BB(6) hunt
Machines / B-4

1RB0RF_1RC0LD_1RD0RA_1LE0LC_1LB0LE_0RC---

B-4Claimed elsewhereBell eats counterbbchallenge ↗Explorer

Upstream result

Claimed elsewhere

The blank-start machine never halts: BECv10.v.TM10 ↗. Recorded commit time: 2026-10-13T13:42:06Z. First public push time is not established.

Absent from the current 663 holdout list. Earlier local observations remain below.

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

Left-wall binary counter eats a 010001 reservoir; overflow leaves a binary-residue junk word; spurts are residue-timed

Upstream
The blank-start machine never halts: BECv10.v.TM10 ↗. Recorded commit time: 2026-10-13T13:42:06Z. First public push time is not established.
Status
Externally Solvedobserving · updated 2026-10-13Not blocking · Stuck at the observing stage. Answer Q1–Q2 whenever; a “no” redirects the work.
idle since Oct 13 16:19 · status.json 2026-10-13
Class
Bell eats counterours: sheet Bell eats counter ≠ ours Binary counter at the left wall eats a 6-cell reservoir; each overflow fossilizes the counter's binary residue as junk that the next cycle re-reads · low confidence
On the list
not on BB6_holdouts_663.txt (line 239 of the previous list) · historical 740 line 239
eqv ×3sim 1e15

Mechanism

How it works: 3 notes
  • Counter pass (rules P0/P1, 80/80): 0^inf <D (011)^a (010001)^b x (010001)^c, x = one-cell phase defect. One pass moves the defect 2^a words right and adds a digit: (a,b,c) -> (a+1, b+2^a, c-2^a) while c >= 2^a.
  • Overflow (rule O, 24/24): when c < 2^a the whole sea is re-laid as a 3-cell field, 0^inf J (011)^(2b+2c) C>, where J is a junk word of exactly 3a+4 cells (the counter's partial state, i.e. a binary residue). Halting needs A to read 1 with a 1 on its right (A1 -> 0RF, F1 undefined). No halt to 2e10 (span 75,979, 36,061 ones).
  • Cycle: J (101)^n B> -> J' (101)^n' B> (n' - n = +28..+72 at the 34k level) or a spurt that doubles the field, 1 0^3 (011)^(2n+12..24) C>. J is the previous counter's residue (c0 + 2^a0) mod 2^A, and it decides which: plateaus of 1, 1, 9, 3 and 31 cycles, spurts at 1.1e7, 3.0e7, 3.3e8, 9.9e8, 1.88e10.

Figures for Checkpoint A

Fig 1 · bbchallenge default view, first 10,000 steps

The site's view. The tape grows left in steps; the fine stripes are the 3- and 6-cell fields being rewritten.

bbchallenge default view, first 10,000 steps
bbchallenge-defaultStart blankRows 10,000 steps squeezed into 500 px rowsWindow cells -200..199, 1 px = 1 cellColors 1 0 or never visited head after a right/left move
Rows: 1 px row = 20 steps; the site blends neighbouring steps
Fig 2 · Span vs log(step): plateaus and spurtsQ2

Each flat stretch is many cycles; each steep rise is one spurt cycle. Compare the plateau lengths.

Span vs log(step): plateaus and spurts
customStart blankRows chart, not a tapeWindow cells 0..80,000, 1 px = 223 cellsColors span (cells visited) gridlines background
Rows: x = log10(step) from 6 to 10.3 (vertical gridline at each power of 10), y = span hi-lo+1 at each new record · Window: vertical axis = span; chart gridline every 10,000 cells; horizontal axis = log10 step 6..10.3
Fig 3 · One ordinary cycle: the reservoir is eatenQ1

Rows go down in time. Watch the orange/blue boundary (the phase defect) move right until blue is gone.

One ordinary cycle: the reservoir is eaten
customStart mid-run: step 110,000,000Rows every 40,000 stepsWindow cells -7850..297, 1 px = 6 cellsColors 3-cell field 010001 left of the phase defect 010001 right of it any other block (junk, defect) blank head
Rows: 751 rows, 3e7 steps: one cycle plus the start of the next · Window: one 6-cell block per pixel; block colour by content · Colors: grey: 011 in any phase; blue: the reservoir; green/purple/cyan/olive = 010001 in other phases
More figures (1)Fig 4: The spurt cycle: the field doubles leftward
Fig 4 · The spurt cycle: the field doubles leftward

Same colours as the cycle map. Here the left edge advances on every sweep instead of the defect.

The spurt cycle: the field doubles leftward
customStart mid-run: step 261,900,000Rows every 100,000 stepsWindow cells -16,778..363, 1 px = 6 cellsColors 3-cell field any other block blank head
Rows: 661 rows, 6.6e7 steps, through the spurt that ends at step 326,852,586 · Window: one 6-cell block per pixel; block colour by content · Colors: grey: 011 in any phase; orange/blue/green/purple/cyan/olive = 010001 in its six phases
Rules (3/4 validated)exact tape rewrites the proof will formalize, each re-checked by simulation
rulefrom ⟶ tocasesstepschecked
P1 counter pass, 1-defect
0∞ <D (011)a (010001)b 1 (010001)c 0∞
⟶ 0∞ <D (011)a+1 (010001)b+2^a 1 (010001)c-2^a 0∞
c >= 2^a; a = 0..9, b = 1..2^a+60, c = 2^a..2^a+300—✓40/40
P0 counter pass, 0-defect
0∞ <D (011)a (010001)b 0 (010001)c 0∞
⟶ 0∞ <D (011)a+1 (010001)b+2^a 0 (010001)c-2^a 0∞
c >= 2^a; a = 0..9, b = 1..2^a+60, c = 2^a..2^a+300—✓40/40
O overflow (shape only)
0∞ <D (011)a (010001)b x (010001)c 0∞, x in {0,1}
⟶ 0∞ J (011)2b+2c C> 0∞ (at the next right record), |J| = 3a+4 cells, J not yet characterised
c < 2^a; a = 0..7—✓24/24
Cycle map (observed only)
0∞ J (101)n B> 0∞
⟶ 0∞ J' (101)n' B> 0∞, n' - n in +9..+75; or spurt 0∞ 1 03 (011)2n+k C> 1 0∞, k in 12..24
which branch: decided by J (a binary residue); not characterised—–untested
Compressed historythe tape as 0∞ <D (011)a (010001)b 0 (010001)c 0∞ at 8 moments: where the rules are read off
0∞ <D (011)a (010001)b 0 (010001)c 0∞
stepabc
56,559,5883131,277
56,564,1294211,269
56,579,3585371,253
56,634,3956691,221
56,842,77671331,157
57,652,75782611,029
60,845,5869517773
73,522,703101,029261
alast 10
1035.7e77.4e7step 56559588: a = 3step 56564129: a = 4step 56579358: a = 5step 56634395: a = 6step 56842776: a = 7step 57652757: a = 8step 60845586: a = 9step 73522703: a = 10
blast 1,029
1,029135.7e77.4e7step 56559588: b = 13step 56564129: b = 21step 56579358: b = 37step 56634395: b = 69step 56842776: b = 133step 57652757: b = 261step 60845586: b = 517step 73522703: b = 1029
clast 261
1,2772615.7e77.4e7step 56559588: c = 1277step 56564129: c = 1269step 56579358: c = 1253step 56634395: c = 1221step 56842776: c = 1157step 57652757: c = 1029step 60845586: c = 773step 73522703: c = 261
Template comparison1RB0RF_1RC0RB_1LD0RA_1LE0LD_1RB0LC_1LA---.v: does not apply · the nearest solved proof, what carries over, and the transitions that differ
01
A1RB0RF
B1RC0LD
C1RD0RA
D1LE0LC
E1LB0LE
F0RC---
file
machines/1RB0RF_1RC0RB_1LD0RA_1LE0LD_1RB0LC_1LA---/1RB0RF_1RC0RB_1LD0RA_1LE0LD_1RB0LC_1LA---.v ⚠ not at pin
module
—
machine
1RB0RF_1RC0RB_1LD0RA_1LE0LD_1RB0LC_1LA--- (6 transitions apart)
diff
d = 4 (start A); SOMDC_Class1.v nonhalt (1LB---_1RC0RF_1LD1RB_1LE0LD_1RB0LB_1RB0RA, start F) also d = 4
note
W4-3 (ours, killed) is a multi-level counter on 00/11 defects whose fossils are inert (block lengths only matter mod 4). Here the counter's leftover is fossilized as junk J and is re-read: J decides the next cycle's start and whether it spurts. W4-3's RIncs-style scan does not cover a junk word that carries a binary residue. SOMDC_Class1 shares the d = 4 distance only; its rule set (one structural counter) has no overflow-to-junk step.
Proof strategy & riskshow the formal proof will go · 3 risks to watch

A proof needs a closed description of the junk words J and the cycle map (J, n) -> (J', n') or spurt, for every reachable J. That is an arithmetic map on n and a binary residue (c0 + 2^a0) mod 2^A, with the spurt as one residue class. Parked unless that map turns out to be a clean binary rule.

  • ▲Residue-driven: the cycle outcome depends on a ~12-bit residue of a slowly growing n; plateau lengths 1, 1, 9, 3, 31 look irregular (possible Collatz-like map).
  • ▲The junk J and the junk-processing phase (several sweeps with right records before each counter starts) are not characterised.
  • ▲Waves 4 and 5 rejected it; the only fixed-constant rule rulefit found (E1(2n,632-n)) is one finite pass of rule P.
Stats & provenance2·1010 steps simulated · 75,979 cells · the status in full · files
simulated
2·1010 steps
tape
75,979 cells · 36,061 nonzeros
growth
span doubles in spurts: 1.7k -> 3.5k (1.1e7) -> 7.4k (3.0e7) -> 16.7k (3.3e8) -> 34.2k (9.9e8) -> 75.0k (1.88e10); in between, plateaus grow ~30-190 cells per cycle; no halt to 2e10
status now
Parked at observe (BEC sweep, cap 1 h). Micro rules are clean: counter pass P0/P1 (0^inf <D (011)^a (010001)^b x (010001)^c -> a+1, b+2^a, c-2^a while c >= 2^a; 80/80) and overflow O (c < 2^a -> 0^inf J (011)^(2b+2c) C>, |J| = 3a+4; 24/24). The macro level is residue-driven: each overflow leaves the counter's binary residue in a junk word J that the next cycle re-reads, and J decides whether the cycle is ordinary (n -> n+9..75) or a spurt (n -> 2n+12..24). Plateaus of 1, 1, 9, 3, 31 cycles; spurts at 1.1e7, 3.0e7, 3.3e8, 9.9e8, 1.88e10; no halt to 2e10. Not flagged as cryptid (residue map not formalized). (status.json, 2026-10-13)
observer's note
Parked at observe (cap 1 h): counter passes and overflow shape validated (104/104), but the cycle map runs on a binary residue fossilized as junk; spurts are residue-timed (plateaus of 1, 1, 9, 3, 31 cycles).
files
observe.json · notes.md · status.json
other viewers
viewer

Proof & checks

No proof work yet.

Files

machines/<tm>/: 5 entries · raw notes, status, scripts, images

namesizechanged
notes.md ↓5.3 KB2026-10-13 16:19
status.json ↓1.2 KB2026-10-13 16:19
observe.json ↓9.0 KB2026-10-13 16:19
img/7 items2026-10-13 16:17
work/0 items2026-10-13 16:02
status.json in full
{
 "tm": "1RB0RF_1RC0LD_1RD0RA_1LE0LC_1LB0LE_0RC---",
 "label": "B-4",
 "status": "STUCK",
 "stage": "observe",
 "confidence": "low",
 "updated": "2026-10-13",
 "reason": "Parked at observe (BEC sweep, cap 1 h). Micro rules are clean: counter pass P0/P1 (0^inf <D (011)^a (010001)^b x (010001)^c -> a+1, b+2^a, c-2^a while c >= 2^a; 80/80) and overflow O (c < 2^a -> 0^inf J (011)^(2b+2c) C>, |J| = 3a+4; 24/24). The macro level is residue-driven: each overflow leaves the counter's binary residue in a junk word J that the next cycle re-reads, and J decides whether the cycle is ordinary (n -> n+9..75) or a spurt (n -> 2n+12..24). Plateaus of 1, 1, 9, 3, 31 cycles; spurts at 1.1e7, 3.0e7, 3.3e8, 9.9e8, 1.88e10; no halt to 2e10. Not flagged as cryptid (residue map not formalized).",
 "family_note": "No 740-list siblings. eqv_1590 lines 650-652: same table from starts B and C (Eqv_v2.v tm definitions), not on the 740 list.",
 "next_goal": "Characterise J: decode the junk word as the binary digits of r = (c0 + 2^a0) mod 2^A and test whether the next cycle's (a0, k, n' - n) and the spurt are a closed function of (r, A) on all ~50 observed cycles; park for good if not."
}
observe.json contract (tools/README-card.md):
2 contract warnings
  • rank: missing
  • template file not in the pinned tree: machines/1RB0RF_1RC0RB_1LD0RA_1LE0LD_1RB0LC_1LA---/1RB0RF_1RC0RB_1LD0RA_1LE0LD_1RB0LC_1LA---.v