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1RB0RA_1LC0LF_1LE0LD_1LB---_1RA1LB_0LB0RC
Upstream result
Claimed elsewhere
The blank-start machine never halts: BECv10.v.TM29 ↗. 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.
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
BECv1 tm108 twin (E1): 3-cell binary counter, unary, marker; rounds ruled (99.7%), the grid-shifting eat is open
- Upstream
- The blank-start machine never halts: BECv10.v.TM29 ↗. Recorded commit time: 2026-10-13T13:42:06Z. First public push time is not established.
- Status
- Externally Solvedtight · updated 2026-10-11Not blocking · Stuck at the tight stage. Answer Q1–Q3 whenever; a “no” redirects the work.idle since Oct 11 08:55 · status.json 2026-10-11
- Class
- Bell eats counterours: Bell eats counter (sheet) · ours adds: BECv1 tm108 twin (E1) with 3-cell counter digits and a grid-shifting eat · med confidence
- On the list
- not on
BB6_holdouts_663.txt(line 191 of the previous list) · historical 740 line 191
Your calls on file 6
- priority call (answered)
- With #29's generic size lemma proved and only the leading-spacer recovery left (true on all 265,642 test words, unproved), fund one last ~2 h stage on it with a hard stop, or park #29 as STUCK now?
- funded
- option: tight · date: 2026-10-11
- 2026-10-10 · deepen
- #29's rounds, overflow and marker are ruled (99.7% of K-transitions to 1e10), but the grid-shifting eat is not. Spend one ~2 h deepen stage ruling the eat, or park #29 as STUCK? (Dennis: go with all recommendations (2026-10-10))
- 2026-10-10 · recovery
- With every #29 round ruled and the size bound proven by test except in rare leading-spacer epochs (where a surviving t has always recovered), fund one ~2 h recovery stage, or park #29 as STUCK? (auto-applied: Claude's recommendation, under Dennis's standing instruction 'do your recommendations and continuously orchestrate' (2026-10-10, while he was away). Override any time.)
- 2026-10-10 · size_invariant
- With #29's eat ruled and safe for every t-free counter, fund one ~2 h stage on the last size invariant (eat-made t units clear before the next eat), or park #29 as STUCK at it? (auto-applied: Claude's recommendation, under Dennis's standing instruction 'do your recommendations and continuously orchestrate' (2026-10-10, while he was at lunch). Override any time.)
- 2026-10-11 · tight
- With #29's generic size lemma proved and only the leading-spacer recovery left (true on all 265,642 test words, unproved), fund one last ~2 h stage on it with a hard stop, or park #29 as STUCK now? (Dennis: go with recommendations (2026-10-11))
Mechanism
How it works: 3 notes
- Tape: counter W of 3-cell units (0 = 000, 1 = 100, spacer 010; MSB left), unary (010)^b, marker 00, then (101)^c. Only E1 differs from tm108: B carries, so digits are 3-cell units.
- Each round the marker steps one unit left (b-1, c+1) and W += 1 (B carries over 100 and spacers, turns at 000); an overflow adds a 3-cell digit at the left end.
- At b = 0 the marker eats W: the 3-cell grid shifts by one cell (1-digits -> spacers, spacers -> 001), c becomes the new unary, the marker is reborn at the right, then mini-eats re-align W. N ~ (4t)^(1/3); no halt to 1e10.
Figures for Checkpoint A
The site's own view. Each zigzag is one round between the counter (left turns) and the marker (right turns).
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 effectively one sample every 20 steps
One row per step. Follow the right turning point leftwards until it meets the left turns, then the run right.
bbchallenge-defaultStart mid-run: step 19,500Rows every step 19,500..20,399Window cells -110..39, 1 px = 0.5 cellsColors 1 0 or unvisited head (last move right/left)
Start: blank run; config in img/eat_start_19500.txt · Rows: 900 rows, each 2 px tall · Window: (each cell 2x2 px); cell numbers are those of the blank run (start cell = 0)
Fig 3 · Blaze, 1 billion steps
Overall shape only. Compare the moving left edge with the nearly fixed right edge; faint horizontal bands are epochs.
bbchallenge-blazeStart blankRows Blaze time blocks of 1,048,576 stepsWindow cells -4288..527, 1 px = 6 cellsColors 0 1 1 only part of the time (or in part of the cells) of that pixel's block
Rows: (each averaged), 954 blocks to step 1e9, stretched to 500 px (1 px = about 2 million steps) · Window: Blaze image: 1 column per 4 cells, 1,204 columns stretched to 800 px · Colors: no head
More figures (1)Fig 4: Left records, left edge pinned
One row per new leftmost cell; an overflow makes three. The pinned edge shows the counter word between epochs.
bbchallenge-defaultStart blankRows left records onlyWindow cells 0..149, 1 px = 0.5 cellsColors 1 0 or unvisited head (last move right/left)
Rows: the start, then one row per new leftmost cell (839 rows to step 10,000,000; 3 rows per counter overflow; not evenly spaced in time) · Window: (each cell 2x2 px); counted from each row's leftmost visited cell (frame = left), the rest of the tape is cut off
Rules (11/12 validated)exact tape rewrites the proof will formalize, each re-checked by simulation
| rule | from ⟶ to | cases | steps | checked |
|---|---|---|---|---|
| R1 A over spacer (= BECv1 HR1) | l A> (101)n r ⟶ l (010)n A> r | — | 7n | ✓60/60 |
| R2 A over carried digit | l A> 111 r ⟶ l 000 A> r | — | 3 | ✓60/60 |
| R3 B over spacer (= HR3) | l (010)n <B r ⟶ l <B (101)n r | — | 3n | ✓60/60 |
| R4 carry over digit 1 | l 100 <B r ⟶ l <B 111 r | E1 = 1LB hands the carry back to B (tm108: E keeps carrying) | 3 | ✓60/60 |
| R5 turn at digit 0 | l 000 <B r ⟶ l 100 A> r | — | 5 | ✓60/60 |
| R6 overflow at the left end | 0∞ <B r ⟶ 0∞ 100 A> r | new MSB digit, 3 cells | 5 | ✓60/60 |
| R7 marker step (= HR2) | l A> 101 00 101 r ⟶ l <B 00 101 101 r | — | 13 | ✓60/60 |
| R8 marker birth (= HE2) | l 010 A> 0∞ ⟶ l <B 00 101 0∞ | — | 6 | ✓60/60 |
| ROUND: one counter increment | 0∞ W (010)b+1 A> 101 00 (101)c 0∞ ⟶ 0∞ inc(W) (010)b A> 101 00 (101)c+1 0∞ | W over {010,000,100}, ends in a digit; W = U 000 V with V in {010,100}* (s, o = counts in V): inc(W) = U 100 V' (V' = V with 100 -> 000); no 000 in W: inc(W) = 100 V'. Holds for 870,221 of 872,741 K-to-K transitions from blank to 1e10 (0 mismatches) | 10b+21+10s+6o | ✓372/372 |
| OVERFLOW: one counter period, left record to left record | 0∞ <B W (101)b 00 (101)c 0∞ ⟶ 0∞ <B 111 W (101)b-2^D 00 (101)c+2^D 0∞ | W over {111,101} (all digits carried), D = number of 111 units, b > 2^D. From blank: 2,382 of 2,382 in-epoch left-record pairs to 1e10; c = 2^D-1 at 2,911 of 2,919 clean left records | — | ✓150/150 |
| EAT shape (b = 0), aligned W: no halt, next K reached | 0∞ W A> 101 00 (101)c 0∞ (b = 0) ⟶ 0∞ W' (010)b' A> 101 00 (101)c' (r') 0∞, marker reborn at the right end | Shape check only (no halt, a K-moment follows). W' is W re-read on a grid shifted by one cell (100 -> 010, 000 -> 000, 010 -> 001) plus local changes; exact form not ruled | — | ✓400/400 |
| EAT cascade: exact rule (open) | eat with 001 units (shifted segments) and pseudo-markers ⟶ open | 2,186 eat/mini-eat transitions and 334 carries into shifted segments to 1e10 are not covered by any exact rule yet | — | –untested |
Compressed historythe tape as 0∞ <B W (101)b 00 (101)c 0∞ (at each left record; W over d = 111, S = 101) at 36 moments: where the rules are read off
0∞ <B W (101)b 00 (101)c 0∞ (at each left record; W over d = 111, S = 101)
| step | W (d = digit, S = spacer; MSB left) | D (digits in W) | b | c |
|---|---|---|---|---|
| 7,904 | d | 1 | 29 | 1 |
| 8,499 | dd | 2 | 27 | 3 |
| 9,572 | ddd | 3 | 23 | 7 |
| 11,241 | dddd | 4 | 15 | 15 |
| 13,034 | d | 1 | 35 | 1 |
| 13,749 | dd | 2 | 33 | 3 |
| 15,062 | ddd | 3 | 29 | 7 |
| 17,211 | dddd | 4 | 21 | 15 |
| 19,592 | ddddd | 5 | 5 | 31 |
| 22,402 | SddSd | 3 | 31 | 7 |
| 24,761 | dSddSd | 4 | 23 | 15 |
| 27,562 | ddSddSd | 5 | 7 | 31 |
| 30,808 | SSdSdd | 3 | 34 | 7 |
| 33,397 | dSSdSdd | 4 | 26 | 15 |
| 100,093,972 | ddddSSddSdSSdSSSSSSSSSSSSSSSSSSSSSSSd | 9 | 179 | 511 |
| 100,500,756 | SSddSSSSdSdSSd | 5 | 684 | 31 |
| 100,715,701 | dSSddSSSSdSdSSd | 6 | 652 | 63 |
| 101,114,874 | ddSSddSSSSdSdSSd | 7 | 588 | 127 |
| 101,790,343 | dddSSddSSSSdSdSSd | 8 | 460 | 255 |
| 102,649,764 | ddddSSddSSSSdSdSSd | 9 | 204 | 511 |
| 103,084,352 | SSddSSSSdSSSSSSdSSd | 5 | 685 | 31 |
| 103,300,017 | dSSddSSSSdSSSSSSdSSd | 6 | 653 | 63 |
| 103,700,630 | ddSSddSSSSdSSSSSSdSSd | 7 | 589 | 127 |
| 104,378,979 | dddSSddSSSSdSSSSSSdSSd | 8 | 461 | 255 |
| 9,822,265,052 | dSSSdSdSSSdd | 5 | 3,484 | 31 |
| 9,823,375,757 | ddSSSdSdSSSdd | 6 | 3,452 | 63 |
| 9,825,566,450 | dddSSSdSdSSSdd | 7 | 3,388 | 127 |
| 9,829,824,959 | ddddSSSdSdSSSdd | 8 | 3,260 | 255 |
| 9,837,850,460 | dddddSSSdSdSSSdd | 9 | 3,004 | 511 |
| 9,851,935,385 | ddddddSSSdSdSSSdd | 10 | 2,492 | 1,023 |
| 9,872,240,918 | dddddddSSSdSdSSSdd | 11 | 1,468 | 2,047 |
| 9,899,736,054 | SSSdddddSSSdSdSSSdd | 9 | 3,005 | 511 |
| 9,913,826,129 | dSSSdddddSSSdSdSSSdd | 10 | 2,493 | 1,023 |
| 9,934,141,962 | ddSSSdddddSSSdSdSSSdd | 11 | 1,469 | 2,047 |
| 9,975,773,479 | SdSdSSSdddddSSSdSdSSSd | 10 | 2,495 | 1,023 |
| 9,996,120,762 | dSdSdSSSdddddSSSdSdSSSd | 11 | 1,471 | 2,047 |
W (d = digit, S = spacer; MSB left)last dSdSdSSSdddddSSSdSdSSSdnot plottable
D (digits in W)last 11blast 1,471clast 2,047Template comparisonBECv1_6x2_solved.v: partly applies · the nearest solved proof, what carries over, and the transitions that differ
| 0 | 1 | |
|---|---|---|
| A | 1RB | 0RA |
| B | 1LC | 0LF |
| C | 1LE | 0LD |
| D | 1LB | --- |
| E | 1RA | 1LBtpl 1LE |
| F | 0LB | 0RC |
differs from the template
- file
BECv1_6x2_solved.v:872- module
- —
- machine
1RB0RA_1LC0LF_1LE0LD_1LB---_1RA1LE_0LB0RC(1 transition apart)- diff
E1: 1LB here vs 1LE in tm108- note
- The right half is identical: tm108's HR1, HR2, HR3 and HE2 (w0 = 101, w0' = 010, w1 = 00) hold here as R1, R7, R3 and R8. The left counter is not: in tm108, E carries over single-cell digits and m0 = 00 separates the counter from the unary. Here B carries (R4), digits are 3-cell units mixed with 010 spacers, and the eat shifts the grid, so solve_BECv1 (and its fixed-width LeftBinaryCounter) cannot apply.
Proof strategy & riskshow the formal proof will go · 3 risks to watch
Not ready for a proof. Next: rule the eat as a transducer on the counter word: the one-cell grid re-read (100 -> 010, 000 -> 000, 010 -> 001), then the mini-eat cascade until W is aligned again. Then look for a regular invariant on such words (BECv7/BECv8 carry-head and two-track transducer proofs are the closest style).
- ▲The eat cascade is long and context-dependent: random {010,000,100,001} words with no 100-001 pair still halt in about 5% of trials, so the invariant must be finer than unit bigrams.
- ▲The eat consumes the counter's bit pattern at eat time (about N mod 2^D). If safety depends on those bits, this becomes arithmetic (cryptid protocol).
- ▲Proof size: likely a BECv7/BECv8-class file (tens of KB), not a one-line certificate.
Stats & provenance1010 steps simulated · 10,628 cells · the status in full · files
- simulated
- 1010 steps
- tape
- 10,628 cells · 6,528 nonzeros
- growth
- span ~ t^(1/3): unary N ~ (4t)^(1/3) units, span ~ 3N cells (10,628 at 1e10)
- status now
- Parked by the agreed hard stop of the funded stage 'tight' (2026-10-11): the leading-spacer recovery lemma is not proved. Proved in the stage (informally, on validated unit rules): a closed form TF of when a leading-spacer eat word keeps a t (one bit pattern per layout; exact on all 265,642 words to 13 units and 103,000 long random or constructed words), the exact word it produces (bin(C_0) t^a inc(W)[a:]), that the next eat never reaches the surviving t, and that the first unit to reach the new v = 110 unit is a C run, never the B carry. Open: the head after that C-meets-v event (no unit rule; observed real = shadow plus a head) and a bound on how many eats the head survives (observed 1-3, 0 halts in every test). Not a cryptid: tightness is an explicit congruence on the layout and halting never depends on the bits. No further stages. (status.json, 2026-10-11)
- observer's note
- Mechanism identified at medium confidence: rounds, overflow, marker step and birth are ruled and validated; the eat (grid shift plus mini-eat cascade, 0.29% of K-transitions to 1e10) is not ruled. Proof work waits for Dennis (CLAUDE.md: med confidence).
- files
- observe.json · notes.md · status.json
Proof & checks
No proof work yet.
Files
machines/<tm>/: 13 entries · raw notes, status, scripts, images
| name | size | changed |
|---|---|---|
| notes.md ↓ | 44 KB | 2026-10-11 08:55 |
| status.json ↓ | 1.3 KB | 2026-10-11 08:55 |
| observe.json ↓ | 14 KB | 2026-10-10 10:12 |
| deepen.json ↓ | 14 KB | 2026-10-11 08:55 |
| data/ | 7 items | 2026-10-10 15:07 |
| decisions/ | 4 items | 2026-10-11 08:55 |
| img/ | 11 items | 2026-10-10 10:09 |
| scripts/ | 6 items | 2026-10-11 08:21 |
| compress_track_auto.txt ↓ | 4.1 KB | 2026-10-10 09:35 |
| compress_track_records_1e8.txt ↓ | 4.1 KB | 2026-10-10 09:35 |
| qsim_summary.jsonl ↓ | 474 B | 2026-10-10 09:35 |
| sim_1e10.jsonl ↓ | 152 B | 2026-10-10 09:36 |
| validation.json ↓ | 1.1 KB | 2026-10-10 10:07 |
status.json in full
{
"tm": "1RB0RA_1LC0LF_1LE0LD_1LB---_1RA1LB_0LB0RC",
"status": "STUCK",
"stage": "tight",
"updated": "2026-10-11",
"reason": "Parked by the agreed hard stop of the funded stage 'tight' (2026-10-11): the leading-spacer recovery lemma is not proved. Proved in the stage (informally, on validated unit rules): a closed form TF of when a leading-spacer eat word keeps a t (one bit pattern per layout; exact on all 265,642 words to 13 units and 103,000 long random or constructed words), the exact word it produces (bin(C_0) t^a inc(W)[a:]), that the next eat never reaches the surviving t, and that the first unit to reach the new v = 110 unit is a C run, never the B carry. Open: the head after that C-meets-v event (no unit rule; observed real = shadow plus a head) and a bound on how many eats the head survives (observed 1-3, 0 halts in every test). Not a cryptid: tightness is an explicit congruence on the layout and halting never depends on the bits. No further stages.",
"funded": {
"option": "tight",
"date": "2026-10-11"
},
"confidence": "med",
"priority_call_answered": "With #29's generic size lemma proved and only the leading-spacer recovery left (true on all 265,642 test words, unproved), fund one last ~2 h stage on it with a hard stop, or park #29 as STUCK now?"
}