BB(6) hunt
Machines / #26

1RB1RA_1LC1RE_---0LD_1LE1LD_0RA0LF_1LF0LB

#26Cryptid candidateBouncer + Chaotic Edgebbchallenge ↗Explorer

Where it stands

Cryptid candidate, parked at the observation

Parked 2026-10-10 with #5 (auto-applied recommendation): exact mirror twin of #5, same cryptid call. Exact mirror twin of #5 (CRYPTID_CANDIDATE 2026-10-10).

Read the full status

The tables are identical under mirror + renaming A..F -> D,E,A,B,C,F, with a different start state. From bounce 2 on, the tapes agree mirrored, with #5's block one cell longer; checked at 102,240/102,240 bounces to 1e10. So it has the same chaotic edge and the same open erosion bound. Rules: bounce, walks, 7 local rules and the halting door, each 60/60, plus the no-00 invariant (1e9 steps, 0 violations). Stopped before proof work; decision.json asks park vs shared Rocq rule reduction.

Observe
Deepen
Informal proof
Rocq
space-time diagram, first 10,000 steps from blank
The first 10,000 steps from a blank tape. Time runs down; white is 1.
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

Mirror image of #5 with renamed states: same chaotic edge eating the block, so the same open erosion problem

Status
Cryptid candidateobserving · updated 2026-10-12Parked · Parked 2026-10-10 with #5 (auto-applied recommendation): exact mirror twin of #5, same cryptid call. The 3 open questions are optional.
idle since Oct 12 10:06 · status.json 2026-10-12
Class
Bouncer + Chaotic Edgeours: Bouncer + Chaotic Edge (sheet) · ours adds: exact mirror twin of #5 (same edge, same open erosion bound) · med confidence
On the list
line 362 of BB6_holdouts_663.txt · historical 740 line 400
#26eqv ×1sim 1e15UBRRBA
Your calls on file 3
priority call (answered)
Park #26 with #5 as one cryptid candidate, or fund the shared Rocq rule reduction (cryptid protocol) for both twins?
parked
Parked 2026-10-10 with #5 (auto-applied recommendation): exact mirror twin of #5, same cryptid call.
decision.json · answered 2026-10-10: park_with_5
#26 is #5 mirrored with renamed states (same edge at every bounce): park it with #5 as one cryptid candidate, or fund the shared Rocq rule reduction now? Decisions →

Mechanism

How it works: 3 notes
  • #26 = #5 mirrored (L<->R), states renamed A..F -> D,E,A,B,C,F, but started in #5's state C.
  • From bounce 2 on, the tape is #5's tape mirrored with one fewer 1 at the wall (all 102,240 bounces to 1e10 steps).
  • So #5's verdict carries over: no-00 invariant, halts only if the edge eats the block; no erosion bound is known.

Figures for Checkpoint A

Fig 1 · bbchallenge default view, first 10,000 stepsQ2viewer ↗

The site's view. White block on the left, textured edge on its right; compare with #5's picture mirrored.

bbchallenge default view, first 10,000 steps
bbchallenge-defaultStart blankRows every step 0..10,000 squeezed into 500 px rows as on the siteWindow cells -200..199, 1 px = 1 cellColors 1 0 or never visited head moving R/L
Rows: each px row blends steps 20y+9 and 20y+10
Fig 2 · #26 beside its twin #5, mirroredQ1

One row per bounce. Compare the two panels cell by cell; red marks every cell where they differ.

#26 beside its twin #5, mirrored
customStart blankRows one row per bounceWindow cells -201..192, 1 px = 1 cellColors 1 0 cell where the two tapes differ gap between the panels
Rows: bounces 1..200: left panel = each new left record of #26, right panel = each new right record of #5 · Window: #26 cells; right panel: #5 cell x drawn at column -x-1, i.e. mirrored and shifted 1 cell · Colors: no head drawn
Fig 3 · The edge eating into the block, to 1e9Q2

One row per 400,000 steps. Follow the textured fringe's left boundary against the white block as time goes down.

The edge eating into the block, to 1e9
bbchallenge-defaultStart blankRows every 400,000 stepsWindow cells -2250..349, 1 px = 1 cellColors 1 0 or never visited dot: head (last move R/L)
Rows: 2,501 rows for steps 0..1e9 · Window: the right 2,600 cells of the 32,607-cell tape; the block runs on left to cell -32,262
More figures (1)Fig 4: Close-up: bounces 54 to 57, every step
Fig 4 · Close-up: bounces 54 to 57, every step

Every step, Explore colours. Red diagonals: A walking right; green: D walking left; zigzags: the 7 rules.

Close-up: bounces 54 to 57, every step
bbchallenge-exploreStart mid-run: step 12,180Rows every step: steps 12,180..12,879 = bounces 54 to 57Window cells -56..73, 1 px = 0.25 cellsColors 1 0 A B C D E F
Start: bounce 54, simulated from the blank tape · Rows: 1 step = 4 px tall · Window: each cell 4 px wide; the whole visited tape · Colors: head cell coloured by state
Rules (12/12 validated)exact tape rewrites the proof will formalize, each re-checked by simulation
rulefrom ⟶ tocasesstepschecked
walk right
x A> 1k y
⟶ x 1k A> y
—k✓60/60
walk left
x 1k <D y
⟶ x <D 1k y
—k✓60/60
bounce
0∞ 1n <D y
⟶ 0∞ 1n+1 A> y
—2n+3✓60/60
T turn
x A> 0 0 y
⟶ x <D 0 1 y
A reads 0: right context 00 / 010 / 011 (complete)3✓60/60
Ca carry
x A> 0 1 0 y
⟶ x 1 1 0 A> y
A reads 0, context 0103✓60/60
Fo fold
x A> 0 1 1 y
⟶ x 1 0 A> 0 y
A reads 0, context 0116✓60/60
E1 re-dive
x 1 1 1 0 <D y
⟶ x 1 0 A> 0 1 y
D reads 0: left context 1110 / 11010 / 10110 / 101010 (complete under no-00)5✓60/60
E2 re-dive
x 1 1 0 1 0 <D y
⟶ x 1 0 1 A> 0 1 y
D reads 0, context 110107✓60/60
P1 pass
x 1 0 1 1 0 <D y
⟶ x <D 0 1 0 0 1 y
D reads 0, context 101105✓60/60
P2 pass
x 1 0 1 0 1 0 <D y
⟶ x <D 0 1 0 1 0 1 y
D reads 0, context 1010106✓60/60
halting door
x 0 0 1 0j 1 0 <D y
⟶ halt
the only route to C0 (D0, E1, F0^j, F1, B0, C0); needs 00 left of the headj+5✓60/60
twin map (bounce k >= 2)
#26: 0∞ <E 1n w 0∞ at step t
⟶ #5: 0∞ rev(w) 1n+1 B> 0∞ at step t+2k
bounce k = k-th new left record of #26 / right record of #5—✓102240/102240
Compressed historythe tape as 0∞ <E 1n w 0∞ at 37 moments: where the rules are read off
0∞ <E 1n w 0∞
stepbounce|w| (edge width)n (block)lodive depth of next tripfirst 16 cells of w
4221-271·1014
31381-3121·1014
2235191-5111·1014
5148232-8281.01·1014
73210302-10321·1014
1,10812374-12101.01·1014
2,01115522-15111·1014
2,24117542-17191.01·1014
2,48820518-20101.01·1014
3,165255618-25211.01·1014
3,754305227-30481.01·1014
4,859355336-35161·1014
6,412406333-40111·1014
9,141457138-45581.01·1014
10,720507939-50111·1014
13,262608844-60381.01·1014
27,3268015652-80101.01·1014
35,93410016076-1001501.01·1014
63,286150161140-150101.01·1014
99,184200195196-200101.01·1014
182,400300268255-300191.01·1014
390,928500325418-500111·1014
695,342700350637-700191.01·1014
1,277,8881,000364923-1,000241.01·1014
2,648,4161,5003711,416-1,5003791·1014
4,513,1882,0003711,924-2,000271.01·1014
9,727,6503,0003892,906-3,0001481.01·1014
16,922,0284,0004293,874-4,000101.01·1014
25,973,7745,0005964,747-5,000271.01·1014
49,346,4007,0007396,604-7,000431.01·1014
98,637,73810,0009299,414-10,0001261.01·1014
185,605,71113,75987613,226-13,7591111.01·1014
220,407,01615,00098714,356-15,000101.01·1014
389,010,18420,0001,46718,876-20,000171·1014
604,389,82225,0001,77023,573-25,000741.01·1014
866,078,56230,0002,00928,334-30,000111·1014
999,879,50232,2622,20630,399-32,262261.01·1014
bouncelast 32,262
32,262241e9log xstep 4: bounce = 2step 31: bounce = 3step 223: bounce = 5step 514: bounce = 8step 732: bounce = 10step 1108: bounce = 12step 2011: bounce = 15step 2241: bounce = 17step 2488: bounce = 20step 3165: bounce = 25step 3754: bounce = 30step 4859: bounce = 35step 6412: bounce = 40step 9141: bounce = 45step 10720: bounce = 50step 13262: bounce = 60step 27326: bounce = 80step 35934: bounce = 100step 63286: bounce = 150step 99184: bounce = 200step 182400: bounce = 300step 390928: bounce = 500step 695342: bounce = 700step 1277888: bounce = 1000step 2648416: bounce = 1500step 4513188: bounce = 2000step 9727650: bounce = 3000step 16922028: bounce = 4000step 25973774: bounce = 5000step 49346400: bounce = 7000step 98637738: bounce = 10000step 185605711: bounce = 13759step 220407016: bounce = 15000step 389010184: bounce = 20000step 604389822: bounce = 25000step 866078562: bounce = 30000step 999879502: bounce = 32262
|w| (edge width)last 2,206
2,206241e9log xstep 4: |w| (edge width) = 2step 31: |w| (edge width) = 8step 223: |w| (edge width) = 19step 514: |w| (edge width) = 23step 732: |w| (edge width) = 30step 1108: |w| (edge width) = 37step 2011: |w| (edge width) = 52step 2241: |w| (edge width) = 54step 2488: |w| (edge width) = 51step 3165: |w| (edge width) = 56step 3754: |w| (edge width) = 52step 4859: |w| (edge width) = 53step 6412: |w| (edge width) = 63step 9141: |w| (edge width) = 71step 10720: |w| (edge width) = 79step 13262: |w| (edge width) = 88step 27326: |w| (edge width) = 156step 35934: |w| (edge width) = 160step 63286: |w| (edge width) = 161step 99184: |w| (edge width) = 195step 182400: |w| (edge width) = 268step 390928: |w| (edge width) = 325step 695342: |w| (edge width) = 350step 1277888: |w| (edge width) = 364step 2648416: |w| (edge width) = 371step 4513188: |w| (edge width) = 371step 9727650: |w| (edge width) = 389step 16922028: |w| (edge width) = 429step 25973774: |w| (edge width) = 596step 49346400: |w| (edge width) = 739step 98637738: |w| (edge width) = 929step 185605711: |w| (edge width) = 876step 220407016: |w| (edge width) = 987step 389010184: |w| (edge width) = 1467step 604389822: |w| (edge width) = 1770step 866078562: |w| (edge width) = 2009step 999879502: |w| (edge width) = 2206
n (block)last 30,399
30,399141e9log xstep 4: n (block) = 1step 31: n (block) = 1step 223: n (block) = 1step 514: n (block) = 2step 732: n (block) = 2step 1108: n (block) = 4step 2011: n (block) = 2step 2241: n (block) = 2step 2488: n (block) = 8step 3165: n (block) = 18step 3754: n (block) = 27step 4859: n (block) = 36step 6412: n (block) = 33step 9141: n (block) = 38step 10720: n (block) = 39step 13262: n (block) = 44step 27326: n (block) = 52step 35934: n (block) = 76step 63286: n (block) = 140step 99184: n (block) = 196step 182400: n (block) = 255step 390928: n (block) = 418step 695342: n (block) = 637step 1277888: n (block) = 923step 2648416: n (block) = 1416step 4513188: n (block) = 1924step 9727650: n (block) = 2906step 16922028: n (block) = 3874step 25973774: n (block) = 4747step 49346400: n (block) = 6604step 98637738: n (block) = 9414step 185605711: n (block) = 13226step 220407016: n (block) = 14356step 389010184: n (block) = 18876step 604389822: n (block) = 23573step 866078562: n (block) = 28334step 999879502: n (block) = 30399
lolast -32,262
-2-32,26241e9log xstep 4: lo = 2step 31: lo = 3step 223: lo = 5step 514: lo = 8step 732: lo = 10step 1108: lo = 12step 2011: lo = 15step 2241: lo = 17step 2488: lo = 20step 3165: lo = 25step 3754: lo = 30step 4859: lo = 35step 6412: lo = 40step 9141: lo = 45step 10720: lo = 50step 13262: lo = 60step 27326: lo = 80step 35934: lo = 100step 63286: lo = 150step 99184: lo = 200step 182400: lo = 300step 390928: lo = 500step 695342: lo = 700step 1277888: lo = 1000step 2648416: lo = 1500step 4513188: lo = 2000step 9727650: lo = 3000step 16922028: lo = 4000step 25973774: lo = 5000step 49346400: lo = 7000step 98637738: lo = 10000step 185605711: lo = 13759step 220407016: lo = 15000step 389010184: lo = 20000step 604389822: lo = 25000step 866078562: lo = 30000step 999879502: lo = 32262
dive depth of next triplast 26
379741e9log xstep 4: dive depth of next trip = 7step 31: dive depth of next trip = 12step 223: dive depth of next trip = 11step 514: dive depth of next trip = 28step 732: dive depth of next trip = 32step 1108: dive depth of next trip = 10step 2011: dive depth of next trip = 11step 2241: dive depth of next trip = 19step 2488: dive depth of next trip = 10step 3165: dive depth of next trip = 21step 3754: dive depth of next trip = 48step 4859: dive depth of next trip = 16step 6412: dive depth of next trip = 11step 9141: dive depth of next trip = 58step 10720: dive depth of next trip = 11step 13262: dive depth of next trip = 38step 27326: dive depth of next trip = 10step 35934: dive depth of next trip = 150step 63286: dive depth of next trip = 10step 99184: dive depth of next trip = 10step 182400: dive depth of next trip = 19step 390928: dive depth of next trip = 11step 695342: dive depth of next trip = 19step 1277888: dive depth of next trip = 24step 2648416: dive depth of next trip = 379step 4513188: dive depth of next trip = 27step 9727650: dive depth of next trip = 148step 16922028: dive depth of next trip = 10step 25973774: dive depth of next trip = 27step 49346400: dive depth of next trip = 43step 98637738: dive depth of next trip = 126step 185605711: dive depth of next trip = 111step 220407016: dive depth of next trip = 10step 389010184: dive depth of next trip = 17step 604389822: dive depth of next trip = 74step 866078562: dive depth of next trip = 11step 999879502: dive depth of next trip = 26
first 16 cells of wlast 1.01·1014
1e141e1441e9log xstep 4: first 16 cells of w = 100000000000000step 31: first 16 cells of w = 100110100000000step 223: first 16 cells of w = 100111010010101step 514: first 16 cells of w = 101010111101111step 732: first 16 cells of w = 100110111011011step 1108: first 16 cells of w = 101010100110111step 2011: first 16 cells of w = 100111010010101step 2241: first 16 cells of w = 101010111101110step 2488: first 16 cells of w = 101010100110111step 3165: first 16 cells of w = 101010111101111step 3754: first 16 cells of w = 101010111101110step 4859: first 16 cells of w = 100101101010110step 6412: first 16 cells of w = 100111010010101step 9141: first 16 cells of w = 101010111010101step 10720: first 16 cells of w = 100111010010110step 13262: first 16 cells of w = 101010111101110step 27326: first 16 cells of w = 101010100110111step 35934: first 16 cells of w = 101010111101111step 63286: first 16 cells of w = 101010100110111step 99184: first 16 cells of w = 101010100110111step 182400: first 16 cells of w = 101010111101110step 390928: first 16 cells of w = 100111010010110step 695342: first 16 cells of w = 101010111101110step 1277888: first 16 cells of w = 101010110010101step 2648416: first 16 cells of w = 100110111011011step 4513188: first 16 cells of w = 101010110010101step 9727650: first 16 cells of w = 101010111101111step 16922028: first 16 cells of w = 101010100110111step 25973774: first 16 cells of w = 101010111010101step 49346400: first 16 cells of w = 101010111101110step 98637738: first 16 cells of w = 101010111101110step 185605711: first 16 cells of w = 101010111010101step 220407016: first 16 cells of w = 101010100110111step 389010184: first 16 cells of w = 100110111011010step 604389822: first 16 cells of w = 101010111010011step 866078562: first 16 cells of w = 100111010010101step 999879502: first 16 cells of w = 101010111101111
Template comparisonBouncer_v3.v TM1: does not apply · the nearest solved proof, what carries over, and the transitions that differ
01
A1RB1RA
B1LC1RE
C---0LD
D1LE1LD
E0RA0LF
F1LF0LB
file
Bouncer_v3.v:44
module
TM1
machine
1LB1RA_0RA0RC_---1RD_1RE1RB_1LF0LE_0RD0LE (10 transitions apart)
diff
—
note
Bouncer_v3 TM1 needs an eventually periodic side: RC i pumps exponents 363+128i and 1+3i, and one BigStep = 128 bounces checked by native computation. #26's edge is aperiodic with positive entropy, so no RC i exists. InfiniteRect_v1 (periodic boundary tokens) and LongNv1 (explicit exponent patterns) assume the same kind of regularity.
Proof strategy & riskshow the formal proof will go · 3 risks to watch

Park with #5 as one cryptid candidate: any erosion bound for #5 transfers verbatim through the mirror map, giving both kills. Cryptid protocol still owes a Rocq rule reduction (bounce + 7 rules + no-00 invariant); one file can do both twins.

  • ▲No deterministic erosion bound is known for the shared edge (#5 research: potentials miss by 5-12x).
  • ▲#26's block is one cell shorter than #5's, so its halting threshold is one cell closer; irrelevant after bounce 40 (block >= 33).
  • ▲The twin map is checked to 1e10 steps; its all-time proof is the mirror identity of the tables plus the wall-model argument.
Stats & provenance1010 steps simulated · 32,607 cells · the status in full · files
simulated
1010 steps
tape
32,607 cells · 31,699 nonzeros
growth
t^0.5 (bouncer: 32,262 bounces by 1e9; 102,241 by 1e10)
status now
Parked 2026-10-10 with #5 (auto-applied recommendation): exact mirror twin of #5, same cryptid call. Exact mirror twin of #5 (CRYPTID_CANDIDATE 2026-10-10). The tables are identical under mirror + renaming A..F -> D,E,A,B,C,F, with a different start state. From bounce 2 on, the tapes agree mirrored, with #5's block one cell longer; checked at 102,240/102,240 bounces to 1e10. So it has the same chaotic edge and the same open erosion bound. Rules: bounce, walks, 7 local rules and the halting door, each 60/60, plus the no-00 invariant (1e9 steps, 0 violations). Stopped before proof work; decision.json asks park vs shared Rocq rule reduction. (status.json, 2026-10-12)
observer's note
Exact mirror twin of #5 (cryptid candidate, 2026-10-10): same edge dynamics, same open erosion bound. Stopped before proof work.
files
observe.json · notes.md · status.json

Proof & checks

No proof work yet.

Files

machines/<tm>/: 6 entries · raw notes, status, scripts, images

namesizechanged
notes.md ↓9.6 KB2026-10-12 10:06
status.json ↓1.4 KB2026-10-12 10:02
observe.json ↓13 KB2026-10-10 13:38
decision.json ↓3.0 KB2026-10-10 13:58
img/6 items2026-10-10 13:36
work/23 items2026-10-10 13:39
status.json in full
{
 "tm": "1RB1RA_1LC1RE_---0LD_1LE1LD_0RA0LF_1LF0LB",
 "status": "CRYPTID_CANDIDATE",
 "stage": "observe",
 "updated": "2026-10-12",
 "confidence": "med",
 "twin": "1RB1RA_0LC0RF_1LD1LC_1RE1LB_---0RA_1RF0RD",
 "reason": "Parked 2026-10-10 with #5 (auto-applied recommendation): exact mirror twin of #5, same cryptid call. Exact mirror twin of #5 (CRYPTID_CANDIDATE 2026-10-10). The tables are identical under mirror + renaming A..F -> D,E,A,B,C,F, with a different start state. From bounce 2 on, the tapes agree mirrored, with #5's block one cell longer; checked at 102,240/102,240 bounces to 1e10. So it has the same chaotic edge and the same open erosion bound. Rules: bounce, walks, 7 local rules and the halting door, each 60/60, plus the no-00 invariant (1e9 steps, 0 violations). Stopped before proof work; decision.json asks park vs shared Rocq rule reduction.",
 "priority_call_answered": "Park #26 with #5 as one cryptid candidate, or fund the shared Rocq rule reduction (cryptid protocol) for both twins?",
 "parked": "Parked 2026-10-10 with #5 (auto-applied recommendation): exact mirror twin of #5, same cryptid call.",
 "rule_reduction": "2026-10-12: Rocq rule reduction compiles (machines/1RB1RA_0LC0RF_1LD1LC_1RE1LB_---0RA_1RF0RD/rocq/rule_reduction.v; no Admitted/Axiom): local rules + no-00 invariant proved; erosion_open stated as open Definition; ~halts <-> erosion_open proved (#5 and twin #26 via flip/perm). NOT a kill."
}