Built and independently checked a block-identity-preserving two-link calibration using ordered endpoints (1,15) of the maintained 55-block cover.

two-link amalgamation

Extract both literal point links and their exact common triple family; independently reconstruct them with bit masks and reject semantic mutations.

Hypothesis: A block-identity-preserving representation exactly reconstructs the ordered point-link pair (1,15) in the maintained 55-cover and rejects mutations of an endpoint, link block, or shared triple.

Test: Generate the canonical two-link payload twice, independently reparse the original cover using bit masks, compare both literal links and common blocks, and require rejection of three hash-rebound mutations.

The deterministic producer, materially different mask checker, source-cover verification, and negative controls establish that literal link and common-block identities are represented correctly. The tested object comes from a 55-cover and has no global 54-cover force.

• The maintained 55-block source covers all 455 triples.
• Points 1 and 15 each occur in 18 source blocks.
• Their extracted links each cover all 91 pairs of the appropriate 14-point ground set.
• Their pair multiplicity is six and their literal shared triple families agree.
• The endpoint, link-block, and shared-triple mutations are rejected.
• No case in the hypothetical 54-cover frontier was excluded.

• python3 scripts/run_two_link_control_v1.py --source sources/ljcr-c1553-55.txt --output-dir artifacts/two-link-control-20260809
• python3 checkers/check_two_link_control_v1.py --source sources/ljcr-c1553-55.txt --instance artifacts/two-link-control-20260809/two-link-1-15.json
• python3 checkers/test_two_link_control_mutations_v1.py --checker checkers/check_two_link_control_v1.py --source sources/ljcr-c1553-55.txt --instance artifacts/two-link-control-20260809/two-link-1-15.json
• sha256sum -c artifacts/two-link-control-20260809/manifest.sha256

• .proof-experiments/20260809-003458-ae8e6b: return code 0 in 0.576 seconds; two 18-block links, 91/91 covered pairs, six common triples, byte-identical regeneration, and all mutations rejected.

checkers/check_two_link_control_v1.py uses integer masks and reparses the source independently of the tuple/set producer; checkers/test_two_link_control_mutations_v1.py requires rejection of three semantic mutations.

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 literal compatibility of adjacent optimal links is more discriminating than aggregate root-cell totals -> this epoch validated the required literal representation but did not yet test pruning.

• The copied Carmine Iorio source contains 55 distinct five-subsets covering all 455 triples.
  Independent mask checker and existing tuple/set checker; source SHA-256 e8188ed441e9548b6e7bb1f8d6d70d0c70007d9ad758157033209f9811f6f5d2. · sources/ljcr-c1553-55.txt · computed
• The ordered point-link pair (1,15) consists of two 18-block C(14,4,2) covers with six exactly shared triples.
  artifacts/two-link-control-20260809/independent-check.json · The displayed maintained 55-cover only. · computed

• Infer existence of a 54-cover from the compatible control pair.
  This epoch's ordered pair (1,15). · The pair was extracted from a 55-block cover and no 54-block completion was constructed. · artifacts/two-link-control-20260809/two-link-1-15.json · A directly checked 54-block cover containing a compatible literal pair.

• Two-link stabilizer and completeness calibration.
  It is the cheapest gate needed to give any later SAT or UNSAT link-pair result a defined exhaustive scope. · Enumerate the skeleton/root/ordered-edge stabilizer twice and compare group elements and induced common-family orbits. · high · open
• Proof-producing OPB calibration.
  A verified RoundingSat/VeriPB/CakePB stack remains the most direct route to admissible cube exclusions. · Run the saved C(5,3,2) cover and equality-format controls after the pinned toolchain becomes available. · high · open
• Outside-subset realization.
  It introduces actual subset identities absent from the exhausted root-cell relaxation. · Encode one surviving profile with exact outside point/pair degrees and direct witness decoding. · normal · open

Objective: Establish a completeness-preserving canonical action for literal adjacent-link triples (L_0,L_1,H).

First action: Read the partition-[15], representative-mask-31 entry in artifacts/joint-orbit-census-20260808/manifest.json and enumerate the stabilizer fixing ordered edge (0,1) in two independent ways.

Stop condition: Redirect if the action, orbit coverage, or finite batch boundary disagrees between implementations.

• Independently enumerate the stabilizer of the partition-[15], root-mask-31 skeleton with ordered edge (0,1).
• Cross-check its induced action on literal six-triple common families and define a finite completeness-preserving first batch.
• Only then test actual 6,6,5^12 adjacent-link pairs, decoding SAT literally and requiring replayable proofs for UNSAT.
• Retain proof-producing OPB calibration as the immediate alternative if the link census cannot be bounded.

• 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 and audited the epoch. GPT-5.6 Terra delegates supplied challenger/prior-art and experiment-verification reconnaissance; their agreement was not treated as validation. Deterministic Python 3.12.3 code performed extraction, checking, mutation testing, hashing, and experiment recording. Web search checked current primary/maintained sources. No SAT solver, CAS, proof assistant, lab job, or unpinned proof toolchain was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

816.9s

Review state

not a result claim

Attempt ID

covering-c1553-20260809-004157-1f6df1

No human review recorded.