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Machines / #32

`1RB0LC_1RC0RC_1LD0RB_1LA0LE_1LD1LF_1LD---`

#32Cryptid candidateSkelet 1-like Class 2bbchallenge ↗Explorer parent: #11

Where it stands

Cryptid candidate, parked at the informal proof

Class 2 close-out stage 3 of 3 (2026-10-12): flagged CRYPTID_CANDIDATE together with R4 (same table), proof work stops. New wide-integer simulator scripts/c2s3_tsim.c (2048-bit steps, 512-bit counts; JCAP=40 reproduces stage 2 byte for byte to 1e37, and every earlier halting step count). #32: no halt to 1e80, first 40 defects frozen from 5.8e14 to 1e80.

Read the full status

N cuts from I(N,360), N = 0..44, to 1e80: exactly N = 2, 7, 12, 17, 22 halt; N >= 23 freeze because the first lower digit (u = 48) runs out in cycle 5. Cutting that digit's u1 too: N = 12 halts for 14 of 24 small u1 and not for 10 (u1 = 1 mod 3 tends to halt, with exceptions); N = 17: 7 of 25; N = 11, 13: 0 of 50. So halting is a residue condition at every level of an unbounded 2-adic/5-adic hierarchy; no invariant. Decision in R4's decision.json (stop_cryptid recommended). Earlier: rule G + sweep case analysis (proof.md), check_proof.py 12/12. Stage-2 re-run (2026-10-12): the workflow re-issued stage 2 after the track had already ended at stage 3; no new proof work (cryptid protocol, decision pending). The kept simulators reproduce the stage-2 and stage-3 dumps byte for byte (1e37, 1e80) and the cut halts (N = 2: 202,227,190). New probe (scripts/c2s2r_mkcut3.py): the second lower digit u2 also switches the outcome (N = 12: a fixed halt for u2 >= 40 moves or disappears once u2 runs out; u1 = 11 halts at u2 = 47..98 and 5 but not 13..40); N = 11/13: 0 of 42 halts. Still CRYPTID_CANDIDATE.

Observe

Deepen

Informal proof

Rocq

Overview

Needs you

R4's call covers this machine R4 and #32 are flagged CRYPTID_CANDIDATE: stop here, or fund a recursive abstract model to follow R4's real orbit, whose top already has the halting residue? 1RB0RE_1LC0RD_1LD0LD_1RA0LC_1RA1RF_1RA---R4

In one sentence

neighbour of #11: one transition away; its run differs (90,039 vs 77,685 cells at 1e9) (status.json relation)

Status: Cryptid candidateinformal proof · updated 2026-10-12Parked · Class 2 close-out stage 3 of 3 (2026-10-12): flagged CRYPTID_CANDIDATE together with R4 (same table), proof work stops.
idle since Oct 12 23:02 · status.json 2026-10-12
Informal proof: proof.mdconditional; see Proof for what is still open
Class: Skelet 1-like Class 2
On the list: line 336 of BB6_holdouts_663.txt · historical 740 line 372
#32eqv ×1sim 1e15
Derived from: 1RB0LE_1RC0RC_1LD0RB_1LA0LE_1LD1LF_1LD---#11 Kill claimed

Your calls on file 3

priority call (answered): Shared with R4: invest in a joint #32/R4 multi-level invariant (proof.md 5 route), or park both?
parked: Stopped by Dennis 2026-10-12 (decision queue: go with recommendations: stop_cryptid): kept as CRYPTID_CANDIDATE, rules written up, no more compute. (decision filed on R4, same table.)
funded: option: class2_closeout · date: 2026-10-12

Mechanism

Figures

Fig 1 · Carry sweeps from a built counter tapeQ1
Every 10 steps from a built counter tape. Dotted diagonals are head sweeps; compare how deep each one goes.

Fig 2 · Edge records to 300,000 stepsQ2 Q3 viewer ↗
Edge records to 300,000 steps. Look at the dashed vertical walls and each band break (left edge steps out).

Fig 3 · Edge records to 5.1 million stepsQ3
The same view to 5.1M steps. Compare its walls and band breaks with Fig 2.

More figures (2)Fig 4–5: bbchallenge Default view, first 10,000 steps · Blaze view, 10 million steps

Rules (5/5 validated)exact tape rewrites the proof will formalize, each re-checked by simulation

rule	from ⟶ to	cases	steps	checked
M_k carry (k = trailing 1-bits)	l (10)^u_k 0² (01)^v_k [(10)^u_i (01)^v_i]_{i=k-1..0} (10)^a 0³ (10)^b B> 0^∞ ⟶ l (10)^u_k+1 (01)^v_k-1 [(10)^u_i 0² (01)^v_i-1]_{i=k-1..0} (10)^a+1 0³ (10)^b+2 B> 0^∞	k=0..5 tested; needs v_i>=1 (i<=k), u_i>=1 (i<k), u_k>=0, a>=1, b>=0; v=1 gives a fused (merged) digit	32 + 8a + 8b + 8sum_{i<k} u_i + 4sum_{i<=k} v_i	✓84/84
O overflow (all bits 1)	0^∞ 10 01 [(10)^u_i (01)^v_i]_{i=1..n} (10)^a 0³ (10)^b B> 0^∞ ⟶ 0^∞ 10 01 00 (01)^u_1 [(10)^v_i-1 0² (01)^u_(i+1)]_{i=1..n-1} (10)^v_n (01)^a (10)^b+3 0³ 10 B> 0^∞	n=1..7 tested; needs v_i>=1 (i<n); left edge moves 3 cells; counter restarts at 1	89 - 4n + 8a + 20b + 4sum u_i + 8sum v_i	✓118/118
init (blank tape to first K)	0^∞ A> 0^∞ ⟶ 0^∞ 10 01 (10)³ 01 (10)² 0³ 10 B> 0^∞	twins: start B -> K((1,2);2,1) in 122 steps; start C -> K((1,1);2,1) in 101 steps	142	✓1/1
B sweep right	B> (01)ⁿ ⟶ (10)ⁿ B>	—	2n	✓10/10
D sweep left	(01)ⁿ <D ⟶ <D (10)ⁿ	—	2n	✓10/10

Compressed historythe tape as 0^∞ 10 01 [(10)^u_i (01)^v_i]_{i=1..n} (10)^a 0³ (10)^b B> 0^∞ at 40 moments: where the rules are read off

0^∞ 10 01 [(10)^u_i (01)^v_i]_{i=1..n} (10)^a 0³ (10)^b B> 0^∞

step	`n`	`u_1..u_n`	`v_1..v_n`	`a`	`b`
148,244	4	67,313,163	1,412,848	62	61
196,569	5	115,151,563	6,628,244,832	94	61
323,918	4	68,319,463	1,283,232	126	125
398,427	5	113,113,947	6,728,874,896	158	61
561,920	5	69,319,463,127	104,241,696	126	125
755,701	6	11,173,131,127	682,887,489,664	190	125
1,267,210	4	70,125,190,127	8,166,464	254	253
1,406,407	5	19,197,179	6.91·10¹³	286	61
1,659,148	5	7.11·10¹³	6,125,648,224	126	125
1,917,105	6	17,156,363,255	7.01·10¹⁵	190	125
2,517,862	6	7.21·10¹⁶	48,483,219,264	254	253
3,255,155	7	1.51·10¹³	7.11·10¹⁸	382	253
5,250,968	6	7.31·10¹⁶	244,016,160,128	510	509
6,469,645	7	1.37·10¹²	7.21·10¹⁹	638	253
9,142,178	4	389,382,382,511	3,212,864,384	510	509
9,463,015	5	13,313,171,399	3.88·10¹⁴	542	61
9,966,524	5	3.9·10¹⁴	3.01·10¹²	126	125
10,405,097	6	1.31·10¹³	3.89·10¹⁶	190	125
11,256,622	6	3.91·10¹⁷	2.81·10¹⁴	254	253
12,174,531	7	1.29·10¹⁶	3.9·10¹⁹	382	253
14,421,112	6	3.92·10¹⁷	2.61·10¹⁵	510	509
15,820,405	7	1.27·10¹⁶	3.91·10²⁰	638	253
18,743,706	7	3.93·10²⁰	2.41·10¹⁷	510	509
22,061,823	8	1.25·10¹⁹	3.92·10²³	766	509
30,571,412	7	3.94·10²⁰	2.21·10¹⁸	1,022	1,021
35,551,585	8	1.23·10¹⁹	3.93·10²³	1,278	509
46,376,294	8	3.95·10²⁴	2.01·10²¹	1,022	1,021
59,038,875	9	1.21·10²³	3.94·10²⁶	1,534	1,021
92,220,944	8	3.96·10²⁵	1.81·10²⁰	2,046	2,045
111,528,109	9	1.19·10²²	3.95·10²⁸	2,558	1,021
153,971,602	8	3.97·10²⁶	1.69·10²¹	2,046	2,045
176,217,463	9	1.17·10²²	3.96·10²⁹	2,558	1,021
222,615,948	9	3.98·10³⁰	1.49·10²⁵	2,046	2,045
275,605,721	10	1.15·10²⁶	3.97·10³³	3,070	2,045
411,458,142	8	3.99·10²⁷	1.28·10²⁴	4,094	4,093
447,518,227	9	1.13·10²⁵	3.98·10³¹	4,606	1,021
513,030,920	9	4·10³¹	1.08·10²⁵	2,046	2,045
579,826,725	10	1.11·10²⁹	3.99·10³⁵	3,070	2,045
734,793,354	10	4.01·10³⁵	8.8·10²⁸	4,094	4,093
924,601,615	11	1.98·10²⁹	4·10³⁹	6,142	4,093

nlast 11

u_1..u_nlast 1.98·10²⁹

v_1..v_nlast 4·10³⁹

alast 6,142

blast 4,093

Template comparisonSBCv6.v TM21: partly applies · the nearest solved proof, what carries over, and the transitions that differ

	0	1
A	1RB	0LE
B	1RC	0RC
C	1LD	0RB
D	1LA	0LE
E	1LD	1LF
F	1LD	---

file: SBCv6.v:3702
module: TM21
machine: 1RB1LB_0LC1RD_0RA1LC_0RB1RE_0RD0LF_---1LE (11 transitions apart)
diff: 10 of 12 transitions differ under the best renaming/mirror (Sk1like_TC_v2 TM1: 9 of 12)
note: Same architecture (LIncs = carries, Ov = re-pairing overflow, BigStep), but TM21's S' configs never recur here (0 real hits in 2e5 steps, all 6 states). Its LWF invariant fails: here digits run out and merge.

1Same machine as #11?

What to check here: whether this machine is its parent's table under a renaming, and whether its run follows the parent's (computed from the two machine strings).

status.json names #11 as the parent (1RB0LE_1RC0RC_1LD0RB_1LA0LE_1LD1LF_1LD---); relation: “neighbour of #11: one transition away; its run differs (90,039 vs 77,685 cells at 1e9)”. Everything below is computed from the two machine strings, not read from notes.

✗ Not the same table. No renaming of #11's states, with or without mirroring, gives this machine's table. Closest: A→A, B→B, C→C, D→D, E→E, F→F (#11's state → this machine's), no mirror, where 1 of 12 transitions differ:

#11's A1 = 0LE predicts this machine's A1 = 0LE; it is 0LC.

Under that map: This machine starts in #11's state A, the same start as #11.

#11	#11's row (read 0, read 1)	σ	predicted row: renamed by σ	this machine's actual row
A	`1RB` `0LE`	→ A	`1RB` `0LE`	`1RB` `0LC`	✗	start of #11start of this machine
B	`1RC` `0RC`	→ B	`1RC` `0RC`	`1RC` `0RC`	✓
C	`1LD` `0RB`	→ C	`1LD` `0RB`	`1LD` `0RB`	✓
D	`1LA` `0LE`	→ D	`1LA` `0LE`	`1LA` `0LE`	✓
E	`1LD` `1LF`	→ E	`1LD` `1LF`	`1LD` `1LF`	✓
F	`1LD` `---`	→ F	`1LD` `---`	`1LD` `---`	✓

Rows aligned by σ: each of #11's states X sits next to this machine's state σ(X). ✓ = the actual row equals #11's row with every target state renamed by σ; --- (halt) must stay ---. Searched: all 720 renamings × with/without mirror.

Fig P1 · bbchallenge default view: #11 and this machine, first 10,000 steps

Same view, same settings on both sides. Look for the same band structure: the tables differ in 1 transition(s) (listed above).

#11 (parent), from blank in its A

not rendered yet

this machine (#32), from blank in its A

not rendered yet

bbchallenge-defaultStart blankRows steps 0 → 10,000, top to bottomWindow cells −200..199, left to rightColors 1 0 or unvisited

tools/diagram.py <tm> --as-site (the site's 400×500 canvas)

Fig P2 · Long run, Blaze (speed): #11 and this machine, 100 million steps

The macro behaviour, identical settings on both sides: each picture is its machine's own visited span stretched to 800 px, so compare the shape and order of the bands, not their absolute width. Speed mode samples one cell per column, so a one-cell shift can swap orange and white inside a band; compare band edges, not colours.

#11 (parent), from blank in its A

not rendered yet

this machine (#32), from blank in its A

not rendered yet

bbchallenge-blazeStart blankRows steps 0 → 1e8Window the visited spanColors 1 0 at the sampled cell

Rows: one snapshot per row (Blaze time blocks), stretched to 500 px · Window: every k-th cell sampled, stretched to 800 px

tools/diagram.py <tm> --mode blaze --speed --as-site --steps 1e8

Trajectory numbers not computed yet: run python3 -B tools/killreview.py 1RB0LC_1RC0RC_1LD0RB_1LA0LE_1LD1LF_1LD--- (about 10 s; cached in img/vs-parent.json).

Proof & checks

proof.md · the informal proof
check_proof.py · the numeric checks of proof.md

Files

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

name	size	changed
notes.md ↓	41 KB	2026-10-12 21:04
proof.md ↓	33 KB	2026-10-10 12:45
status.json ↓	2.3 KB	2026-10-12 23:02
img/	4 items	2026-10-10 06:10
scripts/	29 items	2026-10-12 21:04
check_proof.py ↓	41 KB	2026-10-10 12:40

status.json in full

{
 "tm": "1RB0LC_1RC0RC_1LD0RB_1LA0LE_1LD1LF_1LD---",
 "status": "CRYPTID_CANDIDATE",
 "stage": "informal_proof",
 "updated": "2026-10-12",
 "reason": "Class 2 close-out stage 3 of 3 (2026-10-12): flagged CRYPTID_CANDIDATE together with R4 (same table), proof work stops. New wide-integer simulator scripts/c2s3_tsim.c (2048-bit steps, 512-bit counts; JCAP=40 reproduces stage 2 byte for byte to 1e37, and every earlier halting step count). #32: no halt to 1e80, first 40 defects frozen from 5.8e14 to 1e80. N cuts from I(N,360), N = 0..44, to 1e80: exactly N = 2, 7, 12, 17, 22 halt; N >= 23 freeze because the first lower digit (u = 48) runs out in cycle 5. Cutting that digit's u1 too: N = 12 halts for 14 of 24 small u1 and not for 10 (u1 = 1 mod 3 tends to halt, with exceptions); N = 17: 7 of 25; N = 11, 13: 0 of 50. So halting is a residue condition at every level of an unbounded 2-adic/5-adic hierarchy; no invariant. Decision in R4's decision.json (stop_cryptid recommended). Earlier: rule G + sweep case analysis (proof.md), check_proof.py 12/12. Stage-2 re-run (2026-10-12): the workflow re-issued stage 2 after the track had already ended at stage 3; no new proof work (cryptid protocol, decision pending). The kept simulators reproduce the stage-2 and stage-3 dumps byte for byte (1e37, 1e80) and the cut halts (N = 2: 202,227,190). New probe (scripts/c2s2r_mkcut3.py): the second lower digit u2 also switches the outcome (N = 12: a fixed halt for u2 >= 40 moves or disappears once u2 runs out; u1 = 11 halts at u2 = 47..98 and 5 but not 13..40); N = 11/13: 0 of 42 halts. Still CRYPTID_CANDIDATE.",
 "note": "check_proof.py 12/12 PASS (default seed 79 s; --seed 2026 --n 1000 --quick 52 s). Unclaimed. Same open problem as R4 (mirror, D-start).",
 "priority_call_answered": "Shared with R4: invest in a joint #32/R4 multi-level invariant (proof.md 5 route), or park both?",
 "parent": "1RB0LE_1RC0RC_1LD0RB_1LA0LE_1LD1LF_1LD---",
 "relation": "neighbour of #11: one transition away; its run differs (90,039 vs 77,685 cells at 1e9)",
 "funded": {
  "option": "class2_closeout",
  "date": "2026-10-12"
 },
 "confidence": "med",
 "parked": "Stopped by Dennis 2026-10-12 (decision queue: go with recommendations: stop_cryptid): kept as CRYPTID_CANDIDATE, rules written up, no more compute. (decision filed on R4, same table.)"
}

Rendered 2026-10-16 13:29 by tools/machinepage.py from status.json, the parent's observe.json and the dashboard records · rebuild: python3 -B tools/card.py 1RB0LC_1RC0RC_1LD0RB_1LA0LE_1LD1LF_1LD---