Built . It shows the files as they were then (ages and “working now” follow your clock).
tools/rebuild_pages.sh rebuilds the site within 5 minutes of a change; by hand: python3 -B tools/site.py.Machines / #20
1RB1LE_0RC1RC_0RD0RB_1RE0RF_1LA0LE_---1RB
Where it stands
Parked at the deeper analysis
Parked by Dennis 2026-10-10 (decision queue: park). Deepen round 2: 10 more rules validated (731/731), including 3 halting patterns.
Read the full status
Calls depend on the room after the called block: room 4 swallows 1100, room 2 halts, a call on 11 leaves a phase-shifted 010 callee whose return builds a 1^6 block. The situation census is not closed: new classes appear in epoch 7. Small-parameter configs next to reachable ones halt (640/1584); medium ones do not (0/144). Hand rule-closure is not converging. Unstick with an abstract run-length simulator, a decider search, or Dennis's call
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
Nested bouncer call stack: Y(a,b,c)->Y(a+2,b-1,c+3) per round; epochs grow x2.5-3; mod-3 gap cases
- 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 12:49 · status.json 2026-10-10
- Class
- Chaotic Fractal Type 1ours: sheet Chaotic Fractal Type 1 ≠ ours Fractal call-stack bouncer (FractalType7/TM20 shape) · med confidence
- On the list
- line 10 of
BB6_holdouts_663.txt· historical 740 line 11
Your calls on file 2
- parked
- Parked by Dennis 2026-10-10 (decision queue: park).
- decision.json · answered 2026-10-10: park
- Park #20 (it stays STUCK), or fund one more stage to build an abstract run-length simulator that generates its full call-stack rule table? Decisions →
Mechanism
How it works: 3 notes
- Inner loop Y(a,b,c) = 1^a 001 (10)^b 11 (01)^c E>: each round a+2, b-1, c+3, eating 6 blank cells.
- When b hits 0, E wipes the 1^a block and walks left (Return); the level to its left resumes the same loop.
- When that gap runs out it calls the right level again: a call stack, so each epoch replays shrunken copies.
Figures for Checkpoint A
Rows: entries into E moving right. Compare the small staircases left of each wide white band with earlier rows.
bbchallenge-defaultStart blankRows every entry into state E moving rightWindow cells -16..4214, 1 px = 1 cellColors 1 0 or unvisited head (last move right/left)
Rows: 1,937 rows to step 3,000,000 (1,402 at the right edge = right turnarounds, 535 inside the tape), 9 to 5,473 steps apart · Colors: (10)^b blocks are 1-px stripes that look gray when shrunk, 1^a blocks are solid white
Edge records to 1M steps. Follow each white triangle and the gray (10)^b block beside it.
bbchallenge-defaultStart blankRows left/right recordsWindow cells -16..2383, 1 px = 1 cellColors 1 0 or unvisited head (last move right/left)
Rows: the start, then one row per new record; stopped at the 2,400-row cap at step 999,391 (not evenly spaced in time) · Colors: (10)^b blocks are 1-px stripes that look gray when shrunk
Blaze view to 1e9 steps. Look between the two big domes.
bbchallenge-blazeStart blankRows Blaze time blocks of 1,048,576 stepsWindow cells -64..75,135, 1 px = 94 cellsColors 0 1 1 only part of the time (or in part of the cells) of that pixel's block 1^a blocks (10)^b blocks (half ones)
Rows: (each averaged), 954 blocks to step 1e9, stretched to 500 px (1 px = about 2,000,000 steps) · Window: Blaze image: 1 column per 64 cells, averaged; 1,175 columns stretched to 800 px · Colors: no head
More figures (2)Fig 4–5: Epoch end, steps 15,000 to 24,000 · bbchallenge Default view, first 10,000 steps
Fig 4 · Epoch end, steps 15,000 to 24,000
Default-view zoom: the epoch ends, the head returns left, replays, and a new epoch starts.
bbchallenge-defaultStart mid-run: step 15,000Rows every step 15,000..23,999Window cells -144..255, 1 px = 1 cellColors 1 0 or unvisited head (last move right/left)
Rows: squeezed into 500 px by the site's bilinear filter: px row y blends steps 15,000+18y+8 and 15,000+18y+9, so it is effectively one sample every 18 steps · Window: x-translation 0.85: the start head, cell 196, sits at x = 340
For orientation: the start of the run as bbchallenge.org shows it.
bbchallenge-defaultStart blankRows every step 0..9,999Window cells -200..199, 1 px = 1 cellColors 1 0 or unvisited head (last move right/left)
Rows: squeezed into 500 px by the site's bilinear filter: px row y blends steps 20y+9 and 20y+10, so it is effectively one sample every 20 steps
Rules (6/6 validated)exact tape rewrites the proof will formalize, each re-checked by simulation
| rule | from ⟶ to | cases | steps | checked |
|---|---|---|---|---|
| YY (one round, tail) | L 1a 001 (10)b+1 12 (01)c E> 0d+6 R ⟶ L 1a+2 001 (10)b 12 (01)c+3 E> 0d R | a,b,c,d >= 0; L any; R = 1... (or d=inf) | 4b+8c+30 | ✓87/87 |
| YX (half round) | L 1a 001 (10)b+1 12 (01)c E> 0d+3 R ⟶ L 1a+2 001 (10)b 0 (01)c+2 E> 0d R | a,b,c,d >= 0; tail form (R=0^inf) 63/63 too | 4b+4c+17 | ✓85/85 |
| XY (half round) | L 1a 001 (10)b 0 (01)c E> 0d+3 R ⟶ L 1a 001 (10)b 12 (01)c+1 E> 0d R | a,b,c,d >= 0; tail form 63/63 too | 4c+5 | ✓87/87 |
| YX1 (eat ones) | L 1a 001 (10)b+1 12 (01)c E> 1d+1 R0 ⟶ L 1a+2 001 (10)b 0 (01)c+1 E> 1d R0 | a,b,c,d >= 0; R0 = 0... | 4b+4c+15 | ✓83/83 |
| XY1 (eat ones) | L 1a 001 (10)b 0 (01)c+1 E> 1d+1 R0 ⟶ L 1a 001 (10)b 12 (01)c+1 E> 1d R0 | a,b,c,d >= 0 (fails at c=0: needs >= 1 copy of 01) | 4c+7 | ✓87/87 |
| Return (b = 0) | L0 1a 001 12 (01)c E> 0d+1 R ⟶ L0 <E 0a+1 1100 12c+1 0d R | L0 ends in 0; tail form 63/63 too. Gap leftover 0/1/2 (mod 3) = 3 different call paths, not yet ruled | a+2c+14 | ✓85/85 |
Compressed historythe tape as 0∞ L 1a 001 (10)b 12 (01)c E> 0∞ at 24 moments: where the rules are read off
0∞ L 1a 001 (10)b 12 (01)c E> 0∞
| step | a | b | c | span |
|---|---|---|---|---|
| 1,323 | 5 | 10 | 5 | 86 |
| 2,485 | 19 | 3 | 26 | 128 |
| 4,853 | 2 | 30 | 2 | 160 |
| 5,015 | 4 | 29 | 5 | 166 |
| 10,829 | 38 | 12 | 56 | 268 |
| 16,949 | 58 | 2 | 86 | 328 |
| 24,233 | 4 | 74 | 5 | 356 |
| 50,947 | 78 | 37 | 116 | 578 |
| 78,289 | 120 | 16 | 179 | 704 |
| 114,965 | 4 | 224 | 5 | 816 |
| 343,847 | 226 | 113 | 338 | 1,482 |
| 574,549 | 348 | 52 | 521 | 1,848 |
| 880,549 | 4 | 676 | 5 | 2,176 |
| 3,584,549 | 804 | 276 | 1,205 | 4,576 |
| 6,300,119 | 1,226 | 65 | 1,838 | 5,842 |
| 9,905,729 | 4 | 1,782 | 5 | 6,248 |
| 24,021,257 | 1,768 | 900 | 2,651 | 11,540 |
| 38,137,595 | 2,722 | 423 | 4,082 | 14,402 |
| 56,966,297 | 5 | 5,350 | 5 | 16,956 |
| 213,376,947 | 6,055 | 2,325 | 9,080 | 35,106 |
| 369,764,769 | 9,249 | 728 | 13,871 | 44,688 |
| 578,233,633 | 4 | 13,412 | 5 | 49,072 |
| 704,796,961 | 3,548 | 11,640 | 5,321 | 59,704 |
| 831,281,491 | 6,038 | 10,395 | 9,056 | 67,174 |
alast 6,038blast 10,395clast 9,056spanlast 67,174Template comparisonFractalType7v4.v TM20: partly applies · the nearest solved proof, what carries over, and the transitions that differ
| 0 | 1 | |
|---|---|---|
| A | 1RB | 1LE |
| B | 0RC | 1RC |
| C | 0RD | 0RB |
| D | 1RE | 0RF |
| E | 1LA | 0LE |
| F | --- | 1RB |
differs from the template
- file
FractalType7v4.v:6- module
TM20- machine
1RB0LF_1RC0RA_0RD0RB_1LE0RF_1LB0LE_1LE---(7 transitions apart)- diff
7 of 12 transitions (A1 B0 B1 D0 E0 F0 F1; halt moves F1->F0); no relabel/mirror does better; best in FractalType7v2/v3 is 8- note
- Same architecture: S1 loop (Inc/Incs) + Empty_b return + P call + Column + Good invariant. Its S1/Inc configs do not carry over: 0/20 Inc, our machine halts in 6 steps from S1.
Proof strategy & riskshow the formal proof will go · 3 risks to watch
Copy TM20's skeleton, not its rules: prove XY/YX/XY1/YX1/Return with es + ind (Incs-style), define P u r r' (call returns 0^u), prove one Column lemma per gap residue mod 3, then a Good-style inductive invariant with inequality bounds on the column chain; init via chunks + native_compute; nonhalt via progress_nonhalt.
- ▲Gap leftovers mod 3 vary in the run (start residues 1:41, 2:23, 0:17 of 81 runs); TM20 kept all counts = 0 mod 3. Invariant must track residues.
- ▲Epoch ratio alternates x2.5 / x3 (not affine), so only an inequality invariant can work; exact epoch map unknown.
- ▲Resisted mxdys's FractalType7 LLM batch; template is 7 transitions away, so new Column lemmas, not copy-and-modify.
Stats & provenance109 steps simulated · 75,124 cells · the status in full · files
- simulated
- 109 steps
- tape
- 75,124 cells · 59,751 nonzeros
- growth
- span ~ sqrt(5.6 t) (t ~ 0.18 span^2); left edge frozen at -16 after step 4428; qsim: 1.99e13 steps, 8.5M nonzeros, no halt
- status now
- Parked by Dennis 2026-10-10 (decision queue: park). Deepen round 2: 10 more rules validated (731/731), including 3 halting patterns. Calls depend on the room after the called block: room 4 swallows 1100, room 2 halts, a call on 11 leaves a phase-shifted 010 callee whose return builds a 1^6 block. The situation census is not closed: new classes appear in epoch 7. Small-parameter configs next to reachable ones halt (640/1584); medium ones do not (0/144). Hand rule-closure is not converging. Unstick with an abstract run-length simulator, a decider search, or Dennis's call (status.json, 2026-10-10)
- observer's note
- Mechanism found (TM20-shaped call-stack fractal); inner rules validated; epoch-level map and mod-3 call cases still open. Not Collatz-like so far.
- files
- observe.json · notes.md · status.json
Proof & checks
No proof work yet.
Files
machines/<tm>/: 8 entries · raw notes, status, scripts, images
| name | size | changed |
|---|---|---|
| notes.md ↓ | 14 KB | 2026-10-10 12:49 |
| status.json ↓ | 823 B | 2026-10-10 12:49 |
| observe.json ↓ | 11 KB | 2026-10-10 04:41 |
| deepen.json ↓ | 7.7 KB | 2026-10-10 08:12 |
| decision.json ↓ | 4.4 KB | 2026-10-10 12:49 |
| img/ | 7 items | 2026-10-10 00:53 |
| scripts/ | 26 items | 2026-10-10 08:12 |
| rulefit_out.txt ↓ | 2.7 KB | 2026-10-10 00:43 |
status.json in full
{
"tm": "1RB1LE_0RC1RC_0RD0RB_1RE0RF_1LA0LE_---1RB",
"status": "STUCK",
"stage": "deepen2",
"updated": "2026-10-10",
"confidence": "med",
"recommend": "stuck",
"reason": "Parked by Dennis 2026-10-10 (decision queue: park). Deepen round 2: 10 more rules validated (731/731), including 3 halting patterns. Calls depend on the room after the called block: room 4 swallows 1100, room 2 halts, a call on 11 leaves a phase-shifted 010 callee whose return builds a 1^6 block. The situation census is not closed: new classes appear in epoch 7. Small-parameter configs next to reachable ones halt (640/1584); medium ones do not (0/144). Hand rule-closure is not converging. Unstick with an abstract run-length simulator, a decider search, or Dennis's call",
"parked": "Parked by Dennis 2026-10-10 (decision queue: park)."
}