1RB0RF_1RC0LD_1RD0RA_1LE0LC_1LB0LE_0RC---

Status: STUCK (parked at observe, 2026-10-13; confidence low) Label: B-4 (BEC sweep pick; 740 list line 239; 778 list line 256) Class guess (agent / Dennis): left-wall binary counter eating a 6-cell reservoir; overflow fossilizes a binary residue as junk that the next cycle re-reads (sheet: Bell eats counter) / - Viewer: https://bbchallenge.org/1RB0RF_1RC0LD_1RD0RA_1LE0LC_1LB0LE_0RC---

Pre-checks

• Byte-exact match on data/holdouts/BB6_holdouts_740.txt line 239.
• No claim: not in data/discord/*.txt. Sheet: Results row has class "Bell eats counter" with empty status/notes/done-by; Classifications column "Bell eats counter".
• Claim line already present in coord/claims.tsv (claude, machine, 2026-10-13, BEC sweep).

Family (canon up to renaming + mirror, all 6 starts)

• 740 list: only this machine (start A). No siblings.
• 2026-10-07_eqv_1590.txt group (lines 650-652): this machine, start B 1RB0LC_1RC0RE_1LD0LB_1LA0LD_1RA0RF_0RB--- and start C 1RB0RE_1LC0LA_1LD0LC_1RA0LB_1RD0RF_0RA---. Both are Eqv_v2.v tm definitions (upstream equivalences to this machine), not on the 740 list.

Halting condition

F1 is the only undefined cell. F is entered only from A1 (0RF), so the machine halts iff A reads 1 with a 1 on its right (A> 1 1).

What the tape looks like

Almost all of the tape is one of two fields: - a 3-cell field (011)^n (any phase), and - a 6-cell sea (010001)^m, which carries one phase defect (an extra 0 or an extra 1).

At the left wall sits either a counter (011)^a (a binary counter, 3 cells per digit) or a junk word J of a few dozen cells.

Rules found (validated by direct simulation from constructed configurations)

• P1 / P0, counter pass (40/40 each; a = 0..9, b = 1..2^a+60, c = 2^a..2^a+300): 0^inf <D (011)^a (010001)^b x (010001)^c 0^inf x = 1 (P1) or 0 (P0) -> 0^inf <D (011)^(a+1) (010001)^(b+2^a) x (010001)^(c-2^a) 0^inf if c >= 2^a One pass = 2^a sweeps; each sweep moves the defect one word right. Pass time grows ~4x per digit. The real orbit has b = 2^a + k with k = 5 or 8 (history: k = 5 in the 5.66e7 cycle, k = 8 in the 8.33e7 one). Rulefit's "closed" table E1(2n, 632-n) -> E0(2n+1, 632-n) is this pass in one cycle, with that cycle's reservoir built in.
• O, overflow (24/24; a = 0..7, c < 2^a, both defect types): the next right record shows 0^inf J (011)^(2b+2c) C> 0^inf with |J| = 3a+4 cells The 6-cell sea is re-laid as a 3-cell field of the same length; J holds the counter's partial state. J's content is not yet characterised. So the counter runs from a0 to A, where c0 + 2^a0 lies in [2^A, 2^(A+1)), and the residue r = (c0 + 2^a0) mod 2^A is left behind in J.

Cycles, plateaus and spurts (observed, not validated as rules)

Cycle start = the first right record of each burst: 0^inf J (101)^n B> 0^inf. - Ordinary cycle: J (101)^n -> J' (101)^n', n' - n = +9..+75. At the 34k level: +72, +31, +31, +36, +66, +34, +72, +40, +72, +40, +28, +32, ... Inside one cycle (Fig 3): several junk-processing sweeps with right records (3 cells each), then a counter run (rules P) until overflow (rule O). - Spurt: 0^inf 1 0^3 (011)^(2n+k) C> 1 0^inf, k = 12, 14, 12, 12, 24, at 1.13e7 (n 619 -> 1250), 3.05e7 (1259 -> 2532), 3.27e8 (2841 -> 5694), 9.89e8 (5763 -> 11538) and 1.877e10 (12639 -> 25302). - Plateau lengths (cycles between spurts): 1, 1, 9, 3, 31. Span: 3.5k, 7.4k, 16.7k, 34.2k, 75.0k. - J at the 34k level is 25-42 cells (about 3A+4 with A = 11-12), e.g. (100000100)^2 0^9 1 0^5 1 0^7 1, 1 0^4 (010)^2 (000010)^3 (010000)^2 1.

Verdict for this stage

The micro level is clean (P0, P1, O). The macro level is not: what the next cycle does depends on J, i.e. on a ~12-bit binary residue of a slowly growing n, and the spurt is one residue outcome. Plateau lengths 1, 1, 9, 3, 31 show no pattern. Per the stage brief ("park if the spurts look residue-driven") this is parked as STUCK.

Not flagged CRYPTID_CANDIDATE: the residue map is not formalized, so whether it is pseudo-random is open. It could still be a clean binary rule (e.g. J = binary digits of r, the spurt iff r = 0 or r = 2^A - 1). That is the one test worth funding.

Template comparison

• W4-3 (ours, killed, d = 4 from start A): multi-level counter on 00/11 defects with inert fossils (lengths matter only mod 4). Here the fossil J is re-read and decides the next cycle. Does not transfer.
• SOMDC_Class1.v nonhalt (d = 4, start F): a single structural counter, no overflow-to-junk step. Does not transfer.
• W4-8 (parked fossil bouncer) has the same kind of problem: deposits whose fate depends on residues.

Figures

• img/default_site_1e4.png: site default view.
• img/span_logt.png: span vs log10(step) to 2e10, from the record log (custom chart).
• img/fieldmap_cycle.png: one ordinary cycle, every 40,000 steps from step 1.1e8, 1 px = one 6-cell block coloured by content.
• img/fieldmap_spurt.png: the spurt cycle 2.619e8 to 3.279e8, every 100,000 steps.
• Pre-existing img/default_site.png, img/records_L_3e8.png and img/viewer.html came from the sweep ranking; not used by the card.

Scripts (scratchpad, not shipped)

Rule checks: scratchpad/b4/scripts/rule_P.py (P0/P1/overflow), rule_double.py (first P1 probe). Figures: figs.py. Cycle starts: bursts.py over the 2e10 record log.