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1RB0RD_1LC0LE_0RA0LB_1RC1RF_1LB1RD_0RC---
Where it stands
Parked at the observation
Stage 2: no closed regular language yet. An exact collector shows that the junction words more than 20 cells from the head form a tiny alphabet.
Read the full status
Left of the head: 3, 10, 310, 1023, 3210, 0. Right of the head: 120, 40, 300, 50, 310, 0, plus the counter end. It is complete by step 2.1e6 and unchanged to 1e10. Every 111 sits in the junction 300, whose 3 turns a right run. Closures with fixed junction languages (exact 12-30-cell zone, free order, segment-length classes) still escape after 10^2-10^4 configurations: they build orders and short-segment neighbours that the orbit never builds. No halt to 1.55e11. Not a cryptid (no halting branch); stuck on tooling.
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
100-block segments with one hub marker: each round moves 3^(k+1) blocks across the hub and adds 1 to a unary counter
- Status
- Parkedwave6-stage2 · updated 2026-10-14Not blocking · Stuck at the wave6-stage2 stage. Answer Q1–Q3 whenever; a “no” redirects the work.idle since Oct 14 15:43 (45 h ago) · status.json 2026-10-14
- Class
- Unknownours: sheet Unknown ≠ ours Bell eats counter variant (W5-5's table, 2 cells changed): hub defect + unary counter, ternary transfer · low confidence
- On the list
- line 86 of
BB6_holdouts_663.txt· historical 740 line 96 · observe.json rank #96
Your calls on file 2
- parked
- Dennis 2026-10-14: park (after Wave 6 stages 1-2: no closed regular language)
- 2026-10-14 · park
- Park W6-2 now, or fund a third stage that ports the closure to C with a language carrying segment-length classes and junction order?
Mechanism
How it works: 3 notes
- The tape is runs of 100 blocks joined by markers: one hub marker 0 (W5-5's 0001 defect, mirrored), 101 separators, and a unary counter (101)^c at the right end. HUB(k), exact: the head zigzags left through (101)^c, makes 3^(k+1) short trips at the hub (each moves one 100 block across it), then adds one 101 to the counter; k = number of 101 separators right of the hub.
- When the hub's right segment b drops below 3^(k+1), the outcome branches on b and the neighbours (99 events to 1e9): the hub becomes a 11 marker, moves, or the head sweeps to the left edge. Once per deep cycle (88 cycles to 1.55e11) the head reaches the left edge; then the counter drains one 101 per long trip while inner hubs work in older segments, which later freeze (58, 106, 1452, 393, 165, 338, 838, 12269, 41798).
- No halt to 1.55e11. Head windows (radius 4-10) stop changing after 1e7 steps, but plain NGramCPS fails for n = 2-20. Halting needs A or D to meet 111 moving right (A1 = 0RD, D1 = 1RF, F1 = halt); the real tape has 111 only at deep sweeps, where C passes it moving left. 1 of 2,000 random segment tapes halted, and it was malformed.
Figures for Checkpoint A
The standard site picture: a growing block field with a slanted right edge.
bbchallenge-defaultStart blankRows 10,000 steps squeezed into 500 rowsWindow cells -200..199, 1 px = 1 cellColors 1 0 or unvisited head after a move R/L
Rows: site view, about 20 steps per row
Each round: a zigzag left through the right field, short trips at the 0 marker, a sweep back right.
bbchallenge-defaultStart constructed: 0∞ (010)3 1 (100)6 0 (100)9 (101)10 B> 0∞Rows every step, steps 0..1,360Window cells -90..29, 1 px = 0.5 cellsColors 1 0 or unvisited head after a move R/L
Rows: (rounds end at steps 535, 986, 1,353); 2 px per step · Window: scale 2; cell 0 = the head's start cell
Same start shape plus one 101 separator; count the short trips at the marker in each round.
bbchallenge-defaultStart constructed: 0∞ (010)3 1 (100)4 0 (100)20 101 (100)5 (101)8 B> 0∞Rows every step, steps 0..3,470Window cells -120..29, 1 px = 0.5 cellsColors 1 0 or unvisited head after a move R/L
Rows: (rounds end at steps 2,203 and 3,458); 2 px per step · Window: scale 2; cell 0 = the head's start cell
More figures (1)Fig 4: Whole run to 1e9
Fig 4 · Whole run to 1e9
Right edge grows in steps; the lighter band is the (101) counter field filling and draining.
bbchallenge-defaultStart blankRows every 2,000,000 steps, 501 rows to step 1e9Window cells -69..25,596, 1 px = 4 cellsColors 1 0 or unvisited
Window: first cell of each 4-cell group · Colors: (100) and (101) fields show as different grey textures because of the 4-cell sampling
Rules (3/4 validated)exact tape rewrites the proof will formalize, each re-checked by simulation
| rule | from ⟶ to | cases | steps | checked |
|---|---|---|---|---|
| HUB(0) | 0∞ L 1 (100)a 0 (100)b+3 (101)c B> 0∞ ⟶ 0∞ L 1 (100)a+3 0 (100)b (101)c+1 B> 0∞ | a>=1, c>=2; L never read | 24c+36b+79 | ✓8081/8081 |
| HUB(1) | 0∞ L 1 (100)a 0 (100)b+9 101 (100)m (101)c B> 0∞ ⟶ 0∞ L 1 (100)a+9 0 (100)b 101 (100)m (101)c+1 B> 0∞ | a>=1, m>=1, c>=2 | 24c+108b+36m+643 | ✓1043/1043 |
| HUB(k) | 0∞ L 1 (100)a 0 (100)b [101 (100)m_i] (i=1..k) (101)c B> 0∞ ⟶ 0∞ L 1 (100)a+3^(k+1) 0 (100)b-3^(k+1) [101 (100)m_i] (101)c+1 B> 0∞ | b >= 3^(k+1), a>=1, every m_i>=1, c>=2; 1,200 random (k=0..3) + 8,363 real rounds to 1e9 | 24c + 12*3k+1*b + sum_i 12*3k+1-i*m_i + d_k; d_0..d_3 = -29, -329, -3821, -37625 | ✓9563/9563 |
| EXHAUST | 0∞ L 1 (100)a 0 (100)b [101 (100)m_i] (101)c B> 0∞, b < 3k+1 ⟶ branches on b and the neighbours (not modelled); k=0, b=2: 2a 3 22 (10)c-1 1 -> 2a+4 0 (10)c-1 1 in gap tokens | 99 events at the right edge to 1e9; b=0/1 usually start a deep sweep | — | –untested |
Compressed historythe tape as deep sweep (gap tokens): [frozen segments] 2X (10)Y-1 1, i.e. ... (100)X (101)Y at the right end at 34 moments: where the rules are read off
deep sweep (gap tokens): [frozen segments] 2X (10)Y-1 1, i.e. ... (100)X (101)Y at the right end
| step | cycle (-left edge) | X (last open segment) | Y (counter) |
|---|---|---|---|
| 289,167,913 | 55 | 10 | 61 |
| 312,074,110 | 56 | 3 | 86 |
| 335,100,627 | 57 | 832 | 7 |
| 361,076,172 | 58 | 11 | 310 |
| 387,293,271 | 59 | 332 | 101 |
| 415,402,480 | 60 | 444 | 208 |
| 445,831,719 | 61 | 663 | 246 |
| 480,105,412 | 62 | 920 | 319 |
| 520,463,173 | 63 | 1,250 | 404 |
| 570,554,714 | 64 | 1,665 | 514 |
| 636,195,231 | 65 | 2,190 | 653 |
| 726,679,474 | 66 | 2,854 | 828 |
| 856,843,289 | 67 | 3 | 1,056 |
| 997,186,288 | 68 | 3 | 443 |
| 1,188,757,157 | 69 | 5,199 | 555 |
| 1,473,998,970 | 70 | 5,765 | 1,831 |
| 1,904,622,349 | 71 | 7,607 | 2,019 |
| 2,583,213,392 | 72 | 9,637 | 2,633 |
| 3,651,048,525 | 73 | 3 | 3,317 |
| 4,819,237,170 | 74 | 3,323 | 1,398 |
| 6,231,820,271 | 75 | — | — |
| 7,682,038,190 | 76 | 7,231 | 990 |
| 9,647,439,345 | 77 | 8,224 | 3,808 |
| 12,218,504,626 | 78 | 12,035 | 4,139 |
| 15,829,114,891 | 79 | — | — |
| 19,693,788,184 | 80 | 21,588 | 2,263 |
| 26,142,188,943 | 81 | 23,854 | 8,593 |
| 35,678,011,704 | 82 | 32,450 | 9,349 |
| 50,511,407,219 | 83 | — | — |
| 66,639,836,540 | 84 | — | — |
| 83,778,677,347 | 85 | — | — |
| 103,007,985,720 | 86 | — | — |
| 126,211,222,235 | 87 | 24,021 | 11,907 |
| 155,348,041,670 | 88 | 35,929 | 12,528 |
cycle (-left edge)last 88X (last open segment)last 35,929Y (counter)last 12,528Template comparisonW5-5's: partly applies · the nearest solved proof, what carries over, and the transitions that differ
| 0 | 1 | |
|---|---|---|
| A | 1RBtpl 1RE | 0RD |
| B | 1LC | 0LE |
| C | 0RA | 0LB |
| D | 1RC | 1RF |
| E | 1LB | 1RDtpl 0LD |
| F | 0RC | --- |
differs from the template
- file
- —
- module
W5-5's own .v (KILLED_HALT): bellpart, round = callw + bellpart, base-4 digit lemmas abs0/abs1/absm/pass2/callw_inc- machine
1RE0RD_1LC0LE_0RA0LB_1RC1RF_1LB0LD_0RC---(2 transitions apart)- diff
A0: ours 1RB, W5-5 1RE; E1: ours 1RD, W5-5 0LD (W5-5's table started in its D, in our naming)- note
- Same 3-cell words and the same bell-with-defect round, mirrored: our hub marker 0 is W5-5's 0001 defect. W5-5's defect moves 1 block per round and feeds a signed base-4 counter; here it jumps 3^(k+1) blocks and the counter is unary (101)^c. HUB(0) is W5-5's round with a unary counter; none of the digit lemmas carry over. W5-5's checked-runner route needs a halt, and none is in sight.
Proof strategy & riskshow the formal proof will go · 3 risks to watch
Route 1 (NONHALT, preferred): look for a closed regular language on 3-cell words (block CPS / CTL with the gap-token vocabulary); it would not need the residue arithmetic. Route 2: model the exhaustion branches and the deep cycle exactly, then look for a closed residue table. Stop if the exhaustion law is a pseudo-random residue map.
- ▲Exhaustion branches on b mod 3^(k+1) and re-cuts segments; frozen segment lengths and counter values look irregular (Collatz-type signal). A 111 met by A or D moving right halts, and 111 does occur at deep sweeps.
- ▲Plain NGramCPS fails for n = 2..20, so any regular invariant must use phase or block structure; it may not exist.
- ▲Deep cycles get long (2.9e10 steps per cycle at 1.5e11), so long-run evidence grows slowly.
Stats & provenance1.6·1011 steps simulated · 25,666 cells · the status in full · files
- simulated
- 1.6·1011 steps
- tape
- 25,666 cells · 8,997 nonzeros
- growth
- deep cycles: left edge -1 per cycle; right edge 25,596 at 1e9, 319,363 at 1.55e11
- status now
- Stage 2: no closed regular language yet. An exact collector shows that the junction words more than 20 cells from the head form a tiny alphabet. Left of the head: 3, 10, 310, 1023, 3210, 0. Right of the head: 120, 40, 300, 50, 310, 0, plus the counter end. It is complete by step 2.1e6 and unchanged to 1e10. Every 111 sits in the junction 300, whose 3 turns a right run. Closures with fixed junction languages (exact 12-30-cell zone, free order, segment-length classes) still escape after 10^2-10^4 configurations: they build orders and short-segment neighbours that the orbit never builds. No halt to 1.55e11. Not a cryptid (no halting branch); stuck on tooling. (status.json, 2026-10-14)
- observer's note
- HUB(k) exact and validated (1,200 random + 8,363 real rounds); exhaustion, drain and deep-cycle regimes observed but not modelled; no halting branch found
- files
- observe.json · notes.md · status.json
Proof & checks
No proof work yet.
Files
machines/<tm>/: 7 entries · raw notes, status, scripts, images
| name | size | changed |
|---|---|---|
| notes.md ↓ | 19 KB | 2026-10-14 14:59 |
| status.json ↓ | 2.8 KB | 2026-10-14 15:43 |
| observe.json ↓ | 11 KB | 2026-10-14 14:16 |
| decisions/ | 1 item | 2026-10-14 15:43 |
| img/ | 6 items | 2026-10-14 14:10 |
| scripts/ | 33 items | 2026-10-14 14:58 |
| work/ | 9 items | 2026-10-14 14:59 |
status.json in full
{
"tm": "1RB0RD_1LC0LE_0RA0LB_1RC1RF_1LB1RD_0RC---",
"label": "W6-2",
"status": "STUCK",
"stage": "wave6-stage2",
"updated": "2026-10-14",
"confidence": "low",
"reason": "Stage 2: no closed regular language yet. An exact collector shows that the junction words more than 20 cells from the head form a tiny alphabet. Left of the head: 3, 10, 310, 1023, 3210, 0. Right of the head: 120, 40, 300, 50, 310, 0, plus the counter end. It is complete by step 2.1e6 and unchanged to 1e10. Every 111 sits in the junction 300, whose 3 turns a right run. Closures with fixed junction languages (exact 12-30-cell zone, free order, segment-length classes) still escape after 10^2-10^4 configurations: they build orders and short-segment neighbours that the orbit never builds. No halt to 1.55e11. Not a cryptid (no halting branch); stuck on tooling.",
"siblings": [],
"family_note": "No other 740-list machine shares the table (canon over all 6 starts, renaming + mirror). Starts B, D, E are eqv-1590 members off the list: 1RB0RE_0LC0RA_1LA0LD_1LB1LF_1RA1LD_0LB---, 1RB1RF_0RC0LD_1RD0RA_1LB0LE_1LD1RA_0RB---, 1RB1LE_1RC0RA_0LD0RB_1LB0LE_1LC1LF_0LC--- (upstream Eqv_v2 TM1194/TM1468/TM1778 link them; equivalences, not verdicts).",
"template": "W5-5 (KILLED_HALT) table from its D = 1RE0RD_1LC0LE_0RA0LB_1RC1RF_1LB0LD_0RC--- in our naming; differs in A0 and E1. Applies partly: same bell-with-defect round (HUB(0) = W5-5's round with a unary counter); W5-5's base-4 digit lemmas and its halting runner do not carry over.",
"checks": {
"byte_exact_740": "line 96",
"claims": "none (sheet 2026-10-09: class Unknown only, no status/notes/done-by; no Discord hit)",
"upstream_cdaf693": "not proved (Eqv_v2 mentions only)",
"long_run": "no halt to 1.55e11 steps (scripts/lt.c; still running at stage end)",
"random_segment_halts": "0/300 (2e5 steps) and 1/2,000 (2e7 steps); the one halt is a malformed tape (empty first segment) halting as A> 111; the real tape has 111 only at deep sweeps, met by C moving left",
"ngramcps_c": "HALT reachable for n = 22, 24, 26, 28 (scripts/ngc.c)",
"ctl_searches": "NGPhase, GapTok, SegJ, SegJ2: halt or > 3-4M configs (scripts/ctl2.py, absn.py)",
"exact_alphabet": "scripts/cw2.c, k = 20: complete by step 2,106,481, unchanged to 1e9 and 1e10 (work/cw2_1e9_k20.txt, cw2_1e10_k20.txt)",
"fixed_language_ctl": "fl2-fl6.py from the step-1e6 configuration: escape after 16-13,000 configurations, or over 1M with automatic alphabet growth"
},
"next_goal": "If funded: port the closure to C, with a side state of the last junction word, the class of the segment before it (2-8 or 9+ blocks) and a counter flag, learned from the exact collector. Export a closed result to Astra's NFA certificate package with a 1e6-step startup.",
"parked": "Dennis 2026-10-14: park (after Wave 6 stages 1-2: no closed regular language)"
}