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1RB1LC_1RC---_1LD1LC_1RE0LC_1RF0RE_1RA0RD
Where it stands
Cryptid candidate, parked at the deeper analysis
Stopped by Dennis 2026-10-10: stays cryptid candidate, proof work parked with twin #27 (1RB0RA_1RC0RF_1RD1LE_1RE---_1LF1LE_1RA0LE). Halting reduces exactly to a validated 5-stage chain on the cluster 11.01.00, with arrival phases x,E,x,x,E (60/60 random instances halt).
Read the full status
Seeds of this chain keep forming in the disordered mixed zone: 11 by 2.45e10 steps, about 0.7 per doubling. Their later stages depend only on left-context mod-4 phases, and those match the generic coin rates (about 50/35/13/50%); nothing visible forces them. The step-12,975,111 near miss is seed #3, which got through x,E,x. Under the coin model each seed halts with probability about 1%: probabilistic, cryptid-like. Priority call for Dennis: stop, or continue by decoding the mixed zone (would need a rule forcing the stage phases).
Observe
Deepen
Informal proof
Rocq
About this picture
The standard picture (bbchallenge.org's Default view): each row is the whole tape at one step, time runs downward, and the head's path draws the pattern.
bbchallenge-defaultStart blankRows steps 0 → 10,000, top to bottomWindow cells −200..199, left to rightColors 1 0 or unvisited
Overview
In one sentence
Defect groups drift left at 1, 3/4, 1/2, 3/8.. cells/bounce: exact 16-bounce counter on left, chaotic edge on right
- Status
- Cryptid candidatedeepen2 · updated 2026-10-10Parked · Stopped by Dennis 2026-10-10: stays cryptid candidate, proof work parked with twin #27 (1RB0RA_1RC0RF_1RD1LE_1RE---_1LF1LE_1RA0LE). The 2 open questions are optional.idle since Oct 10 12:49 · status.json 2026-10-10
- Class
- Structural counter + chaotic edgeours: Structural counter + chaotic edge (sheet) · ours adds: drifting defect groups (hierarchical counter) fed by a chaotic right edge · med confidence
- On the list
- line 324 of
BB6_holdouts_663.txt· historical 740 line 358
Your calls on file 2
- parked
- Stopped by Dennis 2026-10-10: stays cryptid candidate, proof work parked with twin #27 (1RB0RA_1RC0RF_1RD1LE_1RE---_1LF1LE_1RA0LE).
- decision.json · answered 2026-10-10: stop
- Stop work on #6 and its twin #27: keep #6 flagged CRYPTID_CANDIDATE and park proof work, rather than spend a stage decoding the mixed zone? Decisions →
Mechanism
How it works: 3 notes
- Tape: (01)^n runs split by single defects (11, 00, 1111); the head zig-zags between them; the wall grows 2 cells/bounce.
- Defect groups drift left from the right edge at exact speeds 1, 3/4, 1/2, 3/8...; left block repeats every 16 bounces.
- The right edge is chaotic (hi ~ 20·sqrt(L)). Halting needs E to sweep an odd (10) run ending in 00: unseen to 1e11.
Figures for Checkpoint A
2 rows per wall bounce, every 4th cell; each white/black edge is a defect. Follow the edges downward.
bbchallenge-defaultStart blankRows the start, then one per new leftmost cell = 2 per wall bounceWindow cells -4,999..1,476, 1 px = 4 cellsColors 1 0 or never visited (top-left) line: head at the wall
Rows: (5,000 rows, steps 0..25,015,029; stopped at the 5,000-row cap); not evenly spaced in time · Window: only the first cell of each 4 is drawn · Colors: Only every 4th cell is drawn, so a
0101... run shows as solid white or solid black (its phase), and every white/black edge inside the tape is a defect (00, 11 or 1111)Right edge pinned, defects only (black). Compare the dense band at the right edge with the slanted lines leaving it.
customStart blankRows the start, then one per new rightmost cellWindow cells -1,599..0, 1 px = 2 cellsColors at least one defect (
00 or 11) among the pixel's 2 cells clean 0101... run not yet visitedRows: (2,819 rows, steps 0..969,848,428; no new right cell from then to 1e9); not evenly spaced in time · Window: counted from the right edge (each row's rightmost visited cell is 0, pinned to the last column; it is absolute cell 2,818 in the last row) · Colors: head not drawn; Each slanted line = a defect drifting left, away from the edge; the dense band at the right = the chaotic edge zone
More figures (3)Fig 3–5: Defects to 1e9, left wall pinned · Blaze, 100M steps · bbchallenge default view, first 10,000 steps
Fig 3 · Defects to 1e9, left wall pinned
Defect groups drift away from the wall; lines curve only because rows are equal in steps, not bounces.
customStart blankRows every 500,000 stepsWindow cells 0..36,470, 1 px = 8 cellsColors at least one defect (two equal neighbours,
00 or 11) among the pixel's 8 cells clean 0101... run not yet visitedRows: steps 0, 500,000, ..., 1,000,000,000 (2,001 rows), so consecutive rows are 500,000 steps apart · Window: counted from the wall (each row's leftmost visited cell is 0, pinned to column 0; it is absolute cell -33,652 in the last row) · Colors: head not drawn; Isolated dots = the head's own working cells at that moment; Lines curve because rows are evenly spaced in steps, not in bounces
Fig 4 · Blaze, 100M steps
The wall grows like sqrt(t); the right edge stays ragged and almost still.
bbchallenge-blazeStart blankRows time blocks of 131,072 stepsWindow cells -10,360..1,751, 1 px = ~15 cellsColors 0 1
Rows: averaged (763 blocks, steps 0..100,000,000), stretched to 500 px: 1 px ~ 200,000 steps · Window: Blaze averages 8 cells per column; its 1,514 columns are stretched to 800 px · Colors: in-between shades = both mixed inside the pixel's block (averaged); no head
The site's view of the first 10,000 steps: zig-zag bounces between defects.
bbchallenge-defaultStart blankRows every step: steps 0..9,999 squeezed into 500 px rows as on bbchallenge.orgWindow cells -200..199, 1 px = 1 cellColors 1 0 or never visited head after a right/left move
Rows: each px row blends steps 20y+9 and 20y+10, so 1 px row = 20 steps · Colors: red/green: pale colours = blended by the squeeze
Rules (8/8 validated)exact tape rewrites the proof will formalize, each re-checked by simulation
| rule | from ⟶ to | cases | steps | checked |
|---|---|---|---|---|
| G16 left block (16 bounces) | 0∞ <D 11 (01)14 (10)a 14 (01)3 12 (10)8 (01)b (10)12 1 (10)c 13 (10)6 (01)18 0 (01)2 r ⟶ 0∞ <D 11 (01)14 (10)a+8 14 (01)3 12 (10)8 (01)b+2 (10)12 1 (10)c+2 13 (10)6 (01)18 0 (01)2 r' | a odd >= 1, b even >= 4, c even >= 2, independent; r = real right part (4 tapes, 1e7..1e9). Other parity classes: 0/12 pass (wrong guess killed). [Notation fixed at assembly: was '<D 011 ...', which puts an extra 0 left of the 11; re-checked 30/30 in sim notation.] | — | ✓32/32 |
| orbit lock | c0 (blank tape) ⟶ G16 skeleton with (a,b,c,d) = (8n+61, 2n, 2n-2, n), L = 32n+26, at every 16th wall visit | observed on the orbit (25 snapshots, n = 25..1051), not a random-parameter test | — | ✓25/25 |
| H halt trigger | E> (10)2n+1 001 ⟶ halt (B reads 1) | sibling E> 10^(2n) 001 -> 01^(2n) 1 1 <C 1 in 4n+3 (safe turn), 40/40 | 4n+5 (busycoq halts_in 4n+4) | ✓40/40 |
| left sweep | (10)n <C ⟶ <C (01)n | — | 2n | ✓40/40 |
| right sweep, even | E> (01)2n ⟶ (10)2n E> | also E> 10^(2n) -> 01^(2n) E> in 4n | 4n | ✓80/80 |
| right sweep, odd | E> (01)2n+1 ⟶ (10)2n+1 D> | also E> 10^(2n+1) -> 01^(2n+1) F> in 4n+2 (F then reads the next cell: 0 0 1 there = halt) | 4n+2 | ✓80/80 |
| wall bounce | 0∞ <C ⟶ 0∞ 1 0 E> | — | 3 | ✓40/40 |
| edge extension | E> 0∞ ⟶ 1 <C 1101 0∞ | the only place B is entered in 1e9 steps (512 times); B always reads 0 there | 8 | ✓40/40 |
Compressed historythe tape as 0∞ <D 11 (01)14 (10)a 14 (01)3 12 (10)8 (01)b (10)12 1 (10)c 13 (10)6 (01)18 0 (01)d 13 (01)6 r at 25 moments: where the rules are read off
0∞ <D 11 (01)14 (10)a 14 (01)3 12 (10)8 (01)b (10)12 1 (10)c 13 (10)6 (01)18 0 (01)d 13 (01)6 r
| step | a | b | c | d | L (=-lo) | hi | defects |
|---|---|---|---|---|---|---|---|
| 1,074,148 | 261 | 50 | 48 | 25 | 826 | 893 | 102 |
| 1,363,638 | 293 | 58 | 56 | 29 | 954 | 981 | 98 |
| 1,824,222 | 341 | 70 | 68 | 35 | 1,146 | 992 | 111 |
| 2,547,476 | 405 | 86 | 84 | 43 | 1,402 | 1,036 | 117 |
| 3,379,994 | 469 | 102 | 100 | 51 | 1,658 | 1,058 | 115 |
| 4,342,350 | 533 | 118 | 116 | 59 | 1,914 | 1,124 | 117 |
| 5,697,176 | 613 | 138 | 136 | 69 | 2,234 | 1,157 | 106 |
| 7,590,424 | 709 | 162 | 160 | 81 | 2,618 | 1,223 | 100 |
| 10,120,334 | 821 | 190 | 188 | 95 | 3,066 | 1,300 | 123 |
| 13,434,250 | 949 | 222 | 220 | 111 | 3,578 | 1,344 | 113 |
| 18,237,176 | 1,109 | 262 | 260 | 131 | 4,218 | 1,388 | 119 |
| 23,714,088 | 1,269 | 302 | 300 | 151 | 4,858 | 1,465 | 152 |
| 31,886,544 | 1,477 | 354 | 352 | 177 | 5,690 | 1,520 | 139 |
| 42,795,146 | 1,717 | 414 | 412 | 207 | 6,650 | 1,553 | 156 |
| 56,264,118 | 1,973 | 478 | 476 | 239 | 7,674 | 1,641 | 150 |
| 75,566,108 | 2,293 | 558 | 556 | 279 | 8,954 | 1,718 | 171 |
| 100,001,538 | 2,645 | 646 | 644 | 323 | 10,362 | 1,751 | 176 |
| 133,437,932 | 3,061 | 750 | 748 | 375 | 12,026 | 1,850 | 171 |
| 177,848,642 | 3,541 | 870 | 868 | 435 | 13,946 | 1,883 | 182 |
| 237,710,744 | 4,101 | 1,010 | 1,008 | 505 | 16,186 | 1,960 | 171 |
| 316,436,342 | 4,741 | 1,170 | 1,168 | 585 | 18,746 | 1,960 | 183 |
| 423,685,322 | 5,493 | 1,358 | 1,356 | 679 | 21,754 | 2,158 | 213 |
| 563,100,552 | 6,341 | 1,570 | 1,568 | 785 | 25,146 | 2,356 | 235 |
| 751,446,202 | 7,333 | 1,818 | 1,816 | 909 | 29,114 | 2,587 | 262 |
| 1,000,348,998 | 8,469 | 2,102 | 2,100 | 1,051 | 33,658 | 2,818 | 275 |
alast 8,469blast 2,102clast 2,100dlast 1,051L (=-lo)last 33,658hilast 2,818defectslast 275Template comparisonBLv3.v TM1: partly applies · the nearest solved proof, what carries over, and the transitions that differ
| 0 | 1 | |
|---|---|---|
| A | 1RB | 1LC |
| B | 1RC | --- |
| C | 1LD | 1LC |
| D | 1RE | 0LC |
| E | 1RF | 0RE |
| F | 1RA | 0RD |
differs from the template
- file
BLv3.v:7- module
TM1 (TM2 shares it)- machine
1RB0RA_1LC0RD_0LD0LB_1RA1LE_0LC1LF_0LA---(11 transitions apart)- diff
8 of 11 transitions differ under best relabeling (A0 A1 B0 C1 D0 E0 E1 F1); BLv3 TM2 8, BLv2 TM1-3 8-9, Bouncer_v4 9- note
- Method carries: columns (01)^n+defect, head passes as a signal stream, per-column transducer + quadRect closure. Lemmas don't: we add 1111 columns, our edge grows, and BLv3's own cut tape halts on our machine at sim step 20,175.
Proof strategy & riskshow the formal proof will go · 3 risks to watch
BLv3-style. 1) es/ind for sweep/wall/edge rules; 2) the 16-bounce left-block rule with a odd, b,c even (multistep_nonhalt + progress_nonhalt_cond on n); 3) the hard part: a closed (regular) set for the edge region that excludes 'E> 10^odd 001' (LongN/InfiniteRect quadRect, or a CTL-style language search first).
- ▲Edge is chaotic and growing (hi ~ 20*sqrt(L), 56 groups at 1e9): a finite closed set may not exist -> STUCK at step 3.
- ▲Halting is a parity event (odd (10) run before a 00 defect); a late halt like BLv2's 3 kills is possible. None to 1e11.
- ▲On mxdys's UBRRBA_TODO list (Dennis: fair game); twin #27 is this exact table started in state E, so one proof should cover both.
Stats & provenance1011 steps simulated · 352,865 cells · the status in full · files
- simulated
- 1011 steps
- tape
- 352,865 cells · 177,158 nonzeros
- growth
- wall L ~ 1.08*sqrt(t) (2 cells/bounce); right edge hi ~ 20*sqrt(L) ~ t^0.25; defects 99 -> 275 (1e6 -> 1e9)
- status now
- Stopped by Dennis 2026-10-10: stays cryptid candidate, proof work parked with twin #27 (1RB0RA_1RC0RF_1RD1LE_1RE---_1LF1LE_1RA0LE). Halting reduces exactly to a validated 5-stage chain on the cluster 11.01.00, with arrival phases x,E,x,x,E (60/60 random instances halt). Seeds of this chain keep forming in the disordered mixed zone: 11 by 2.45e10 steps, about 0.7 per doubling. Their later stages depend only on left-context mod-4 phases, and those match the generic coin rates (about 50/35/13/50%); nothing visible forces them. The step-12,975,111 near miss is seed #3, which got through x,E,x. Under the coin model each seed halts with probability about 1%: probabilistic, cryptid-like. Priority call for Dennis: stop, or continue by decoding the mixed zone (would need a rule forcing the stage phases). (status.json, 2026-10-10)
- observer's note
- Left counter found and validated; edge chaotic but no Collatz-like arithmetic (gaps grow linearly). Needs Dennis's call on the edge approach.
- files
- observe.json · notes.md · status.json
Proof & checks
○ Checkpoint B: no note from Dennis found
- notes.md L54: - Checkpoint questions are now yes/no questions about the figures. Moved off the card (strategy calls, not figure reading; settle them in proof.md / Checkpoint B):
Files
machines/<tm>/: 13 entries · raw notes, status, scripts, images
| name | size | changed |
|---|---|---|
| notes.md ↓ | 18 KB | 2026-10-10 12:49 |
| status.json ↓ | 1.1 KB | 2026-10-10 12:49 |
| observe.json ↓ | 13 KB | 2026-10-10 04:41 |
| deepen.json ↓ | 6.3 KB | 2026-10-10 07:09 |
| decision.json ↓ | 4.0 KB | 2026-10-10 12:49 |
| data/ | 3 items | 2026-10-10 07:09 |
| img/ | 8 items | 2026-10-10 01:55 |
| scripts/ | 30 items | 2026-10-10 07:09 |
| qsim.jsonl ↓ | 13 KB | 2026-10-10 00:08 |
| qsim_n1.jsonl ↓ | 654 B | 2026-10-10 00:11 |
| qsim_n2_summary.jsonl ↓ | 10 KB | 2026-10-10 00:34 |
| sim_records_1e11.jsonl.gz ↓ | 3.6 MB | 2026-10-10 00:24 |
| sim_records_1e9.jsonl.gz ↓ | 374 KB | 2026-10-10 00:07 |
status.json in full
{
"tm": "1RB1LC_1RC---_1LD1LC_1RE0LC_1RF0RE_1RA0RD",
"status": "CRYPTID_CANDIDATE",
"stage": "deepen2",
"updated": "2026-10-10",
"reason": "Stopped by Dennis 2026-10-10: stays cryptid candidate, proof work parked with twin #27 (1RB0RA_1RC0RF_1RD1LE_1RE---_1LF1LE_1RA0LE). Halting reduces exactly to a validated 5-stage chain on the cluster 11.01.00, with arrival phases x,E,x,x,E (60/60 random instances halt). Seeds of this chain keep forming in the disordered mixed zone: 11 by 2.45e10 steps, about 0.7 per doubling. Their later stages depend only on left-context mod-4 phases, and those match the generic coin rates (about 50/35/13/50%); nothing visible forces them. The step-12,975,111 near miss is seed #3, which got through x,E,x. Under the coin model each seed halts with probability about 1%: probabilistic, cryptid-like. Priority call for Dennis: stop, or continue by decoding the mixed zone (would need a rule forcing the stage phases).",
"parked": "Stopped by Dennis 2026-10-10: stays cryptid candidate, proof work parked with twin #27 (1RB0RA_1RC0RF_1RD1LE_1RE---_1LF1LE_1RA0LE)."
}