BB(6) hunt
Machines / W6-3

1RB1LC_1LA1RF_0RD1RD_0RA0LE_1LA0LE_0RC---

W6-3Cryptid candidateUnknownbbchallenge ↗Explorer

Where it stands

Cryptid candidate, parked at the observation

Observe done (about 1 h 50 min). The mechanism is a 0011 defect walking through 110 fields: the head shuttles between the defect and a unary counter at the right end, one block per round trip.

Read the full status

Three exact visit rules R1-R3 (main walk, walk that eats the second field, the same walk inside the second field) are validated 25/25 each from random instances. When the active defect reaches the junk before the counter, the head sweeps to the left edge and a new epoch starts. The epoch law, fitted on 22 resets to 1.63e10, is N' ~ N + 1.22M, M' ~ 0.30N - 0.58M (eigenvalues 1.20, -0.78); each phase ends on a remainder (mod 6, 8, 2) that picks the junk and the next branch. That is the pre-registered W6-3 stop rule (a field divided, branches on residues), so the cryptid protocol applies: rules formalized in observe.json, flagged, stopped. Unlike H-4, no branch is known to halt: halting needs D to read 0011 from its left, which no observed branch does, and ~5e5 epochs (Alistaire's 10^73975 steps) passed without a halt. A proof would need a closed census of branch shapes plus a 2-D band invariant on M/N (0.06..0.25 seen).

Observe
Deepen
Informal proof
Rocq
space-time diagram, first 10,000 steps from blank
The first 10,000 steps from a blank tape. Time runs down; white is 1.
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

A 0011 defect walks through 110 fields off a right counter; epochs reset via a 2-D map that branches on remainders

Status
Cryptid candidateobserving · updated 2026-10-14Parked · Observe done (about 1 h 50 min). The 3 open questions are optional.
idle since Oct 14 16:43 (44 h ago) · status.json 2026-10-14
Class
Unknownours: sheet Unknown ≠ ours Nested defect-walk counter (budget + round counter at two levels); 2-D residue-branching epoch map: cryptid-like · med confidence
On the list
line 262 of BB6_holdouts_663.txt · historical 740 line 291 · observe.json rank #291
eqv ×13sim 1e15
Your calls on file 3
priority call (answered)
Cryptid-like (pre-registered stop): the epoch law branches on remainders, but no halting branch is known. Park it, or fund one 2 h stage to build an exact epoch accelerator and census the branch shapes for closure?
parked
Dennis 2026-10-14: park
2026-10-14 · park
W6-3's epoch law branches on remainders (the pre-registered stop): park it, or fund one 2 h stage?

Mechanism

How it works: 3 notes
  • Trips: the head shuttles between a 0011 defect (left wall) and a unary counter at the right end; each round trip moves the defect one 110 block right, and every 8 trips add 2 blocks to the counter (rule R1).
  • Two levels: the same walk also eats the second field (R2: x+16, y-8, z-6) and runs inside it (R3: a+4, b-2). When the active defect reaches the junk before the counter, the head sweeps to the left edge and a new epoch starts.
  • Epoch law (fitted, 22 resets to 1.6e10): N' ~ N + 1.22M, M' ~ 0.30N - 0.58M (eigenvalues 1.20, -0.78); phases end on remainders (mod 6, 8, 2) that pick the junk and the next branch. Halting needs D to read 0011 from its left; never seen.

Figures for Checkpoint A

Fig 1 · bbchallenge default view, 10,000 stepsviewer ↗

The site's view. The striped area is the 110 field; the ragged right edge is the counter.

bbchallenge default view, 10,000 steps
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: 1 px row = 20 steps · Colors: red/green: pale = blended by the squeeze
Fig 2 · One visit: trips off the defectQ1

Each black wedge is one round trip. Follow the left tip of the wedges from row to row.

One visit: trips off the defect
bbchallenge-defaultStart constructed: 0∞ (110)10 0011 (110)40 16 (110)6 (11011110)2 16 02 D> 0∞Rows every 8 steps, 6,000 steps (751 rows)Window cells -202..11, 1 px = 1 cellColors 1 0 or never visited head after a right/left move
Colors: black wedges = the field erased to 100/001 on the leftward pass
Fig 3 · Epochs to 3 million stepsQ2

Thin diagonals are defects crossing the field; each new diagonal from the left edge is a reset.

Epochs to 3 million steps
bbchallenge-defaultStart blankRows every 3,000 stepsWindow cells -66..1248, 1 px = 1 cellColors 1 0 or never visited head after a right/left move
Rows: 3,000,000 steps (1,001 rows)
More figures (1)Fig 4: Right records, 3 million steps
Fig 4 · Right records, 3 million steps

One row per new rightmost cell. The vertical streaks are the defect paths seen at record times.

Right records, 3 million steps
bbchallenge-defaultStart blankRows right records onlyWindow cells -66..1248, 1 px = 1 cellColors 1 0 or never visited head after a right/left move
Rows: (one row per new rightmost cell), 3,000,000 steps
Rules (4/5 validated)exact tape rewrites the proof will formalize, each re-checked by simulation
rulefrom ⟶ tocasesstepschecked
R1 main walk (P1)
0∞ (110)a 0011 (110)b 16 (110)c (11011110)2 16 02 D> 0∞
⟶ 0∞ (110)a+8 0011 (110)b-8 16 (110)c+2 (11011110)2 16 02 D> 0∞
b >= 8; 8 trips of one block eachmeasured per instance (e.g. 5,966 at (41,27,50)); not fitted✓25/25
R2 walk eating the second field (Q1)
0∞ (110)x 0011 (110)y 1011 (110)z (11011110)2 16 02 D> 0∞
⟶ 0∞ (110)x+16 0011 (110)y-8 1011 (110)z-6 (11011110)2 16 02 D> 0∞
y >= 8, z >= 6measured per instance (e.g. 17,086 at (118,66,52)); not fitted✓25/25
R3 walk inside the second field (Q3)
0∞ (110)p 0011 (110)q 16 (011)2 03 16 (110)a 0011 (110)b (11011110)2 16 02 D> 0∞
⟶ 0∞ (110)p 0011 (110)q 16 (011)2 03 16 (110)a+4 0011 (110)b-2 (11011110)2 16 02 D> 0∞
b >= 2; a + 2b conservedmeasured per instance; not fitted✓25/25
halting pattern
0∞ (110)5 D> 0011 (110)4 0∞
⟶ halt
the only way to halt: D moving right reads the first 0 of 0011 (A0, B1, F1)4✓1/1
epoch law (reset to reset), fitted
0∞ <E (001)N J word^M R 0∞
⟶ 0∞ <E (001)N' J' word^M' R' 0∞, N' ~ N + 1.22M + 92, M' ~ 0.30N - 0.58M - 38
residues of the phase ends (mod 6, 8, 2) pick J', R' and the next branch (Q1 then P1, or Q3 first); residuals up to +-550 / +-330—–untested
Compressed historythe tape as 0∞ <E (001)N J word^M R 0∞ at 23 moments: where the rules are read off
0∞ <E (001)N J word^M R 0∞
stepNM
2,032,99131972
3,168,09141628
4,681,94745843
7,679,01368270
12,185,873783147
18,852,531985149
28,624,6571,20293
44,343,8311,408341
66,995,7611,894113
97,482,0072,072213
147,640,3492,506623
218,584,0653,241473
323,194,7173,801695
472,935,4074,751355
710,419,4075,4711,366
1,057,265,2637,298909
1,570,250,0578,3531,615
2,324,688,33310,5111,551
3,447,311,41512,5852,113
5,102,449,07715,4052,440
7,551,201,89718,6713,037
11,167,615,14322,7253,655
16,295,935,26526,7024,690
Nlast 26,702
26,7023192e61.6e10log xstep 2032991: N = 319step 3168091: N = 416step 4681947: N = 458step 7679013: N = 682step 12185873: N = 783step 18852531: N = 985step 28624657: N = 1202step 44343831: N = 1408step 66995761: N = 1894step 97482007: N = 2072step 147640349: N = 2506step 218584065: N = 3241step 323194717: N = 3801step 472935407: N = 4751step 710419407: N = 5471step 1057265263: N = 7298step 1570250057: N = 8353step 2324688333: N = 10511step 3447311415: N = 12585step 5102449077: N = 15405step 7551201897: N = 18671step 11167615143: N = 22725step 16295935265: N = 26702
Mlast 4,690
4,690282e61.6e10log xstep 2032991: M = 72step 3168091: M = 28step 4681947: M = 43step 7679013: M = 70step 12185873: M = 147step 18852531: M = 149step 28624657: M = 93step 44343831: M = 341step 66995761: M = 113step 97482007: M = 213step 147640349: M = 623step 218584065: M = 473step 323194717: M = 695step 472935407: M = 355step 710419407: M = 1366step 1057265263: M = 909step 1570250057: M = 1615step 2324688333: M = 1551step 3447311415: M = 2113step 5102449077: M = 2440step 7551201897: M = 3037step 11167615143: M = 3655step 16295935265: M = 4690
Template comparisonBECv5.v TM1: partly applies · the nearest solved proof, what carries over, and the transitions that differ
01
A1RB1LC
B1LA1RF
C0RD1RD
D0RA0LE
E1LA0LE
F0RC---
file
BECv5.v:30
module
TM1
machine
1RB1RA_1LC1LE_1RF1LD_1RE0LD_0LB0RA_---0RC (11 transitions apart)
diff
architecture only (no shared transitions)
note
W5-3 (our kill, BECv5 TM1 architecture): a defect walks through a periodic word while a right counter counts trips, plus a left-edge eat; one level, a binary counter, 5 residue cases, 1-D invariant 1 <= N <= 2p. Here the counter is unary, the same walk runs at two levels (R1, R3), and the epoch map is 2-D with eigenvalues 1.20 and -0.78, so a proof needs a 2-D band (e.g. 0.05N <= M <= 0.3N) plus a closed census of branch shapes. No upstream proof of this table; 291 is only in Eqv lemmas (Eqv.v TM44, Eqv_v3.v TM437).
Proof strategy & riskshow the formal proof will go · 3 risks to watch

Pre-registered stop: the epoch law divides fields and branches on remainders, so park as a cryptid candidate. If funded: build an exact epoch accelerator from R1-R3 and the reset branches, check it against direct runs to 2e10, then census the branch shapes far out to see whether they close.

  • ▲The branch set (J x R x phase, plus interleaved two-defect visits) may be large or not closed; 185 raw visit shapes by 1e8 (uncanonicalized).
  • ▲The 2-D invariant band must survive residue perturbations; the -0.78 eigenvalue makes M/N oscillate (0.06..0.25 seen).
  • ▲152 is only Eqv-linked (not the same table): a 291 proof transfers only through upstream Eqv lemmas resting on BBinf (two .v files).
Stats & provenance2·1010 steps simulated · 94,226 cells · the status in full · files
simulated
2·1010 steps
tape
94,226 cells
growth
epochs grow ~1.20x (fitted eigenvalue); span 94,226 at 1.63e10; 23 resets to 1.63e10, no halt
status now
Observe done (about 1 h 50 min). The mechanism is a 0011 defect walking through 110 fields: the head shuttles between the defect and a unary counter at the right end, one block per round trip. Three exact visit rules R1-R3 (main walk, walk that eats the second field, the same walk inside the second field) are validated 25/25 each from random instances. When the active defect reaches the junk before the counter, the head sweeps to the left edge and a new epoch starts. The epoch law, fitted on 22 resets to 1.63e10, is N' ~ N + 1.22M, M' ~ 0.30N - 0.58M (eigenvalues 1.20, -0.78); each phase ends on a remainder (mod 6, 8, 2) that picks the junk and the next branch. That is the pre-registered W6-3 stop rule (a field divided, branches on residues), so the cryptid protocol applies: rules formalized in observe.json, flagged, stopped. Unlike H-4, no branch is known to halt: halting needs D to read 0011 from its left, which no observed branch does, and ~5e5 epochs (Alistaire's 10^73975 steps) passed without a halt. A proof would need a closed census of branch shapes plus a 2-D band invariant on M/N (0.06..0.25 seen). (status.json, 2026-10-14)
observer's note
Visit rules R1-R3 exact and validated (25/25 each). The epoch law is a 2-D piecewise-affine map (eigenvalues 1.20, -0.78) whose branches are picked by remainders mod 6/8/2: the pre-registered W6-3 stop rule. No halting branch is known; closure of the branch set is unproved.
files
observe.json · notes.md · status.json

Proof & checks

No proof work yet.

Files

machines/<tm>/: 7 entries · raw notes, status, scripts, images

namesizechanged
notes.md ↓6.2 KB2026-10-14 14:07
status.json ↓2.2 KB2026-10-14 16:43
observe.json ↓10 KB2026-10-14 14:07
decisions/1 item2026-10-14 16:43
img/5 items2026-10-14 14:07
scripts/7 items2026-10-14 14:05
work/7 items2026-10-14 14:02
status.json in full
{
 "tm": "1RB1LC_1LA1RF_0RD1RD_0RA0LE_1LA0LE_0RC---",
 "label": "W6-3",
 "status": "CRYPTID_CANDIDATE",
 "stage": "observe",
 "updated": "2026-10-14",
 "confidence": "med",
 "reason": "Observe done (about 1 h 50 min). The mechanism is a 0011 defect walking through 110 fields: the head shuttles between the defect and a unary counter at the right end, one block per round trip. Three exact visit rules R1-R3 (main walk, walk that eats the second field, the same walk inside the second field) are validated 25/25 each from random instances. When the active defect reaches the junk before the counter, the head sweeps to the left edge and a new epoch starts. The epoch law, fitted on 22 resets to 1.63e10, is N' ~ N + 1.22M, M' ~ 0.30N - 0.58M (eigenvalues 1.20, -0.78); each phase ends on a remainder (mod 6, 8, 2) that picks the junk and the next branch. That is the pre-registered W6-3 stop rule (a field divided, branches on residues), so the cryptid protocol applies: rules formalized in observe.json, flagged, stopped. Unlike H-4, no branch is known to halt: halting needs D to read 0011 from its left, which no observed branch does, and ~5e5 epochs (Alistaire's 10^73975 steps) passed without a halt. A proof would need a closed census of branch shapes plus a 2-D band invariant on M/N (0.06..0.25 seen).",
 "siblings": [],
 "sibling_note": "No other start or mirror of this table is on the 740 or 778 lists (canon from all 6 starts). Starts B and E are in the 1590 equivalence file (Eqv_v3.v TM10, Eqv_v2.v TM1055). 152 (1RB1LF_0LC0RE_1LA1RD_0LB1LB_1RC1RD_0LD---) is not the same table; it is linked only through upstream Eqv lemmas.",
 "holdout_line_740": 291,
 "upstream": "No upstream proof of this table. 291 appears only in Eqv lemmas (Eqv.v TM44, Eqv_v3.v TM437), which are equivalences, not verdicts. No claim in data/discord or data/sheet (Results row 28: Unknown, no status, Alistaire's simulation note).",
 "priority_call_answered": "Cryptid-like (pre-registered stop): the epoch law branches on remainders, but no halting branch is known. Park it, or fund one 2 h stage to build an exact epoch accelerator and census the branch shapes for closure?",
 "parked": "Dennis 2026-10-14: park"
}