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1RB1LA_1RC1RE_1RD0RD_1LA1RC_1RF0LE_1RA---
Where it stands
Parked at the observation
Halting hunt H-4 (2026-10-13): exact accelerated model (work/exact/xm.py: shift rules + symbolic suffix memos, all from the table) validated exactly from the blank tape through the first overflow to the rel-2e13 checkpoint (full 1e8-cell tapes) and against a fresh 3e11-step direct continuation. No halt up to step 5.636e76 (10^76.75). Epoch 2 is a counter of counters; the active counter eats (11010101)^6.29e6 at ~4.6 copies per decade, so its overflow (the next point where halting is decided) is projected near 10^(1.4e6) steps, out of reach. Not a kill; no certification route.
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
Binary counter over segments of 6-cell blocks; it eats a finite reservoir, and what happens after (~1e13+) is unseen
- Status
- Parkedhalting-hunt exact model · updated 2026-10-13Not blocking · Stuck at the halting-hunt exact model stage. Answer Q1–Q3 whenever; a “no” redirects the work.idle since Oct 13 23:42 · status.json 2026-10-13
- Class
- Shift-overflow structural counterours: sheet Shift-overflow structural counter ≠ ours SO structural counter: binary counter stored between 6-cell-block segments, widening into a finite reservoir · low confidence
- On the list
- line 245 of
BB6_holdouts_663.txt· historical 740 line 269 · observe.json rank #45
Your calls on file 3
- priority call (answered)
- More budget for the epoch map (exact boundary-gadget rules + an abstract simulator to watch 2-3 overflows), or park this machine?
- parked
- Closed 2026-10-13: the 2e13-step direct run from loop 288M finished (no halt, 597/597 refs; work/r5_post.log) and the seeded qsim hit its 4 h cap at step 4,969,937,411,350,948 (no halt). Superseded by the H-4 exact model (work/exact/).
- 2026-10-10 · watch
- Before any more agent time on R5, run one niced background qsim (block 12) for up to 24 h to watch the counter reach the left prefix, and park agent work until it reports? (Dennis: go with all recommendations (2026-10-10))
Mechanism
How it works: 3 notes
- Cycle: from the right edge the head zigzags left (rule Z: 20 steps per block, 101110 -> 111110), bounces off the first boundary that does not carry, then runs right (RS: 6 steps per block). The right edge grows 4 cells per cycle. Halting needs
0 <A 101(rule H). - The boundaries between block segments hold the bits of a binary counter: which boundary a cycle reaches follows the binary ruler sequence exactly (37,885/37,885 from step 5e4 to 1e10). Segment sizes double per bit (5, 23, 93, 374, 1496, ~6000 blocks at 1e9). Steps 0..~3.6e4 are a different, left-growing counter (init).
- The counter grows leftwards into a reservoir (10)^m: m goes 58 -> 11 by step 7.5e9, losing 5 then 2 per new top bit. qsim (block 12): the reservoir is gone by 3.4e12, older prefix gadgets are eaten by 7.7e12, and there is no halt to 8e13. The prefix left after that, 1^4 (01)^11 1 (10)^4, is the open question.
Figures for Checkpoint A
Top quarter: the early phase grows on both sides. Below it, compare the frozen left block with the right part.
bbchallenge-defaultStart blankRows left/right recordsWindow cells -59..1102, 1 px = 1 cellColors 1 0 or never visited head just moved right/left
Rows: the start, then one row each time the head reaches a new leftmost or rightmost cell (1,162 rows, steps 0..400,000); rows are not equal time · Colors: default colours
One row per cycle. Compare where the orange bars start, row to row; their right parts are all alike.
customStart mid-run: step 9,406,481Rows one row (2 px tall) per cycleWindow cells -60..1539, 1 px = 2 cellsColors cells the head swept during that cycle tape it did not reach in that cycle never visited
Start: rows are the real run from blank; no rebuilt tape · Rows: i.e. per new right record after a leftward excursion of more than 20 cells: 272 cycles, steps 9,406,481..14,286,019 · Window: the right part of the tape, up to cell ~5,900, is cut off
120 steps from the real tape. Follow the head colours through one 20-step repeat; compare blocks before and after.
bbchallenge-exploreStart mid-run: step 9,848,484Rows every step (121 rows, steps 9,848,484..9,848,604)Window cells 4902..4957, 1 px = 0.1 cellsColors 1 0
Start: the real tape at that step, passed in with --from-config · Window: each cell is 10 px wide; drawn as -44..11 relative to the head at the start · Colors: explore colours; the head cell is coloured by state: A red, B orange, C blue, D green, E magenta, F cyan
More figures (2)Fig 4–5: Blaze, 10 million steps · 16 cycles across the whole tape
The overall shape: span grows about like sqrt(t) to the right while the left end stays put.
bbchallenge-blazeStart blankRows Blaze time blocks of 16,384 stepsWindow cells -60..4984, 1 px = 6.3 cellsColors 0 1 mixed
Rows: (averaged), 611 blocks stretched to 500 px, so 1 px row ~ 20,000 steps (steps 0..10,000,000) · Window: about: 1,261 engine px of 4 cells each, stretched to 800 px · Colors: paler orange: each pixel averages its cells over its time block; no head drawn
Fig 5 · 16 cycles across the whole tape
The slanted lines are the zigzag fronts moving left; their lower ends show how deep each cycle went.
bbchallenge-defaultStart mid-run: step 9,817,765Rows every 400 stepsWindow cells -59..4998, 1 px = 4 cellsColors 1 0 or never visited head just moved right/left
Start: the real tape at that step, passed in with --from-config · Rows: (663 rows, steps 9,817,765..10,082,765), about 40 rows per cycle · Window: every 4th column sampled, so the 6-cell blocks alias into stripes; drawn as -4994..63 relative to the head at the start · Colors: default colours
Rules (8/9 validated)exact tape rewrites the proof will formalize, each re-checked by simulation
| rule | from ⟶ to | cases | steps | checked |
|---|---|---|---|---|
| Z zigzag left (L-pass) | (101110)n <A 1111111 0 ⟶ <A 1111111 0 (111110)n | any n >= 0, any context (the head never leaves the shown cells) | 20n | ✓90/90 |
| RS run right (R-pass) | D> (111110)n ⟶ (101011)n D> | any n >= 0, any context | 6n | ✓90/90 |
| H the only way to halt | 0 <A 101 ⟶ halt | F1 is the only undefined transition and F is entered only from E0, so every halt goes through this pattern | 4 (A0, B1, E0, then F reads 1) | ✓50/50 |
| RC0 right end, bit 0 -> 1 | X G S0 (110101)n 01 C> 0∞ ⟶ X G S1 (110101)n 01 C> 0∞ | G = 1^7 (01)^3 110 1^9 (01)^2 110 1^7 0; S0 = 1^8 (10)^4 1^9 (01)^6 1 (10)^3 1^5; S1 = 1^8 (10)^4 1^8 (10)^4 1^7 (01)^7; X = any left context (not reached) | 26n+108 | ✓100/100 |
| RC1 right end, n+1 | X G S1 (110101)n 01 C> 0∞ ⟶ X G S2 (110101)n+1 01 C> 0∞ | S2 = 1^8 (10)^4 1^8 (10)^4 1^6 (10)^4 1^5 | 26n+44 | ✓100/100 |
| RC3 right end, back to S0, n+1 | X G S3 (110101)n 01 C> 0∞ ⟶ X G S0 (110101)n+1 01 C> 0∞ | S3 = 1^8 (10)^4 1^8 (10)^6 1^3 (01)^6 | 26n+44 | ✓100/100 |
| RC2 right end carries left | X G S2 (110101)n 01 C> 0∞ ⟶ X' G S3 (110101)n 01 C> 0∞ | X' = X after one deeper pass (bit flips at the boundaries to the left); seen on the orbit, not yet an exact rule | — | –untested |
| D binary-ruler law for cycle depths | cycle k (right record after a leftward excursion > 20 cells) ⟶ cycles that reach level j+1 are exactly every 2nd cycle that reaches level j | levels found as nested local minima of each cycle's leftmost cell; checked on the real orbit, steps 5e4..1e10 (13 levels); one spacing of 3 at steps 41,783..47,893, the end of the early phase | — | ✓37885/37885 |
| M reservoir use per new top bit | 16 (10)m [top gadget] ⟶ 16 (10)m-5, then 16 (10)m-7 | the 11 consecutive changes 58 -> 53 -> 51 -> ... -> 16 -> 11 on the real orbit (direct, to 1e10); 66 -> 58 at the start does not fit | — | ✓11/11 |
Compressed historythe tape as 0∞ 14 (01)11 1 (10)4 17 0 16 (10)3 16 (10)4 16 (10)3 16 (10)7 16 (10)m [counter gadgets + block segments] C> 0∞ at 17 moments: where the rules are read off
0∞ 14 (01)11 1 (10)4 17 0 16 (10)3 16 (10)4 16 (10)3 16 (10)7 16 (10)m [counter gadgets + block segments] C> 0∞
| step | m (reservoir pairs) | right edge cell | source |
|---|---|---|---|
| 37,397 | 66 | 246 | direct |
| 45,549 | 58 | 342 | direct |
| 47,893 | 53 | 358 | direct |
| 53,183 | 51 | 390 | direct |
| 66,489 | 46 | 454 | direct |
| 103,687 | 44 | 582 | direct |
| 220,745 | 39 | 838 | direct |
| 625,191 | 37 | 1,350 | direct |
| 2,115,721 | 32 | 2,374 | direct |
| 7,823,015 | 30 | 4,422 | direct |
| 30,142,857 | 25 | 8,518 | direct |
| 118,403,239 | 23 | 16,710 | direct |
| 469,407,113 | 18 | 33,094 | direct |
| 1,869,346,983 | 16 | 65,862 | direct |
| 7,460,955,529 | 11 | 131,398 | direct |
| 3.38·1012 | 0 | ~2.8M (span) | qsim: reservoir gone; next gadget (10)^7 down to (10)^2 |
| 7.68·1012 | 0 | ~4.2M (span) | qsim: prefix eaten down to 1^4 (01)^11 1 (10)^4 |
m (reservoir pairs)last 0right edge celllast ~4.2M (span)sourcelast qsim: prefix eaten down to 1^4 (01)^11 1 (10)^4not plottable
Template comparisonSOC_2_4_v4.v TM204: does not apply · the nearest solved proof, what carries over, and the transitions that differ
| 0 | 1 | |
|---|---|---|
| A | 1RB | 1LA |
| B | 1RCtpl 1LC | 1RE |
| C | 1RD | 0RDtpl 0LC |
| D | 1LA | 1RC |
| E | 1RF | 0LEtpl 0RB |
| F | 1RA | --- |
differs from the template
- file
SOC_2_4_v4.v:655- module
TM204- machine
1RB1LA_1LC1RE_1RD0LC_1LA1RC_1RF0RB_1RA---(3 transitions apart)- diff
B0 1RC->1LC, C1 0RD->0LC, E1 0LE->0RB- note
- Nearest proved machine (3 cells away): a plain BinaryCounter_v2 proof with different words. The class templates SBCv6a/SBCv10/SOBLv1-3 are 8-11 cells away. Longitudinal.v, whose segRLs lemmas SOBLv3 uses (k passes become k*2^len), fits the pass-halving segment structure best.
Proof strategy & riskshow the formal proof will go · 3 risks to watch
First pin down the epoch map: exact rules for the boundary bit flips and the top gadget, then a fast abstract simulator to watch 2-3 overflows. Only if the overflows look self-similar: a Longitudinal.v (segRLs) proof with a binary-counter invariant plus an epoch induction. init covers steps 0..~5e4 (the early left counter).
- ▲Halting is decided by the overflow, which has not been seen. After the reservoir and prefix gadgets are gone (~1e13), the counter must reach blank tape on the left and seed a new reservoir, as it did once at step ~3.6e4. Maybe ~1e16 steps, past what qsim reaches.
- ▲The inner boundary gadgets (4 states each, in two block phases) and the top gadget are only read off the orbit; RC2, the deep right-end step, has no exact rule.
- ▲A proof needs an invariant over an unbounded list of segments plus an epoch-level argument; no template within 2 cells.
Stats & provenance1010 steps simulated · 152,154 cells · the status in full · files
- simulated
- 1010 steps
- tape
- 152,154 cells · 107,017 nonzeros
- growth
- span ~ t^0.5 (48,282 cells at 1e9; 152,154 at 1e10); left edge fixed at -59 since step 35,809; qsim (block 12, steps exact) has no halt to 8e13
- status now
- Halting hunt H-4 (2026-10-13): exact accelerated model (work/exact/xm.py: shift rules + symbolic suffix memos, all from the table) validated exactly from the blank tape through the first overflow to the rel-2e13 checkpoint (full 1e8-cell tapes) and against a fresh 3e11-step direct continuation. No halt up to step 5.636e76 (10^76.75). Epoch 2 is a counter of counters; the active counter eats (11010101)^6.29e6 at ~4.6 copies per decade, so its overflow (the next point where halting is decided) is projected near 10^(1.4e6) steps, out of reach. Not a kill; no certification route. (status.json, 2026-10-13)
- observer's note
- Mechanism found within the current epoch (binary counter over block segments; 6 exact rules validated plus the binary-ruler law at 37,885/37,885). Confidence is low because the long-run overflow (after ~1e13) decides halting and has not been observed. No sign of a cryptid so far.
- files
- observe.json · notes.md · status.json
Proof & checks
No proof work yet.
Files
machines/<tm>/: 6 entries · raw notes, status, scripts, images
| name | size | changed |
|---|---|---|
| notes.md ↓ | 19 KB | 2026-10-13 23:13 |
| status.json ↓ | 1.8 KB | 2026-10-13 23:13 |
| observe.json ↓ | 14 KB | 2026-10-10 10:34 |
| decisions/ | 1 item | 2026-10-10 23:12 |
| img/ | 7 items | 2026-10-10 10:26 |
| work/ | 42 items | 2026-10-13 21:34 |
status.json in full
{
"tm": "1RB1LA_1RC1RE_1RD0RD_1LA1RC_1RF0LE_1RA---",
"status": "STUCK",
"stage": "halting-hunt exact model",
"updated": "2026-10-13",
"reason": "Halting hunt H-4 (2026-10-13): exact accelerated model (work/exact/xm.py: shift rules + symbolic suffix memos, all from the table) validated exactly from the blank tape through the first overflow to the rel-2e13 checkpoint (full 1e8-cell tapes) and against a fresh 3e11-step direct continuation. No halt up to step 5.636e76 (10^76.75). Epoch 2 is a counter of counters; the active counter eats (11010101)^6.29e6 at ~4.6 copies per decade, so its overflow (the next point where halting is decided) is projected near 10^(1.4e6) steps, out of reach. Not a kill; no certification route.",
"parked": "Closed 2026-10-13: the 2e13-step direct run from loop 288M finished (no halt, 597/597 refs; work/r5_post.log) and the seeded qsim hit its 4 h cap at step 4,969,937,411,350,948 (no halt). Superseded by the H-4 exact model (work/exact/).",
"priority_call_answered": "More budget for the epoch map (exact boundary-gadget rules + an abstract simulator to watch 2-3 overflows), or park this machine?",
"followup": "work/r5_followup.md; work/exact/ (2026-10-13 exact model)",
"label": "H-4",
"holdout_line_740": 269,
"hunt": {
"outcome": "no_halt_to_horizon",
"horizon_steps": "56369047383409532163277608077205788781704361728584047204766564806533884147248",
"horizon_log10": 76.75,
"model": "work/exact/xm.py",
"runs": "work/exact/far3.jsonl (from rel-2e13 ckpt), work/exact/farc1.jsonl",
"validation": "anchors1/2/4.jsonl, postcheck_v1/v2.jsonl, test_blank.py (1e2..1e10)",
"line43": "claimed; model exact vs sim to 1e9; far43.jsonl: no halt to 4.69e12",
"next_decision_point": "~10^(1.4e6) steps (extrapolated fuel use of the active epoch-2 counter)"
}
}