{
 "tm": "1RB0LC_1RC0RA_1RD0RF_0LE---_1LB1LA_1LD1RA",
 "bucket_reason": "Confidence is still med after the funded hub_invariant stage. The hub invariant H* is written out and passes the decided closure test, but it closes only with a margin that keeps small-value corner events out.",
 "question": "Fund one stage to rule #16's small-value corner events and pin the block-seed clause of H*, so that H* closes without a margin, before proof.md?",
 "options": [
  {
   "id": "corner_rules",
   "label": "One stage: rule the corner events",
   "consequence": "About 2 h, 1-2 light processes, no Coq. For each of the 9 corner families (Push with d<4 or p<3, ToEdge1 d<4, P-mode right end or RightEndP with P<4, start with P0<2, hub a0<3, an eat that finishes a chunk exactly), derive the outcome by exact simulation from random instances with large other values, add it to the macro simulator, and check that it lands back in H*. Also derive the short transitions (collapse completion, Absorb start) in closed form and narrow the seed clause to linear relations. Target: 0 leaks in 10^4 orbits x 40 traversals with no margin, at small levels too. Exits: closed -> proof.md; a corner family that leaves H* for good -> park."
  },
  {
   "id": "proof_now",
   "label": "Write proof.md now",
   "consequence": "Start the hub-to-hub induction on H* (lemmas G, C, S on top of the validated macro rules) and list the 9 corner families and the seed clause as open lemmas. The proof stays incomplete until they are ruled."
  },
  {
   "id": "park",
   "label": "Park",
   "consequence": "Status becomes parked at hub_invariant. H*, the closure tests and the corner census stay in notes.md and scripts/. #39 and R7 lose their lead."
  }
 ],
 "recommended": "corner_rules",
 "rationale": [
  "H* closes on 10^4 random hubs over one traversal, and over 40 traversals at levels >= 10^9.",
  "Only 9 small-value corner families and a too-wide seed clause leak; each has one small parameter.",
  "The reference passes all 175 corner events tested; the facts are linear, so not cryptid-like."
 ],
 "evidence": [
  {
   "kind": "fact",
   "text": "From blank, all 12,000 right ends are in H*. Every transition is growth (shift + reflection), collapse (B(1) < 0) or a short seed.",
   "href": "scripts/hubinv_H_blank_12000_HR.txt"
  },
  {
   "kind": "fact",
   "text": "One traversal: 10,000/10,000 random H* hubs are ruled and land in H* (margin 64). Over 40 traversals at levels >= 1e9: 10,000/10,000.",
   "href": "scripts/hubinv_H_R1_mu64_902.txt"
  },
  {
   "kind": "fact",
   "text": "Without the margin, 104/10,000 orbits from small levels hit a corner event (9 families, 518 in a census of 4,000 orbits).",
   "href": "scripts/hubinv_corners_711.txt"
  },
  {
   "kind": "fact",
   "text": "Accelerated simulator: 300 hubs x 2e9 steps, 0 halts, right ends on the macro orbit in order; 175 corner instances, 0 halts.",
   "href": "scripts/hubinv_accel_704_R_v2.txt"
  }
 ],
 "effort_if_yes": "One stage: about 2 h of agent time and 1-2 light processes (macro simulator, exact simulation, accelerated simulator). No Coq.",
 "updated": "2026-10-10",
 "answer": {
  "option": "corner_rules",
  "note": "Dennis: go with recommendations (2026-10-11)",
  "date": "2026-10-11"
 }
}