{
 "tm": "1RB0LC_1LC0RE_1LA1LD_1LA1LB_0RF1RA_---0RE",
 "label": "W5-6",
 "status": "STUCK",
 "stage": "parked (funded stage3 ended at its stop rule)",
 "updated": "2026-10-13",
 "confidence": "med",
 "reason": "Parked 2026-10-13 (Dennis 2026-10-13: 'go with recommendations' -> stage3; its stop rule: no closed form after 2 h means park, with no further asking). Funded stage stage3 found no closed-form invariant. Greatest closed set n >= g(w) at 22 cells: 179,610 states, g = 1 for 178,926, max g = 16. Max g doubles every 2 cells (2/4/8/16 at 16-22 cells), and g is not a function of the 1-runs (at 20 cells, 130 states with runs <= 3 have g > 1). New exact object: the forward-least closed set (least n per cycle start from the real seeds) has 0 halts at 18/20/22 cells (5,071 / 14,547 / 40,998 states) and lies in a small grammar G* = (d|F)* (nothing | L with k0 = 1 | S 0^j 1 | L S 0^j 1). On it n >= Phi + 1 (30,242 / 30,242 parsable at 22 cells) and h >= 2^(D-1). The real orbit to step 1.78e7 lies in G* (204 / 204 cycle starts). But no window built from those bounds is closed: max(Phi+1, 2^(D-1)) gives 571 exits at 18 cells, the S-freeze bound still 472, and pure digit windows exit or halt. The coupling needs history (the n at the last odd eat / last L), which is not a function of the word. The bounded checks stay clean: 0 halts in every forward-least set and in every window closure that uses 2^(D-1) or the Phi bound. 280 (line 280) is parked with it.",
 "siblings": [
  "1RB0LC_1LC0RE_1LA1LD_1LA1LF_0RB1RA_1LC---"
 ],
 "family_note": "No other 740 entry shares 88's table (canon over all starts, renaming + mirror). 280 (line 280) is a different table with the same orbit: 88's B split by entry. The runs coincide while 88's F reads 1 and 88's B entered by D1 reads 0, so one orbit proof excluding both reads covers both machines.",
 "solved_relative": "1LB0RD_1LC1LE_1RA0LB_0RF1RC_1LC1LA_---0RD (IndBECv1.v:626, Others nonhalt17, start B of this table)",
 "checks": {
  "byte_exact_740": "line 88",
  "claims": "none (sheet results row 1010: class only; no Discord hit)",
  "upstream_9cf9e88": "not proved (only start B of the table)"
 },
 "stage1_wave5": {
  "date": "2026-10-13",
  "outcome": "progress",
  "regular_counter_language": "impossible (free closure halts: data/stage1/free_closure_any.txt, free_closure_min12.txt)",
  "token_rules": "T1-T4 validated 400/400 (scripts/stage1/tokrules.py)",
  "random_starts": "0 halts / 1,300 (data/stage1/randstart_*.txt)",
  "coupled_closure": "0 halts; value-window exits 2,875 / 42.0M checks at 20 cells (data/stage1/coupled_closure.txt)",
  "effective_value_window": "0 exits on 4,664 checked states at 18 cells; 6 near-boundary exits on 13,443 at 20 cells (scripts/stage1/cclos_veff.c)"
 },
 "stage2_wave5": {
  "date": "2026-10-13",
  "outcome": "progress",
  "confidence": "med",
  "phi_closed_form": "0 mismatches vs simulated v_eff on 2,416 / 5,989 / 15,089 parsable closure states at 16 / 18 / 20 cells (scripts/stage2/phi.h, cclos_phi.c)",
  "inc_on_G0": "exact at every length (cell-level carry argument, notes.md); 6,111/6,111 canonical G0 words to 16 cells (scripts/stage2/g0check.py)",
  "upper_window": "not invariant: odd eat on z = 11 0^m 1 gives Phi = 1; real run step 21,875 (1S001, n = 28)",
  "lower_window_phi": "n >= Phi - 3 not closed (8 exits at 18 cells, all pending-gain 11-top words); lambda up to 2 still exits",
  "n_ge_50_closure": "0 halts, 0 r=1 at 16/18/20 cells (1,880 / 6,819 / 22,786 states; 40.3M transitions at 20)",
  "greatest_closed_g": "20 cells: 56,845 states, g = 1 for 56,674, max g = 8 (long 1-run junk); real seeds inside (data/stage2/gfix20_n1.out)"
 },
 "next": "Parked; no new decision (stop rule). Reopen only with a history-carrying invariant: state (w, k0, n, m), where m is the n at the last odd eat, and window n >= max(Phi+1, 2^(D-1)), m >= 2^dS for the fresh S. Untested; see notes.md, Funded stage (stage3).",
 "funded": {
  "option": "stage3",
  "date": "2026-10-13"
 },
 "stage3_wave5": {
  "date": "2026-10-13",
  "outcome": "park (stop rule)",
  "confidence": "med",
  "greatest_closed_g_22": "179,610 states, 380.6M transitions, 971 unsafe, g = 1 for 178,926, max g 16 (data/stage3/gfix22_n1.out, g22_gt1.txt)",
  "forward_least_set": "0 halts / 0 r=1 at 18/20/22 cells (5,071 / 14,547 / 40,998 states; 126.2M transitions at 22), all in G*, n >= Phi+1 on all parsable states (scripts/stage3/hmin.c, data/stage3/hmin*.txt)",
  "junk_grammar": "G* = (d|F)* T, T in {nothing, L (k0=1), S 0^j 1 (k0=0), L S 0^j 1 (k0=0)}; real orbit to 1.78e7: 204/204 cycle starts in G*",
  "windows": "no closed window: 2^(D-C) exits for C=1..4 (halts for C=2..4); max(Phi+1, 2^(D-1)) 571 exits; plus S-freeze bound 472-483 exits and 268 states outside G* (data/stage3/window_tests.txt)"
 }
}