BB(6) hunt
Machines / #17

1RB0LF_0RC0RB_1LC1LD_1RE0RD_---0RA_1LA0LF

#17ParkedUnknownbbchallenge ↗Explorer

Where it stands

Parked at the deeper analysis

Parked by Dennis 2026-10-10 (decision queue: park). Deepen 2: no proof route in reach.

Read the full status

Micro rules and the left epoch map are exact. The tail is a fossil-processing particle system whose particle catalogue keeps growing (363 types; new ones in E7 and E8), so round 1's saturation claim fails after E4. No n-gram closed language exists (plain CPS n<=20, parity CPS n<=14). E8 rebuilds the right end without its 1^k run. Simulation-only safety: no halt to 4.31e13 (Quick_Sim, cross-checked at cell level), and the only near-halts (D1) are the 6 of E0 and E3; the E8 rebuild was re-run at cell level with 0 D1. Not a cryptid on current evidence (right-end schedule fits epochs = 0 or 3 mod 4). Priority call for Dennis: park, or fund a multi-day particle-level simulator plus an invariant on particle sequences.

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

Bouncer on a 10-background with domain walls; self-similar epochs a'=3a+6, c'=3a+c+2 (exact, 5/5)

Status
Parkeddeepen2 · updated 2026-10-10Not blocking · Stuck at the deepen2 stage. Answer Q1–Q3 whenever; a “no” redirects the work.
idle since Oct 10 18:19 · status.json 2026-10-10
Class
Unknownours: sheet Unknown ≠ ours Self-similar multi-wall bouncer (x3 epochs) · med confidence
On the list
line 564 of BB6_holdouts_663.txt · historical 740 line 628
#17eqv ×1table ×2sim 1e15
Your calls on file 2
parked
Parked by Dennis 2026-10-10 (decision queue: park).
decision.json · answered 2026-10-10: park
#17's cheap proof routes are closed: epoch induction is blocked on the tail, and no regular closed language exists at the sizes tried. Park it, or fund a multi-day particle-level simulator plus an invariant on particle sequences? Decisions →

Mechanism

How it works: 3 notes
  • Tape = alternating 10 background plus a few walls (00, 11, (010)^2, dense 1011 blocks).
  • Sweeps flip 10<->01 and bounce off walls; phases (fixed sweep programs) chain into epochs, span x3 per epoch.
  • Epoch anchors P(a,c,T): a' = 3a+6, c' = 3a+c+2 exactly. The tail rule T -> T' is the open question.

Figures for Checkpoint A

Fig 1 · First 1,500 steps from blankQ1viewer ↗

Every step from blank; thicker stripes are walls. Follow the head and the thin stripes it crosses.

First 1,500 steps from blank
bbchallenge-defaultStart blankRows every step: steps 0-1,500 in 4 columns of 375Window cells -42..25, 1 px = 1/2 cellColors 1 0 or never visited head that just moved R/L
Rows: plus a zoom of steps 1,176-1,280 · Window: (each cell is 2x2 px); zoom panel: cells -38..6, each cell 7x7 px
Fig 2 · Epoch 2 vs epoch 3, scaled to matchQ2Q3

Right panel overlays epochs 2 and 3 (matched scale): black = both, blue = 2 only, red = 3 only.

Epoch 2 vs epoch 3, scaled to match
customStart mid-run: step 45,249,547Rows 450 rows per epochWindow cells -36,880..79, 1 px = 80 cellsColors epoch 2 only epoch 3 only both
Start: (epoch-2 anchor P) and step 439,293,481 (epoch-3 anchor P), both on the blank-tape run · Rows: anchor to next anchor: every 875,654 steps (epoch 2), every 7,523,671 steps (epoch 3) · Window: (epoch 2); epoch 3: cells -110,640..239, 1 px = 240 cells; cell 0 at the right edge of both · Colors: panels 1-2: as the walls view (grey background, blue wall, orange (1011)^n block, white never visited); panel 3 (overlay, walls only)
More figures (3)Fig 3–5: Walls over time, 440 million steps · Records view: epochs nest at 3× scale · Blaze view, 1 billion steps
Fig 3 · Walls over time, 440 million steps

Blue lines are walls; green ticks mark epoch starts. Each epoch is 3× wider and about 9× longer.

Walls over time, 440 million steps
customStart blankRows every 500,000 stepsWindow cells -36,800..63, 1 px = 64 cellsColors 1010… background wall at least 5/8 ones never visited tick: epoch start (anchor P)
Rows: steps 0-439,500,000, 880 rows · Colors: grey: either phase; blue: a 00 or 11 among the pixel's cells; the head's own pair ignored; orange: (1011)^n-type block; head not drawn
Fig 4 · Records view: epochs nest at 3× scale

Rows count records, so each epoch is 3× taller and wider; left of the tail the picture repeats.

Records view: epochs nest at 3× scale
customStart blankRows every 48th left/right recordWindow cells -36,768..95, 1 px = 48 cellsColors 1010… background wall at least 5/8 ones never visited tick: epoch start (anchor P)
Rows: records 48..36,816; record 36,823 = the epoch-3 anchor · Colors: grey: either phase; blue: a 00 or 11 among the pixel's cells; the head's own pair ignored; orange: (1011)^n-type block; head not drawn
Fig 5 · Blaze view, 1 billion stepsviewer ↗

Overall shape only; the walls are too thin to see at this scale.

Blaze view, 1 billion steps
bbchallenge-blazeStart blankRows Blaze time blocksWindow cells -65,088..63, 1 px = 64 cellsColors no 1s or never visited half 1s (1010… background) 3/4 1s ((1011)^n) all 1s
Rows: 1 row = 1,048,576 steps, averaged (quality); 954 rows, the last one partial · Window: the engine's 1018x954 image; the site stretches it to 800x500 · Colors: green ticks in the margin = epoch starts
Rules (5/5 validated)exact tape rewrites the proof will formalize, each re-checked by simulation
rulefrom ⟶ tocasesstepschecked
Epoch map (anchor to anchor)
0∞ <A (10)3 (010)2 (10)a (01)2 1 (10)4 (01)2 1 (10)c T
⟶ 0∞ <A (10)3 (010)2 (10)3a+6 (01)2 1 (10)4 (01)2 1 (10)3a+c+2 T'
a even >=2, c odd >=3 (always on orbit). c even: c'=3a+c+3. c=1: c'=3a+5. T' unknown~150a2, depends on T✓49/49
Burst cycle
0∞ <A (10)3 (010)2 (10)a+2 (01)2 1 (10)b r
⟶ 0∞ <A (10)3 (010)2 (10)a (01)2 1 (10)b+6 r
a even >=2 (odd a: other cycle, never on orbit); any b>=0; r never read20a+210✓420/420
Slow-phase cycle (epoch 1, ~1e7)
0∞ <A (10)3 (010)2 (10)a (01)b+2 02 (1011)2 (10)c (01)d 02 (10)e (01)f+4 (010)2 (1110)g R
⟶ 0∞ <A (10)3 (010)2 (10)a+2 (01)b 02 (1011)2 (10)c+2 (01)d+2 02 (10)e (01)f (010)2 (1110)g+2 R
a,b,c,e,f odd; d even >=2 (d=0 fails); g any; R = right part frozen in this phase20(a+b)+10(c+d+e+f)+340✓86/86
sligocki low-level [0] (early burst-type)
0∞ (01)3 (10)2 (01)2a+11 (10)3 <F (01)2b+4 (010)2 1 (10)2 1 (110)2 1 0 13 (10)2 16 0∞
⟶ 0∞ (01)3 (10)2 (01)2a+9 (10)3 <F (01)2b+10 (010)2 1 (10)2 1 (110)2 1 0 13 (10)2 16 0∞
—40a+344✓10/10
sligocki low-level [1] (early 5-counter phase)
0∞ (01)3 (10)2 0 (10)2 02 1 (01)2a+4 (10)2b+11 12 (01)2c+5 (10)2 (01)2d+7 <A (10)2 (01)2e+4 0 (01)2 12 0∞
⟶ 0∞ (01)3 (10)2 0 (10)2 02 1 (01)2a+8 (10)2b+7 12 (01)2c+9 (10)2 (01)2d+5 <A (10)2 (01)2e+10 0 (01)2 12 0∞
b, d shrink by 2: needs a mod split80a+80b+40c+40d+1360✓10/10
Compressed historythe tape as 0∞ <A (10)3 (010)2 (10)a (01)2 1 (10)b (01)2 1 (10)c T at 13 moments: where the rules are read off
0∞ <A (10)3 (010)2 (10)a (01)2 1 (10)b (01)2 1 (10)c T
stepabclen(T)
544,2011684217481
701,0712502217?
5,363,49951047231,527
6,401,649240814723?
6,601,1491401,114723?
6,712,23921,528723?
45,249,5471,53642,2554,603
57,001,2971864,0542,255?
439,293,4814,61446,86513,835
545,008,38147412,4246,865?
3,824,945,14913,848420,70941,563
4,700,080,4194,11429,20620,709?
35,431,165,69741,550462,255124,667
alast 41,550
41,55025.4e53.5e10log xstep 544201: a = 168step 701071: a = 2step 5363499: a = 510step 6401649: a = 240step 6601149: a = 140step 6712239: a = 2step 45249547: a = 1536step 57001297: a = 186step 439293481: a = 4614step 545008381: a = 474step 3824945149: a = 13848step 4700080419: a = 4114step 35431165697: a = 41550
blast 4
29,20645.4e53.5e10log xstep 544201: b = 4step 701071: b = 502step 5363499: b = 4step 6401649: b = 814step 6601149: b = 1114step 6712239: b = 1528step 45249547: b = 4step 57001297: b = 4054step 439293481: b = 4step 545008381: b = 12424step 3824945149: b = 4step 4700080419: b = 29206step 35431165697: b = 4
clast 62,255
62,2552175.4e53.5e10log xstep 544201: c = 217step 701071: c = 217step 5363499: c = 723step 6401649: c = 723step 6601149: c = 723step 6712239: c = 723step 45249547: c = 2255step 57001297: c = 2255step 439293481: c = 6865step 545008381: c = 6865step 3824945149: c = 20709step 4700080419: c = 20709step 35431165697: c = 62255
len(T)last 124,667
1.2e54815.4e53.5e10log xstep 544201: len(T) = 481step 5363499: len(T) = 1527step 45249547: len(T) = 4603step 439293481: len(T) = 13835step 3824945149: len(T) = 41563step 35431165697: len(T) = 124667
Template comparisonLongNv1.v TM1: partly applies · the nearest solved proof, what carries over, and the transitions that differ
01
A1RB0LF
B0RC0RB
C1LC1LD
D1RE0RD
E---0RA
F1LA0LF
file
LongNv1.v:51
module
TM1
machine
1LB0RD_0LC0LB_0RD1LB_1RD1RE_1RF---_0RA1LA (12 transitions apart)
diff
12/12 transitions differ (8/12 after best mirror+renaming); Bouncer_v3.v TM1: 11/12 (9/12)
note
No rule or config carries over (from LongNv1 TM1's start ours halts in 3 steps). The technique does: segRLs_n history induction P n -> P (S n) fits our x3 epoch induction.
Proof strategy & riskshow the formal proof will go · 3 risks to watch

Per-phase cycle lemmas (es + ind), chained with follow into Epoch: P(a,c,T) -->+ P(3a+6,3a+c+2,T'). Then induct over epochs with progress_nonhalt_cond (invariant: a even, c odd, Inv(T)). Inv(T) = tail language closed under one epoch, via Longitudinal sideRLs/segRLs_n (Bouncer_v3, LongNv1) or LongN closed sets.

  • ▲Tail T is rewritten every epoch (73-100% of it is read); its rule T->T' is unknown and may be chaotic.
  • ▲Each epoch has many 5-7-counter phases; a hand proof could exceed 50 KB.
  • ▲Halt pattern D> 1^k 00 exists and the tail has 0^2/0^3 walls; non-halting depends on the tail invariant.
Stats & provenance4·1010 steps simulated · 384,466 cells · the status in full · files
simulated
4·1010 steps
tape
384,466 cells · 192,262 nonzeros
growth
span x3 per epoch (time x8.5-9.9), ~2*sqrt(t); right edge only 56 -> 84
status now
Parked by Dennis 2026-10-10 (decision queue: park). Deepen 2: no proof route in reach. Micro rules and the left epoch map are exact. The tail is a fossil-processing particle system whose particle catalogue keeps growing (363 types; new ones in E7 and E8), so round 1's saturation claim fails after E4. No n-gram closed language exists (plain CPS n<=20, parity CPS n<=14). E8 rebuilds the right end without its 1^k run. Simulation-only safety: no halt to 4.31e13 (Quick_Sim, cross-checked at cell level), and the only near-halts (D1) are the 6 of E0 and E3; the E8 rebuild was re-run at cell level with 0 D1. Not a cryptid on current evidence (right-end schedule fits epochs = 0 or 3 mod 4). Priority call for Dennis: park, or fund a multi-day particle-level simulator plus an invariant on particle sequences. (status.json, 2026-10-10)
observer's note
Left recursion is exact and affine (parities invariant, no Collatz branching). Tail rule open. Sheet: Level-0 tab, class Unknown, no notes; not in Discord lists.
files
observe.json · notes.md · status.json

Proof & checks

No proof work yet.

Files

machines/<tm>/: 28 entries · raw notes, status, scripts, images

namesizechanged
notes.md ↓19 KB2026-10-10 12:49
status.json ↓1,011 B2026-10-10 12:49
observe.json ↓10 KB2026-10-10 04:41
deepen.json ↓8.2 KB2026-10-10 08:39
decision.json ↓4.3 KB2026-10-10 12:49
img/15 items2026-10-10 07:58
scripts/39 items2026-10-10 08:40
anchors.json ↓1.9 KB2026-10-10 00:59
cfg_9786531.txt ↓13 KB2026-10-10 00:49
compress_track_1e8.txt ↓8.0 KB2026-10-10 00:55
epoch_cases.json ↓47 KB2026-10-10 00:53
epoch_cases2.json ↓28 KB2026-10-10 00:53
epoch_cases3.json ↓17 KB2026-10-10 00:54
epoch_validation.jsonl ↓3.1 KB2026-10-10 00:53
epoch_validation2.jsonl ↓2.3 KB2026-10-10 00:53
epoch_validation3.jsonl ↓1.2 KB2026-10-10 00:54
every1e6_snap.jsonl.gz ↓151 KB2026-10-10 00:41
every1e7_snap.jsonl.gz ↓16 KB2026-10-10 00:39
every2e8_snap.jsonl.gz ↓7.8 KB2026-10-10 00:44
every5e4_snap.jsonl.gz ↓70 KB2026-10-10 00:42
records_1e9.jsonl.gz ↓576 KB2026-10-10 00:30
records_4e10.jsonl.gz ↓3.4 MB2026-10-10 00:52
records_6e9.jsonl.gz ↓1.5 MB2026-10-10 00:47
rulefit.json ↓28 KB2026-10-10 00:56
rulefit.txt ↓956 B2026-10-10 00:56
sim_1e9_end.jsonl ↓152 B2026-10-10 00:29
sim_1e9_time.txt ↓42 B2026-10-10 00:29
tails.json ↓61 KB2026-10-10 00:53
status.json in full
{
 "tm": "1RB0LF_0RC0RB_1LC1LD_1RE0RD_---0RA_1LA0LF",
 "status": "STUCK",
 "stage": "deepen2",
 "updated": "2026-10-10",
 "reason": "Parked by Dennis 2026-10-10 (decision queue: park). Deepen 2: no proof route in reach. Micro rules and the left epoch map are exact. The tail is a fossil-processing particle system whose particle catalogue keeps growing (363 types; new ones in E7 and E8), so round 1's saturation claim fails after E4. No n-gram closed language exists (plain CPS n<=20, parity CPS n<=14). E8 rebuilds the right end without its 1^k run. Simulation-only safety: no halt to 4.31e13 (Quick_Sim, cross-checked at cell level), and the only near-halts (D1) are the 6 of E0 and E3; the E8 rebuild was re-run at cell level with 0 D1. Not a cryptid on current evidence (right-end schedule fits epochs = 0 or 3 mod 4). Priority call for Dennis: park, or fund a multi-day particle-level simulator plus an invariant on particle sequences.",
 "parked": "Parked by Dennis 2026-10-10 (decision queue: park)."
}