/machines/1RB0LE_1LC1RD_1LA0RB_1RC1RB_1LF0LC_---0RC/notes.md · raw

1RB0LE_1LC1RD_1LA0RB_1RC1RB_1LF0LC_---0RC

Status: STUCK (stage informal_proof: edge lemma open; see proof.md) Class guess (agent / Dennis): Bouncer + Chaotic Edge: translating period-10 bouncer, and a one-sided chaotic edge map on the right / _ Spreadsheet notes / Discord thread: Results row 903 has a blank status, class "Bouncer + Chaotic Edge", and no notes, sources, links, strikethrough or comments. The only Discord mention is mxdys's UBRRBA_TODO list (2026-08-24); Dennis ruled that list fair game. It is not on dyuan01's longitudinal list. Near-twins #34 1RB0LC_1LC0RE_1RA1LD_1LA1LC_1RF0RA_---0LA and R6 1RB1LD_1RC0LA_1LA0RE_1LB1LA_1RF0RB_---0LB are mirror images with the same period-10 bulk words. Viewer: https://bbchallenge.org/1RB0LE_1LC1RD_1LA0RB_1RC1RB_1LF0LC_---0RC

Observation

Diagrams are in img/. The most telling one is edge_cycle_records.png (one row per bounce). Full viewers: img/viewer.html and img/edge_cycle.html.
How each card diagram was made (re-run 2026-10-10: byte-identical PNGs; label fields in observe.json and scripts/make_observe.py come from these runs). All via tools/diagram.py "$TM":
edge_cycle_records.png: --mode records:L --steps 1.2e6 --scale 2 --from-config @work/C20_D0.cfg. Constructed start 0^inf <A (1101101101)^20 X0 D0 0^inf: D0 = work/D_cycle0.txt, the real tail at step 784,041, but with bulk a=20 instead of the real 59 (the probe map does not depend on a). 321 rows = 321 bounces; cells -320..725 relative to the start head.
records_L_1e8_right1200.png (new, replaces records_L_1e8_frame_right.png on the card, where the band was a 5% sliver): --mode records:L --frame right --width 1200 --steps 1e8, i.e. the right 1,200 columns of the old image, pixel for pixel.
blaze_1e7.png: --mode blaze --steps 1e7 --as-site. default_site.png: --as-site.
At 1e9 steps the span is lo=-13959, hi=6604, with 14,332 nonzeros. Both edges grow like √t: lo ≈ -0.44√t, hi ≈ +0.21√t. There is no halt.
Bulk. The bulk is (1101101101)^a, anchored at the left wall. It translates 1 cell left per bounce: each bounce adds one left record, in state A.
Right sweep: 12 steps per block.
Left sweep: 58 steps per block.
So one bounce costs 70a + O(1) steps.
7-bounce cycle. This holds exactly from step 784,041 (a=59) to at least 1e9 (1,951 cycles):
C(a, D) := 0^inf <A (1101101101)^a X0 D 0^inf
X0 = 110111100110011101100100100111101100100110110111010011 (54 cells, fixed).
Six bounces never touch D. One bounce (the "probe") enters D.
The cut moves +3 cells per cycle, so the bulk gains a block and the junction eats 3 cells of D.
Probe interface. At the boundary one cell left of the X0|D cut (between the last two cells of X0), the head makes 16 round trips (32 crossings), identical in every cycle (3,000 checked, check IFACE): (in, out) = (B,C)(D,E)(C,A)(D,C)(B,C)(D,F)(C,A)(B,E)(D,E)(B,C)(B,E)(B,C)(D,A)(C,A)(C,A)(B,C). At the cut itself the sequence is not fixed (2 distinct sequences). (Corrected 2026-10-10; this line previously said "crosses exactly 16 times".)
Deep tail D.
Its length is 144–564 cells over 5.5·10⁶ cycles (edge map), with no drift.
The probe reaches 45–350 cells into D. The right edge grows in jumps of 30, 60, 90 or 120 cells (about 1 cycle in 13).
The first 24 cells of D take only 8 values. Deeper cells are chaotic: 3,786 distinct per-cell crossing sequences over 120 cycles, with no saturation.
Minimal forbidden words of D (length ≤ 8): 000, 0101, 01101111.
Edge map (scripts/edgemap.c): iterating D → P(D) at a=5 reproduces the real orbit's D at cycle 1951 (step 999,751,742) exactly.
Real step at cycle n = 784041 + E(n) + 490·Σ(a_k−5), with a_k = 59+k. This is exact at n=1951.
Run to 5.5·10⁶ cycles (≈ 7.4·10¹⁵ real steps; stopped for budget): no halt, no junction break, and no repeated D (exact hash).
Halting. The machine halts only via 001 C> 0 (C0→A1→E0→F0). This has not occurred.
qsim (block 3) gives no acceleration: 200k loops reach 1.16M steps, with 3 trivial rules. rulefit found no validated rules: it fits whole-tape hubs, and the edge is chaotic.

Candidate rules

All of these were validated by scripts/validate.py → work/validate.json, by direct simulation at random small and large values. D is random or taken from the orbit.

rule	from → to	steps	tests
wall	`0^inf <A r` → `0^inf 1 B> r`	1	30/30
right sweep	`1 B> (0110110111)^n` → `(0111101101)^n 1 B>`	12n	16/16
left sweep	`(1011110110)^n 11110101 <E 0` → `11110101 <E 0 (1101101101)^n`	58n	16/16
bounce k→k+1, k=1..5	`<A blk^a X_k D` → `<A blk^(a+[k=5]) X_(k+1) D` (D untouched, any D)	70a+β_k, β=(9,473,55,49,77)	80/80
cycle close k=6	`<A blk^a X6 011 D` → `<A blk^a X0 D`	70a+9	16/16
probe k=0	`<A blk^a X0 D` → `<A blk^a X1 011 P(D)` (P independent of a)	70a + c(D), c ∈ [2235, 10775]	180/180 on orbit D; 25/25 step law
halt	`001 C> 0` → halt	4	20/20
cycle	C(a,D) → C(a+1, P(D))	490a + O(\|D\|²)	1951/1951 real cycles

blk = 1101101101. The junction words (fixed in all 1,944 cycles checked to 1e9):

X0 110111100110011101100100100111101100100110110111010011
X1 1001001001100100100100110110110011101100100110110111010
X2 11011001001100100100100110110110011101100100110110111010
X3 101110100110110010011101100100100111101100100110110111010
X4 1101001101100100110011101100100100111101100100110110111010
X5 11011011001001100110011101100100100111101100100110110111010
X6 10011100110011101100100100111101100100110110111010

What killed the alternatives: - Random iid D: 104/200 break the cycle (the junction changes). There are no halts. - Random D from the SFT avoiding {000, 0101, 01101111}: 76/300 break in one cycle, and 8 of the survivors leave the SFT. That SFT is not closed; the invariant must be finer.

Checkpoint A (Dennis)

(pending)

Informal proof

2026-10-10: proof.md written. It is complete except the edge lemma (E): a closed language L for the tail D under the probe map, which is still open. Status is STUCK at informal_proof. - Proved rules (check_proof.py, all PASS, unknown-context checks): - the shift rules RS and LS, and the wall rules WS and WE; - the junction rules J1–J6; - the D-free bounces B1–B6, with step counts 70a+β; - CYC, which is conditional on (E); - INIT: c0 reaches C_0(59, D_0) in 784,041 steps. - Refuted: orbit-learned SFT_k for k ≤ 22 (junction breaks). k-factor sets do not saturate. - 2026-10-10 skeptic revision (review log in proof.md §9): (E) restated honestly as the whole difficulty and sharpened to (E′), a one-sided right-part system with the fixed 16-round-trip protocol (checks IFACE, E′). The SFT refutation was extended to k = 24–36 with verified chains (work/sft_refutations/, scripts/edge_sft/verify_refutations.py). Plain n-gram CPS does not close, either on the whole machine (n ≤ 26) or on the edge system (n ≤ 24; scripts/edge_cps/). Init is routine (Bouncer_v3 pattern), with an earlier entry C_1(58, 011 D_0) at 758,939. §7 citations fixed. Still STUCK; the priority call (more budget on E′?) is with Dennis.

Formalization log

Outcome

Card data pass (2026-10-10)

The card now shows at most 3 short mechanism bullets and yes/no questions that point at figures by number (primary figures first). The text they replaced is kept here. - Figure order on the card: Fig 1 = img/edge_cycle_records.png, Fig 2 = img/records_L_1e8_right1200.png, Fig 3 = img/blaze_1e7.png, Fig 4 = img/default_site.png (Figs 1-3 primary). - Mechanism, full observer version: - Bulk (1101101101)^a sits on a left wall; each bounce shifts it 1 cell left (70a steps). - A fixed 54-cell junction X0 cycles through 7 shapes; the bulk gains 1 block per 7 bounces. - 6 of 7 bounces never touch the tail D; the 7th sends the same 16 head crossings into D. - D stays 144-564 cells (no drift); right edge grows in 30-cell jumps; content chaotic. - Only way to halt: C reading 0 with 001 on its left (C0, A1, E0, F0). Never seen. - Checkpoint questions before the rewrite (some were decisions, not questions about a figure): - edge_cycle_records.png: agree the striped bulk and the junction stair are routine, and only the chaotic tail on the right is hard? - records_L_1e8_right1200.png: does the right band look bounded to you, so we hunt a regular-language invariant for D rather than a counter rule? - OK to spend the next stage (2h) searching for a closed automaton for the edge map D -> P(D) outside Rocq first?

Decision (2026-10-10)

Question: Continue investing in the edge lemma (E') or park the machine? Answer: park (Park: STUCK at informal_proof, keep proof.md as the conditional reduction). Dennis: go with all recommendations (2026-10-10). Parked by Dennis 2026-10-10 (decision queue: park; proof.md kept as the conditional reduction).