W6-5 · 1RB0LB_0LC0RE_1LA1LD_0LB1LD_1RA0RF_1RA--- (740 line 333)

Status: CRYPTID_CANDIDATE (observe, 2026-10-14, about 2 h). Confidence on the mechanism: med. Class: sheet "Chaotic Bell Class 4" (results.csv note "Possible bouncer"). Ours: layered Bell / budget-eating counter whose layer law is x4/3 with a mod-3 branch. Viewer: https://bbchallenge.org/1RB0LB_0LC0RE_1LA1LD_0LB1LD_1RA0RF_1RA---

Checks

• Byte-exact on data/holdouts/BB6_holdouts_740.txt line 333 (also 778 list line 355).
• No claim: sheet results.csv has the class and "Possible bouncer" only; discarded-machines.csv says "unanalysed"; direct-simulation.csv lists it as not simulated to 1e15. No hit in data/discord/*.txt.
• coord/claims.tsv: no earlier line for this tm or for the class; claimed as Wave 6 W6-5. Astra's equivalence-frontier.json lists line 333 with proofs: [] (inventory only, no claim).
• Siblings (same table, canon up to renaming + mirror, from all 6 starts): none on the 740/778 lists except start A itself. Starts C, E, F are in eqv_1590 lines 122, 128, 132 (276's equivalence group, as the critic said); the machine itself is eqv_1590 line 1169.
• Family (critic's W6-5 group): 479 and 145 share one table (145 = 479's table from B). 333, 683 and 276 each have their own table. The critic's "record twins" claim (same skeletons, time-shifted) was not re-checked here.

Halting condition

F is entered only by E1 (0RF), and F1 is the missing transition. E is entered only by B1 (0RE). So the machine halts exactly when B reads 111 moving right: B> 1 1 1.

Mechanism (three levels)

Words: every long region of the tape is a power of one of four periodic words: - H6 = rotations of 110000 (100001, 000011, 011000, ...), - K6 = rotations of 110010 (001011, 100101, 010110, ...), - P4 = rotations of 1100 (1001, 0011, ...), the unary round counter at the right end, - P3 = rotations of 110.

1. Trip level. The head shuttles between the right end and an active boundary. Three short trips only cross the counter 1001^c (D sweeps it unchanged: 1001^n <D -> <D 1001^n) and re-phase the block next to it. The fourth trip crawls left through the budget region with a local zig-zag and converts one block at the boundary. Fig cycle_closeup_P shows one such 4-trip cycle.
2. Phase level. Each phase converts a budget region one block per cycle and adds 2 blocks to the counter. Three cycle rules, all validated from random instances (rulefit check): - R1 (K6 eats H6, e.g. 7.2e9..1.33e10): 0^inf 1011 110010^a 1^2 0^4 1101 100001^(b+2) 1001^c A> 0^inf -> ... 110010^(a+1) ... 100001^(b+1) 1001^(c+2) A>, 60/60 (b+2 >= 2, any c >= 0; also 36/40 with b+1 >= 1, all 4 failures at b = 0, the last block, which is the phase end). - R2 (the 1e8 hub): 0^inf 1011^3 001011^a 0^4 110^2 000110^(b+2) 01^2 1 0^4 110010^(p+1) 110000^(q+3) 1^3 01 1001^c A> -> a+1, b+1, c+2, 40/40. - R3 (the 5e8 hub, two 12-blocks Y = 010110000110 become one 24-block X = 010110010110000110000110): 0^inf 110^3 X^a 010110^2 000110^3 110 Y^(b+3) 000110^(p+1) 01^2 100001^(q+1) 1001^c A> -> a+1, b+1, c+2, 40/40. - In each phase the sum (grown + remaining) is conserved and the counter value is 2 x (blocks converted) + const (phase 6: c = 2g + 2 or 3 at the A record).
3. Epoch level (the stop). When a budget runs out, the counter (about 2n P4 blocks = 8n cells) is re-read as a new 6-cell layer of about 4n/3 blocks, and the next phase depends on n mod 3. Experiment (scripts/vary.py, work/budget_residue_experiment.txt): the real phase-6 configuration at 1.29e10 with the remaining budget changed so the phase budget is n = 9996..10001, each run 1.3e9 steps, record-aligned:

So the layer law is n' = (4n + r)/3 with r depending on n mod 3 (r = 7 for residue 2; 5 for residue 1 as read at that snapshot), and the residue picks one of three successor phases. Main run: 9996 -> 13333 -> 17774/17775 (4/3 each time, offsets +15 and -7 on 4n).

Phase table from blank (scripts/layers.py on work/snapshots_every_1e8_to_1e11.jsonl; boundaries at 1e8 resolution)

Template check

• No proved table within 5 transitions (critic). Architecture comparison with W5-3 (1RB1RA_1LC1LE_1RF1LD_1RE0LD_0LB0RA_---0RC.v, read): W5-3 has walk lemmas (Wk, W2Q: a defect walks through 10 pairs) plus a binary counter (BinInc) and five eat cases closed by one size bound. Our R1-R3 are the same kind of linear walk lemmas, but our counter is unary and our phase ends feed a x4/3 layer law with a mod-3 branch; W5-3/W5-4 have nothing like it. Template applies: partly (round level only).
• 683's table halts from its B (RWLAccHaltv6.v, per the wave-6 ranking; not re-checked). Does not transfer.

Cryptid check

Pre-registered W6-5 stop rule: "the epoch law is x m/k with a residue split: cryptid protocol". Met: m/k = 4/3 and the residue mod 3 selects among three successor phases, two of which reach back into older layers. Rules formalized (R1-R3 + the phase-end table above), flagged, stopped. No halting branch seen: halting needs B> 111, and no phase seen produces it.

Files

• scripts/longrun.py (tmsim snapshots every K, compressed), align.py (run to next right record), regions.py / layers.py (region table in blocks), vary.py (budget residue experiment), shift.py (shift-rule finder).
• work/: snapshots_every_1e8_to_1e11.jsonl, layers_every_1e8_to_1e11.txt, budget_residue_experiment.txt, phase6_record_aligned.jsonl, rulefit.txt, track_1e9.txt, siblings_canon.txt.