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1RB1RF_1LC0RB_1RD0LC_1LE1RA_0RC1LB_---1RE
Where it stands
Parked at the observation
Parked by Dennis 2026-10-10 (park_sim): niced background sim to 1e12 as a cheap halt check, work/sim_1e12.jsonl. Observe done: period-5 sea with 2-state defect walls forming nested binary counters (7 exact local rules validated on random instances; inner counter laws 33,140/33,140 and 5,545/5,545 on the orbit). Confidence is low because the global law (engine-dissolving epochs, bit creation, edge regions; regime change at ~2.7e9) is unknown, and a halting route (C reading 0 before 110) exists in the defect algebra. Proof work waits for Dennis.
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
Period-5 sea swept by a zig-zag head; defect walls toggle like binary counters; the global epoch law is unknown
- Status
- Parkedobserving · updated 2026-10-10Not blocking · Stuck at the observing stage. Answer Q1–Q3 whenever; a “no” redirects the work.idle since Oct 10 13:59 · status.json 2026-10-10
- Class
- Unknownours: sheet Unknown ≠ ours Nested binary counters of toggling defect walls in a period-5 sea, with engine-dissolving epochs (multi-region) · low confidence
- On the list
- line 562 of
BB6_holdouts_663.txt· historical 740 line 625 · observe.json rank #49
Your calls on file 3
- priority call (answered)
- One more stage on the epoch/bit-creation law (exact wall catalogue + abstract wall simulator), or park as STUCK at observe?
- parked
- Parked by Dennis 2026-10-10 (park_sim): niced background sim to 1e12 as a cheap halt check, work/sim_1e12.jsonl.
- decision.json · answered 2026-10-10: park_sim
- Spend one more stage on the epoch/bit-creation law (wall catalogue plus an abstract wall simulator), or park R9 as STUCK at observe? Decisions →
Mechanism
How it works: 3 notes
- Sea and walls: the tape is mostly the period-5 sea 11100. Right sweeps (B) shift every block 2 cells right and left sweeps (C) shift it back, 7 steps per block. The head turns only at 2-state defect walls. A right-wall bit is the insert 000 (= 0), which reflects a right sweep and becomes 100 (= 1); 100 lets the sweep through and is reset on the way back. Left-wall bits (gap-1 vs run-2) do the same to left sweeps. So the central engine drives a binary counter on each side (counter laws hold on 33,140/33,140 and 5,545/5,545 orbit turns).
- Above that it is not understood. Counter overflows feed a second engine/counter pair at the right end and a structure at the left edge. Up to 2.73e9 the inner engine keeps dissolving (43 epochs between 1e9 and 2.73e9, 29e6 to 56e6 steps apart): a wall walks left one block per bounce, eating a 4/5-density sea (11110) back into 11100, and then the engine re-forms. After 2.73e9 there are none in the inner region. Each edge visit adds 3 cells (2,021 cells at 1e10), and edge visits keep slowing down.
- Halting: every halt is C reading 0 just before 110 (rule H), for example a right sweep meeting B> 1^n 0 1 0, or a D sweep meeting 110. Neither is seen to 1e10. Cryptid check: nothing Collatz-like. Everything observed is binary counting or linear drift, but the unknown epoch/bit-creation law could still hide parity branching.
Figures for Checkpoint A
Fig 1 · Edge records to 10 billion steps
One row per new edge cell. Compare the two edges' slopes, then follow the wavy grey lines inside.
bbchallenge-defaultStart blankRows the start, then one per new leftmost or rightmost cellWindow cells -729..1291, 1 px = 1 cellColors 1 0 or never visited head at a new right/left edge
Rows: (2,021 rows, steps 0..9,957,807,009); not evenly spaced in time
Time runs down. Note which dark column each right excursion from the engine (x ~ 200) stops at.
bbchallenge-defaultStart mid-run: step 1,000,000,000Rows every 8 stepsWindow cells 250..1000, 1 px = 1 cellColors 1 0 head after a right/left move
Start: head at cell 502 in state B moving right · Rows: 2,001 rows (steps 1e9 .. 1e9 + 16,000) · Window: (column x = cell 250 + x); right-counter bits sit at cells 680, 733, 778, 808, 821, 862, 867, 875
Each line is a wall the head keeps bouncing off. Note where lines are born and which way they drift.
customStart blankRows 800 log-spaced time bins from step 1e3Window cells -549..988, 1 px = 1 cellColors no turn right turning point (R -> L) left turning point (L -> R)
Rows: (top) to 1e9 (bottom); a turning point is a sweep's extreme cell before the head moves 8+ cells back · Colors: dark = both; darker = more turns in the bin (log scale)
More figures (2)Fig 4–5: Blaze view, 1 billion steps · bbchallenge Default view, first 10,000 steps
Fig 4 · Blaze view, 1 billion steps
Time runs down. Edges grow on both sides; the paler vertical bands are defect-rich zones.
bbchallenge-blazeStart blankRows Blaze time blocks of 1,048,576 stepsWindow cells -549..988, 1 px = 1 cellColors 0 1 a cell that is 1 for part of its time block
Rows: (954 rows, each averaged), steps 0..1e9
Fig 5 · bbchallenge Default view, first 10,000 steps
For orientation: what bbchallenge.org shows for this machine.
bbchallenge-defaultStart blankRows 10,000 steps squeezed into 500 px rowsWindow cells -200..199, 1 px = 1 cellColors 1 0 or never visited head after a right/left move
Rows: 1 px row = 20 steps; the site blends steps 20y+9 and 20y+10
Rules (10/11 validated)exact tape rewrites the proof will formalize, each re-checked by simulation
| rule | from ⟶ to | cases | steps | checked |
|---|---|---|---|---|
| S_R right sweep over the sea | B> (11100)n ⟶ (00111)n B> | any n >= 1, random 12-cell contexts on both sides | 7n | ✓200/200 |
| S_L left sweep over the sea | (00111)n <C ⟶ <C (11100)n | any n >= 1, any context | 7n | ✓200/200 |
| RB0 right bit 0 reflects, becomes 1 | (00111)n B> 000 ⟶ <C (11100)n 100 | n >= 1; the turn and the start of the return sweep | 7n+1 | ✓200/200 |
| RB1 right bit 1 passes the sweep | B> 100 ⟶ 111 B> | any context | 5 | ✓200/200 |
| RB1r return sweep resets a passed bit | (00111)n 111 <C ⟶ <C (11100)n 000 | n >= 1; together RB1 then RB1r take bit 1 -> 0 | 7n+3 | ✓200/200 |
| LB0 left bit 0 (gap 1) reflects, becomes run 2 | 00011 10111 (00111)n <C ⟶ 00011 00111 (00111)n B> | n >= 1, constructed context. The pass-through case (left bit 1) depends on the phase of the sea on its right and is not yet an exact rule | 14n+13 | ✓200/200 |
| D_R D sweep: 3/5 sea -> 4/5 sea | D> (11100)n ⟶ (11101)n D> | any n >= 1. A block 110.. instead of 111.. makes F read 0, which halts | 5n | ✓200/200 |
| H the only way to halt | 0 <C 110 or C> 0110 ⟶ halt | C0, D1, A1, then F reads 0. F is entered only by A1, A only by D1 and D only by C0, so every halt has this form (200 random contexts per direction) | 4 | ✓400/400 |
| CR inner right counter = binary +1 | bits b0..b7 = inserts 000 (0) / 100 (1) in the 11100 sea (cells 680..875 at 1e9); a right sweep leaves the engine ⟶ turns at the first 0 bit j; bits < j become 0 and bit j becomes 1 | real orbit, steps 1e9..1.03e9: every right turn in cells 600..900 after a left turn left of cell 600; 33,139/33,139 next states are exact +1. Depth counts 16,634 / 8,318 / 4,158 / 2,080 / 1,040 / 520 / 260 / 130 | — | ✓33140/33140 |
| CL inner left counter = binary +1 | 4 low bits in cells 315..435: run-2 defect (1) / gap-1 defect 3 cells right (0) ⟶ turns at the first 0 bit; lower bits -> 0, that bit -> 1 | real orbit, steps 1e9..1.01e9, every left turn after a right turn right of the zone; 5,371/5,371 exact +1; 346 carries past bit 3 | — | ✓5545/5545 |
| EP engine-dissolving epochs (open) | inner engine + counters ⟶ the engine dissolves; a wall walks left 5 cells per bounce, eating the 11110 sea; the engine re-forms further left | Wall-walk detector (8+ left turns in a row, each 5 cells left of the last): 136 runs from 5e5 to 2.73e9. Between 1e9 and 2.73e9 they form 43 epochs, 2.9e7 to 5.6e7 steps apart. 5 runs near the right end (3.7e9..4.6e9), none after that to 1e10. No exact rule yet | — | –untested |
Compressed historythe tape as span lo..hi of the visited tape; drift = wall-walk runs so far (8+ left turns in a row, each 5 cells left of the last; one epoch can give 2-3 runs) at 15 moments: where the rules are read off
span lo..hi of the visited tape; drift = wall-walk runs so far (8+ left turns in a row, each 5 cells left of the last; one epoch can give 2-3 runs)
| step | lo | hi | cells | drift |
|---|---|---|---|---|
| 1,000 | -12 | 28 | 41 | 0 |
| 3,000 | -15 | 37 | 53 | 0 |
| 10,000 | -21 | 61 | 83 | 0 |
| 30,000 | -30 | 70 | 101 | 0 |
| 100,000 | -51 | 118 | 170 | 0 |
| 300,000 | -81 | 175 | 257 | 0 |
| 1,000,000 | -123 | 256 | 380 | 2 |
| 3,000,000 | -177 | 361 | 539 | 2 |
| 10,000,000 | -285 | 529 | 815 | 9 |
| 30,000,000 | -381 | 715 | 1,097 | 9 |
| 100,000,000 | -432 | 796 | 1,229 | 9 |
| 300,000,000 | -465 | 844 | 1,310 | 13 |
| 1,000,000,000 | -549 | 988 | 1,538 | 30 |
| 3,000,000,000 | -684 | 1,216 | 1,901 | 136 |
| 10,000,000,000 | -729 | 1,291 | 2,021 | 141 |
lolast -729hilast 1,291cellslast 2,021driftlast 141Template comparisonCPS_LRU_v3.v: does not apply · the nearest solved proof, what carries over, and the transitions that differ
| 0 | 1 | |
|---|---|---|
| A | 1RB | 1RFtpl 0RF |
| B | 1LC | 0RB |
| C | 1RD | 0LC |
| D | 1LE | 1RA |
| E | 0RC | 1LB |
| F | --- | 1REtpl 0LE |
differs from the template
- file
CPS_LRU_v3.v:2133- module
- —
- machine
1RB0RF_1LC0RB_1RD0LC_1LE1RA_0RC1LB_---0LE(2 transitions apart)- diff
A1 1RF->0RF, F1 1RE->0LE- note
- Nearest proved machines by table (2 cells away): a CPS_LRU_v3 certificate (this one; it stops growing at 124 cells by 1e8), CPS_LRU_v4 and RWL_mod_v1. All three are decider certificates, not structural proofs. The targeting row's verify/CounterCmp_v1.v (TM1) compares two unary counters, which is a different mechanism. Kill #12's recursive run-length counter is the closest kill in spirit, but its tape is runs of 1s, not a period-5 sea with toggling walls. No template applies.
Proof strategy & riskshow the formal proof will go · 3 risks to watch
Not ready for a proof. Next: (1) an exact catalogue of every wall shape in both sea phases; (2) an abstract walls-and-counters simulator checked against the TM to 1e10; (3) the epoch and bit-creation law, plus an invariant that rules out C reading 0 before 110 (B> 1^n 0 1 0, D> 110).
- ▲Several levels: two engine/counter pairs, edge structures and engine-dissolving epochs; the regime changed at ~2.7e9, so 1e10 steps may not show every regime.
- ▲The defect algebra has real halting routes (B> 1^n 0 1 0, D> 110), so non-halting needs a global invariant on defect shapes, not just the counter laws.
- ▲Nobody has simulated it to 1e14 (sheet). qsim does not accelerate it (block size 1, 0 rules by 5.4e6 steps), and direct simulation of the growing gaps between edge visits is slow.
Stats & provenance1010 steps simulated · 2,021 cells · the status in full · files
- simulated
- 1010 steps
- tape
- 2,021 cells · 1,224 nonzeros
- growth
- +3 cells per edge visit; visits slow down (left edge about every 4e7 steps near 1.5e9, about every 1.5e9 near 8e9); 1,538 cells at 1e9
- status now
- Parked by Dennis 2026-10-10 (park_sim): niced background sim to 1e12 as a cheap halt check, work/sim_1e12.jsonl. Observe done: period-5 sea with 2-state defect walls forming nested binary counters (7 exact local rules validated on random instances; inner counter laws 33,140/33,140 and 5,545/5,545 on the orbit). Confidence is low because the global law (engine-dissolving epochs, bit creation, edge regions; regime change at ~2.7e9) is unknown, and a halting route (C reading 0 before 110) exists in the defect algebra. Proof work waits for Dennis. (status.json, 2026-10-10)
- observer's note
- Observe done. Low confidence: the sea sweeps, wall toggles and both inner counter laws are validated, but the global epoch/bit-creation law is not, so proof work waits for Dennis.
- 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 ↓ | 7.4 KB | 2026-10-10 13:59 |
| status.json ↓ | 967 B | 2026-10-10 12:52 |
| observe.json ↓ | 13 KB | 2026-10-10 11:03 |
| decision.json ↓ | 3.6 KB | 2026-10-10 12:49 |
| img/ | 5 items | 2026-10-10 10:59 |
| work/ | 11 items | 2026-10-10 12:49 |
status.json in full
{
"tm": "1RB1RF_1LC0RB_1RD0LC_1LE1RA_0RC1LB_---1RE",
"status": "STUCK",
"stage": "observe",
"updated": "2026-10-10",
"reason": "Parked by Dennis 2026-10-10 (park_sim): niced background sim to 1e12 as a cheap halt check, work/sim_1e12.jsonl. Observe done: period-5 sea with 2-state defect walls forming nested binary counters (7 exact local rules validated on random instances; inner counter laws 33,140/33,140 and 5,545/5,545 on the orbit). Confidence is low because the global law (engine-dissolving epochs, bit creation, edge regions; regime change at ~2.7e9) is unknown, and a halting route (C reading 0 before 110) exists in the defect algebra. Proof work waits for Dennis.",
"parked": "Parked by Dennis 2026-10-10 (park_sim): niced background sim to 1e12 as a cheap halt check, work/sim_1e12.jsonl.",
"priority_call_answered": "One more stage on the epoch/bit-creation law (exact wall catalogue + abstract wall simulator), or park as STUCK at observe?"
}