residual budget when ell_yz is bounded only by the fixed endpoint degrees.

Writing a_y=r_y-4 gives nonnegative excesses summing to four. Since ell_yz<=min(r_y,r_z), each positive codegree excess is at most min(a_y,a_z), whose sum is at most 4-a_y=8-r_y. This is exactly the proposed filter.

• For every forced root-link degree vector and every partial or complete link respecting its target degrees, sum_{z!=y} max(0,ell_yz-4)<=8-r_y is implied by degree capacities.
• Consequently, the proposed residual-budget predicate rejects no child in a degree-type-specific canonical augmenter.
• The exact covering range remains 30<=C(15,6,3)<=31.

• python3 scripts/audit_root_link_filter_redundancy_v1.py --receipt artifacts/epoch10-20260808/root_link_filter_redundancy_receipt.json
• python3 checkers/check_root_link_filter_redundancy_v1.py artifacts/epoch10-20260808/root_link_filter_redundancy_receipt.json
• A fresh generator rerun was byte-for-byte identical to the receipt.
• The generator checked 2380 labelled vectors and 33320 endpoint cases; the independent checker passed five corruption controls.

• .proof-experiments/20260808-214030-cbe54f: generator returned PASS in 0.38 seconds and produced the 2380-vector receipt.
• .proof-experiments/20260808-214035-cdcd63: independent checker returned PASS in 0.073 seconds and rejected five corruptions.

checkers/check_root_link_filter_redundancy_v1.py uses integer partitions and explicit Cartesian contribution enumeration rather than the generator's labelled weak compositions and closed-form maximum.

not_requested

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

Original model outcome

progress

Public classification

progress

• Certified link-orbit SAT methodology for C(12,6,4) -> audit link predicates before catalogue scale-up -> the proposed predicate was sound but redundant.

• The root-link degree excesses a_y=r_y-4 are nonnegative and sum to four.
  Pair coverage gives r_y>=4 and twelve 5-blocks have degree sum 60. · Every root link of a hypothetical 30-block C(15,6,3) cover. · proved
• The residual-budget inequality follows from fixed target degrees alone.
  Human proof plus exhaustive generator and independent checker. · All five degree types and all degree-capacity-respecting partial or complete links. · proved
• The saved receipt covers 2380 labelled degree vectors and 33320 endpoint cases.
  Hash-bound generator receipt and independent partition reconstruction. · Weak compositions of four into fourteen coordinates. · computed

• Use the residual-budget inequality as an additional pruning filter in a fixed-degree root-link canonical augmenter.
  All five forced degree types and every partial or complete state respecting target degree capacities. · The filter is algebraically implied by the maintained degree capacities. · artifacts/epoch10-20260808/root_link_filter_redundancy_lemma.md and independently checked receipt · A materially different predicate involving extension information not implied by fixed target degrees.

• Extension-aware missed-triple residual-capacity filter
  It uses information absent from the redundant degree-only inequality and may reject links that cannot be completed by eighteen residual blocks. · For each point y, compute link-uncovered non-root triples incident with y and test the sound capacity bound supplied by residual degree 12-r_y. · high · open
• Degree-preserving constructive local search
  A 30-block witness settles the target immediately and is independent of catalogue feasibility. · Run matched deterministic seeds against unconstrained block replacement under identical evaluation budgets. · normal · open
• Small unfiltered nauty root-link calibration
  It directly measures catalogue growth if no useful prefilter survives. · Generate a hash-bound, independently replayed frontier under a small fixed node cap. · normal · open

Objective: Find a nonredundant extension-feasibility discriminator for root links.

First action: Prove and audit whether the number of link-uncovered non-root triples incident with y can exceed the residual covering capacity 10(12-r_y).

Stop condition: Redirect if the candidate bound is implied by degree capacities or rejects no bounded control; advance only after an independent checker exhibits a legal state it prunes.

• Derive a missed-non-root-triple capacity bound using exact residual degrees 12-r_y.
• Test whether that bound rejects any degree-feasible synthetic or complete link before implementing canonical augmentation.
• If no nonredundant predicate survives, compare a small unfiltered nauty catalogue calibration with matched degree-preserving constructive search.

• 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/math/9502238 ↗
• https://arxiv.org/abs/2607.23766 ↗

GPT-5.6 Sol was principal investigator. GPT-5.6 Terra delegates supplied advisory challenger and experiment-design memos; Sol independently rederived and rejected their selected filter hypothesis, and model agreement was not validation. Deterministic tools were Python 3.12.3, the computational-researcher experiment harness, SHA-256, and Git inspection. A bounded web status query was attempted; same-day preserved source audits supplied the usable status baseline. No SAT solver, CAS, proof assistant, DRAT/LRAT checker, or spawned sub-agent was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

788.0s

Review state

not a result claim

Attempt ID

covering-c1563-20260808-214507-29230d

No human review recorded.