{
 "tm": "1RB1LB_1RC0LA_1RD0RE_1LA0LB_1RF---_1RB1LD",
 "label": "W7-2",
 "status": "OPEN",
 "stage": "informal_proof",
 "updated": "2026-10-14",
 "confidence": "high",
 "confidence_note": "both starts covered at the informal level by checked symbolic runs (check_proof.py ALL OK); soundness rests on scripts/engine.py, validated by section B, not yet by an independent implementation or Rocq",
 "holdout_line_740": 175,
 "reason": "proof.md (start-parametric): INV = {N(Y): Y >= 22} u {Q(W): W >= 14}; Lemma N: N(Y) -->+ N(2^18 Y + 32859022); Lemma Q: Q(W) -->+ Q(2^18 W + 34431880); both proved by symbolic runs with empty side-condition logs, no residue condition. Start A (175): blank -->* N(508932094) (= qsim M(508932080) + 14). Start D (489): blank -->* D(X0, 10456559309013950571, 939468133961604901), Lemma D: D(X, Y2, Y1) -->+ D(2^20 X + 349479900, Y2 - 120, Y1 - 24) applied 39144505581733537 times, then the Y1-exhaustion run D(2^20 z + 349479900, 5759218639205926131, 13) -->+ Q(2^33 z + 23036877419765819664) for every z.",
 "siblings": [
  "1RB0RC_1LC1RC_1LD0RB_1LA0LE_1LF---_1LC1RA"
 ],
 "sibling_note": "489 = this table from start D (mirrored, renamed); canon(489,A) = canon(175,D). proof.md covers 489 too (start D enters cycle Q). Starts B, C, E, F are not on the 740 list; start F is upstream Eqv_v2.v TM595 tm (halting-equivalent to 175, unproved).",
 "upstream": "No upstream proof of any start; Eqv_v2.v TM595 links start F to 175 only.",
 "next": "Formalize: two cycle lemmas (15 segments each, Diff-rule families + 7 shift rules), Lemma D with its iteration, and the opening runs (657,961 and 8.9M + 339,452 engine moves); a trace-replaying tactic or reflective checker is the realistic route. Checkpoint B review of proof.md first (non-blocking).",
 "proof": "proof.md",
 "check": "check_proof.py (ALL OK, work/check_proof_all.txt)"
}