LESR · Root 6217 local analysis (Paper 09C–09U)
BCODR-LUC-06 · Frontier spine closure against the A_ref tail
Neo.K / Aletheia
Recovered 2026-10-07
Frontier Spine Closure Against the A_ref Tail: Permanent NOT-F3 Correction, Five New Tight-Reference Certificates, and the 9→1 Collapse of the Selected Spine
Corrects Paper 08's parent ledger: of the 200 Cycle-11 root-6217 parents, 8 lie entirely outside the F3-far target domain (permanent NOT-F3: 106, 110, 127, 132, 135, 162, 165, 166) and must not be reopened; the 5 earlier A_ref parents stay; and for five parents that had been closed only against A₃⁺ (101, 103, 104, 164, 167) new finite certificates against A_ref = 0.8349865 are produced (parent 164 needs 10,651 nodes, with minimum slack about 8.63e-9). The corrected ledger is 200 → 192 → 187 → 182; the selected BCODR frontier shrinks from 9 parents to 1 — root 131, which already has a numerical candidate A ≈ 0.8349862484 < A_ref at Cycle 17 and so cannot be pruned by A_ref.
At the authors' own research authority the ledger of active tail parent responsibilities is corrected from Paper 08's 195 to 182 (a parent-level accounting statement that does not prove the tail closed); root 131 is a candidate that A_ref cannot prune, and the global shape of root 6217 stays open.
This is one of the files the 'missing' lists named; it was recovered only on 2026-10-07: GPT first recovered the paper and two JSON files, and Neo then supplied the original package zip (8 files; the paper, the two JSON files and the verifier script are byte-identical to what had been recovered, and there are also a relation graph, a STATE file and a VALIDATION file). The paper's body is mostly English. The JSON's structure was checked here (the leaf paths of the five trees form complete binary partitions; node, leaf and minimum-slack figures agree with the paper's table); each leaf's area lower bound needs the UESFCM Cycle 17 kernel to replay, which is in no recovered package and was not re-run here. The package's VALIDATION.json records the authors' own runtime replay (PASS, 11,679 nodes, minimum slack 8.63e-9; node and leaf counts agree with the structure checked here), not an independent replay, so the PASS remains the authors' statement only. 'Closure' and 'certificate' are research-level words; a publication-level interval and rounding audit is, by the paper's own account, a later obligation.