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 / #9
1RB0LD_0RC1RA_1RD1RF_1LA0LE_0RA0LC_0RA---
Where it stands
Parked at the deeper analysis
Parked 2026-10-11 (Dennis: go with recommendations): Keep parked. Parked by the stop rule of the funded 'induct' stage (2026-10-10): the left zone is not shown stable or growing.
Read the full status
Done: a left window map Phi (the left part changes only at arrivals, and the next reset is fixed by the window itself), validated on the real gen-1 to gen-2 step (6/6 runs reproduce the 12 real left-zone events exactly); reset 2 with exact near runs has no nested event; x2 run growth follows from counter arithmetic (real gap ratios 2 +- 0.01). Open: over generations 2-6 the left zone is safe where tested (predicted gen-3/4 zones: 0/80 nested events each) but jumps in size (raw prefix 50, 168, 96, 128, 212 cells), possibly a 2-cycle (g vs g-2 agree on 53, 91, 99 cells), so no invariant for all generations. Reopen by iterating Phi further (cheap) to test the 2-cycle.
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
Bouncer on 11111010 with 4-state digit blocks (base-4 carry); 1 reset at 3e7 left static walls; no halt to 2e10
- Status
- Parkedinduct parked · updated 2026-10-11Not blocking · Stuck at the induct parked stage. Answer Q1–Q3 whenever; a “no” redirects the work.idle since Oct 11 08:19 · status.json 2026-10-11
- Class
- Shift-overflow structural counterours: sheet Shift-overflow structural counter ≠ ours Shift-overflow counter: base-4 digit blocks in a bouncer, plus a one-time reset that leaves walls · med confidence
- On the list
- line 569 of
BB6_holdouts_663.txt· historical 740 line 633
Your calls on file 6
- parked
- Parked 2026-10-11 (Dennis: go with recommendations): Keep parked.
- funded
- option: induct · date: 2026-10-10 · auto: true
- 2026-10-10 · induct
- Fund one stage on #9's generation induction (show every reset body grows at most x2 per marker and keeps a large enough left zone), or park the machine? (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 · left_zone
- Fund one more deepen stage on #9's left zone (parametric rules for zero-length runs, plus validated marker episodes), aiming to reach high confidence and go on to proof.md? (Dennis: go with all recommendations (2026-10-10))
- 2026-10-10 · reset
- Fund one more stage on #9's reset (front rule at the Q-territory edge, randomised marker episodes, the inner-counter capacity bound), aiming at high confidence and proof.md? (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.)
- decision.json · answered 2026-10-11: park
- Keep #9 parked, as the stop rule says, or fund one stage to test whether its left zone settles into a 2-cycle across generations? Decisions →
Mechanism
How it works: 3 notes
- Tape: runs of P=11111010 split by 6-cell digit blocks D0-D3; the head sweeps from the right edge to the first D0/D1.
- Each sweep steps every visited digit D0>D1>D2>D3>D0 (base-4 carry); D3>D0 moves one P across, so runs double leftward.
- At 2.97e7 the carry hit the left end: an 8e6-step rebuild left static walls X=11; digits cross them unchanged (to 2e10).
Figures for Checkpoint A
Time runs down; step 3e7 is about 30% of the way down. Look along both edges for any break.
bbchallenge-blazeStart blankRows Blaze time blocks of 131,072 stepsWindow cells -48..16,559, 1 px = 20.8 cellsColors 0 1 mixed
Rows: (averaged), 763 blocks stretched to 500 px, so 1 px row ~ 200,000 steps (steps 0..100,000,000) · Colors: paler orange: each pixel averages its cells over its time block; no head drawn
One row per 2nd sweep; colour shows how the 8-cell word is shifted. Watch the top half's colour edges.
customStart blankRows one row per 2nd sweep endWindow cells -40..16,551, 1 px = 8 cellsColors shift 0..7 block that is not a copy of P not visited yet
Rows: (head at the right edge in state D): 2,069 rows, steps 17..99,998,776. Not equal time: rows ~200 steps apart at the top, ~100,000 at the bottom, and between rows 1,093 and 1,094 (from the top) 8.0M steps are skipped (29,754,243 -> 37,788,160: the reset never reaches the right edge) · Colors: away from digits the tape repeats the 8-cell word P = 11111010, and colour = how P is shifted in that 8-cell block (red, orange, yellow, green, cyan, blue, purple, magenta = shift 0..7); colour edge = a digit block (6 cells: colour steps back 2, e.g. green -> orange) or a wall X = 11 (2 cells: colour steps forward 2)
The left quarter after the reset, to 1e9. Look where the slanted lines meet the vertical ones.
customStart blankRows one row per 6th sweep endWindow cells -40..13,559, 1 px = 8 cellsColors shift 0..7 block that is not a copy of P not visited yet
Rows: (head at the right edge in state D): 2,177 rows, steps 527..999,316,836. Not equal time: rows ~1,000 steps apart at the top, ~950,000 at the bottom, and between rows 363 and 364 (from the top) 8.1M steps are skipped (29,646,275 -> 37,788,160: the reset) · Window: the left quarter of the tape, an exact crop of img/phase_1e9.png; all 7 walls left by the reset (cells ~190..8,750) are in it, and cells 13,560..52,247 (not shown) hold only the newest digit runs · Colors: away from digits the tape repeats the 8-cell word P = 11111010, and colour = how P is shifted in that 8-cell block (red, orange, yellow, green, cyan, blue, purple, magenta = shift 0..7); colour edge = a digit block (6 cells: colour steps back 2, e.g. green -> orange) or a wall X = 11 (2 cells: colour steps forward 2)
More figures (2)Fig 4–5: The reset, Blaze view · Left/right records to 9.47M steps
Fig 4 · The reset, Blaze view
8.1M steps from step 29,754,243: the inner bouncer regrows from the left.
bbchallenge-blazeStart mid-run: step 29,754,243Rows Blaze time blocks of 8,192 stepsWindow cells -37..8770, 1 px = 11 cellsColors 0 1 mixed
Start: the last right-edge visit before the reset; head at cell 8,747 · Rows: (averaged), 989 blocks stretched to 500 px, so 1 px row ~ 16,200 steps (steps 29,754,243..37,854,243) · Colors: paler orange: each pixel averages its cells over its time block; no head drawn
Before the reset: digit boundaries are straight lines.
bbchallenge-defaultStart blankRows left/right recordsWindow cells -32..4967, 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 (5,000 rows = the row cap, steps 0..9,473,093; rows are not equal time)
Rules (8/8 validated)exact tape rewrites the proof will formalize, each re-checked by simulation
| rule | from ⟶ to | cases | steps | checked |
|---|---|---|---|---|
| edge | l P^n A ⟶ l' P^n B | l P^n B --> l' P^(n+1) A | every sweep; tail alternates A/B, edge +4 cells | — | ✓120/120 |
| turn@D0 | l D0 P^a A ⟶ l D1 P^a B (from B: l D1 P^(a+1) A) | head turns at D0; l untouched | 38a+22 (A) / 38a+30 (B) | ✓61/61 |
| turn@D1 | l D1 P^a A ⟶ l D2 P^a B (from B: l D2 P^(a+1) A) | head turns at D1; l untouched | 38a+20 (A) / 38a+28 (B) | ✓59/59 |
| carry@D2 | l D2 P^c R ⟶ l* D3 P^c R' | carry continues into l (l* = l after its own visit) | +38c+14 on top of the turn | ✓69/69 |
| carry@D3 | l D3 P^c R ⟶ l* P D0 P^(c-1) R' | c>=1; one P moves left across the digit | +38c+36 on top of the turn | ✓71/71 |
| wall pass | l X P^c R ⟶ l* X P^c R' | X=11 (phase +2 wall) is transparent to the carry | — | ✓24/24 |
| D1 meets wall | l D1 X P^c R ⟶ l* X P D0 P^(c-1) R' | empty run between D1 and X; carry continues | — | ✓24/24 |
| full-sweep model (real orbit) | E(T; n_i, b_i) at a right-edge D record ⟶ next D record = rules above applied once | gen 1 at 1e7 (297 sweeps) + gen 2 at 1e9 (596); D-X adjacency sweeps excluded | — | ✓893/893 |
Compressed historythe tape as 0∞ L .. b3 P^n3 b2 P^n2 b1 P^n1 b0 P^n0 T D> 0∞ ; P=11111010, D0=111010 D1=101111 D2=101011 D3=111111 X=11; T=A: last P ends under head (..1111101 D> 0∞), T=B: P^n0 101 D> 0∞ at 30 moments: where the rules are read off
0∞ L .. b3 P^n3 b2 P^n2 b1 P^n1 b0 P^n0 T D> 0∞ ; P=11111010, D0=111010 D1=101111 D2=101011 D3=111111 X=11; T=A: last P ends under head (..1111101 D> 0∞), T=B: P^n0 101 D> 0∞
| step | T | n0 | b0 | n1 | b1 | n2 | b2 | n3 | b3 | #D | #X |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 10,009,637 | B | 314 | D3 | 155 | D0 | 79 | D3 | 39 | D1 | 12 | 5 |
| 10,027,525 | A | 314 | D0 | 156 | D1 | 79 | D3 | 39 | D1 | 12 | 5 |
| 10,039,479 | B | 314 | D1 | 156 | D1 | 79 | D3 | 39 | D1 | 12 | 5 |
| 10,051,439 | A | 315 | D2 | 156 | D1 | 79 | D3 | 39 | D1 | 12 | 5 |
| 10,069,371 | B | 315 | D3 | 156 | D2 | 79 | D3 | 39 | D1 | 12 | 5 |
| 10,091,867 | A | 315 | D0 | 157 | D3 | 78 | D0 | 40 | D2 | 12 | 5 |
| 10,103,859 | B | 315 | D1 | 157 | D3 | 78 | D0 | 40 | D2 | 12 | 5 |
| 10,115,857 | A | 316 | D2 | 157 | D3 | 78 | D0 | 40 | D2 | 12 | 5 |
| 10,136,867 | B | 316 | D3 | 156 | D0 | 79 | D1 | 40 | D2 | 12 | 5 |
| 10,154,869 | A | 316 | D0 | 157 | D1 | 79 | D1 | 40 | D2 | 12 | 5 |
| 10,166,899 | B | 316 | D1 | 157 | D1 | 79 | D1 | 40 | D2 | 12 | 5 |
| 10,178,935 | A | 317 | D2 | 157 | D1 | 79 | D1 | 40 | D2 | 12 | 5 |
| 10,196,981 | B | 317 | D3 | 157 | D2 | 79 | D1 | 40 | D2 | 12 | 5 |
| 10,218,073 | A | 317 | D0 | 158 | D3 | 79 | D2 | 40 | D2 | 12 | 5 |
| 10,230,141 | B | 317 | D1 | 158 | D3 | 79 | D2 | 40 | D2 | 12 | 5 |
| 10,242,215 | A | 318 | D2 | 158 | D3 | 79 | D2 | 40 | D2 | 12 | 5 |
| 10,266,327 | B | 318 | D3 | 157 | D0 | 80 | D3 | 40 | D3 | 12 | 5 |
| 10,284,443 | A | 318 | D0 | 158 | D1 | 80 | D3 | 40 | D3 | 12 | 5 |
| 10,296,549 | B | 318 | D1 | 158 | D1 | 80 | D3 | 40 | D3 | 12 | 5 |
| 10,308,661 | A | 319 | D2 | 158 | D1 | 80 | D3 | 40 | D3 | 12 | 5 |
| 10,326,821 | B | 319 | D3 | 158 | D2 | 80 | D3 | 40 | D3 | 12 | 5 |
| 10,350,381 | A | 319 | D0 | 159 | D3 | 79 | D0 | 40 | D0 | 12 | 5 |
| 10,362,525 | B | 319 | D1 | 159 | D3 | 79 | D0 | 40 | D0 | 12 | 5 |
| 10,374,675 | A | 320 | D2 | 159 | D3 | 79 | D0 | 40 | D0 | 12 | 5 |
| 40,005,946 | A | 56 | X | 378 | D3 | 81 | D3 | 82 | X | 20 | 11 |
| 100,058,178 | B | 892 | D0 | 83 | X | 229 | D3 | 312 | X | 20 | 11 |
| 400,090,666 | B | 1,948 | D0 | 839 | D1 | 300 | X | 322 | D3 | 20 | 11 |
| 1,600,152,606 | A | 3,965 | D3 | 1,846 | D0 | 1,125 | D1 | 183 | X | 20 | 11 |
| 6,400,057,808 | B | 7,952 | D2 | 3,841 | D3 | 2,121 | D0 | 994 | D2 | 20 | 11 |
| 20,000,291,798 | A | 14,060 | D1 | 6,895 | D3 | 3,648 | D0 | 1,757 | D0 | 20 | 11 |
Tlast Anot plottable
n0last 14,060b0last D1not plottable
n1last 6,895b1last D3not plottable
n2last 3,648b2last D0not plottable
n3last 1,757b3last D0not plottable
#Dlast 20#Xlast 11Template comparisonSBCv6a.v TM1: partly applies · the nearest solved proof, what carries over, and the transitions that differ
| 0 | 1 | |
|---|---|---|
| A | 1RB | 0LD |
| B | 0RC | 1RA |
| C | 1RD | 1RF |
| D | 1LA | 0LE |
| E | 0RA | 0LC |
| F | 0RA | --- |
- file
SBCv6a.v:15- module
TM1- machine
1LB1RE_0LC0RB_1RD0LA_0RA0RD_0RF0RA_1RD---(10 transitions apart)- diff
9/12 transitions differ after best renaming+mirror; SBCv10 TM4/TM5, SOBLv1 TM2, Bouncer_v1 TM1: 8; look-alike Bouncer_v1 TM2: 10- note
- No proved neighbour is within 8 transitions, and its blocks (10011001) never appear here. Only the method transfers: Longitudinal segRLs/sideRLs passes, plus RIncs/WF over a digit list, fit gen 1; nothing covers the reset.
Proof strategy & riskshow the formal proof will go · 3 risks to watch
Mirror SBCv6a TM1 (Longitudinal, flip tm): pass lemmas for P^n, D0-D3, X, D1.X via es/ind; BigStep over an Inductive digit list with a WF invariant; multistep_nonhalt to a post-reset config, then progress_nonhalt_cond. First close the block alphabet (D2.X, X.D1 transients; left-prefix overflow).
- ▲Reset not modelled: if the left overflow recurs (after 2e10, beyond our sim), each rebuild may nest new walls, so the proof needs a generation invariant.
- ▲Rule table not closed: D2.X and X.D1 adjacency create extra transient blocks ((10)^5 1^3 ..).
- ▲No template within 8 transitions: new-mechanism proof, likely SBCv10-sized (~50 KB).
Stats & provenance2·1010 steps simulated · 227,260 cells · the status in full · files
- simulated
- 2·1010 steps
- tape
- 227,260 cells · 146,198 nonzeros
- growth
- ~1.61*sqrt(t) cells (+4 cells per sweep); 56,806 sweeps by 2e10
- status now
- Parked 2026-10-11 (Dennis: go with recommendations): Keep parked. Parked by the stop rule of the funded 'induct' stage (2026-10-10): the left zone is not shown stable or growing. Done: a left window map Phi (the left part changes only at arrivals, and the next reset is fixed by the window itself), validated on the real gen-1 to gen-2 step (6/6 runs reproduce the 12 real left-zone events exactly); reset 2 with exact near runs has no nested event; x2 run growth follows from counter arithmetic (real gap ratios 2 +- 0.01). Open: over generations 2-6 the left zone is safe where tested (predicted gen-3/4 zones: 0/80 nested events each) but jumps in size (raw prefix 50, 168, 96, 128, 212 cells), possibly a 2-cycle (g vs g-2 agree on 53, 91, 99 cells), so no invariant for all generations. Reopen by iterating Phi further (cheap) to test the 2-cycle. (status.json, 2026-10-11)
- observer's note
- Counter rules validated (8 rules, random + 893 real sweeps); no Collatz-like arithmetic; reset and D-X transients still open
- files
- observe.json · notes.md · status.json
Proof & checks
○ Checkpoint B: no note from Dennis found
- notes.md L60: - Checkpoint questions are now yes/no questions about the figures. Moved off the card (strategy calls, not figure reading; settle them in proof.md / Checkpoint B):
Files
machines/<tm>/: 8 entries · raw notes, status, scripts, images
| name | size | changed |
|---|---|---|
| notes.md ↓ | 33 KB | 2026-10-11 08:19 |
| status.json ↓ | 1.1 KB | 2026-10-11 08:19 |
| observe.json ↓ | 15 KB | 2026-10-10 04:41 |
| deepen.json ↓ | 21 KB | 2026-10-10 15:18 |
| decision.json ↓ | 2.3 KB | 2026-10-11 08:19 |
| decisions/ | 3 items | 2026-10-10 15:17 |
| img/ | 9 items | 2026-10-10 02:00 |
| scripts/ | 36 items | 2026-10-10 14:56 |
status.json in full
{
"tm": "1RB0LD_0RC1RA_1RD1RF_1LA0LE_0RA0LC_0RA---",
"status": "STUCK",
"stage": "induct_parked",
"updated": "2026-10-11",
"reason": "Parked 2026-10-11 (Dennis: go with recommendations): Keep parked. Parked by the stop rule of the funded 'induct' stage (2026-10-10): the left zone is not shown stable or growing. Done: a left window map Phi (the left part changes only at arrivals, and the next reset is fixed by the window itself), validated on the real gen-1 to gen-2 step (6/6 runs reproduce the 12 real left-zone events exactly); reset 2 with exact near runs has no nested event; x2 run growth follows from counter arithmetic (real gap ratios 2 +- 0.01). Open: over generations 2-6 the left zone is safe where tested (predicted gen-3/4 zones: 0/80 nested events each) but jumps in size (raw prefix 50, 168, 96, 128, 212 cells), possibly a 2-cycle (g vs g-2 agree on 53, 91, 99 cells), so no invariant for all generations. Reopen by iterating Phi further (cheap) to test the 2-cycle.",
"funded": {
"option": "induct",
"date": "2026-10-10",
"auto": true
},
"confidence": "med",
"parked": "Parked 2026-10-11 (Dennis: go with recommendations): Keep parked."
}