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Machines / W6-5

`1RB0LB_0LC0RE_1LA1LD_0LB1LD_1RA0RF_1RA---`

W6-5Claimed elsewhereChaotic Bell Class 4bbchallenge ↗Explorer

Upstream result

Claimed elsewhere

The blank-start machine halts: PR_ChaoticBell4.v.TM2 ↗.

Absent from the current 663 holdout list. Earlier local observations remain below.

Overview

In one sentence

Phases convert one budget block per 4-trip cycle; each new layer is ~4/3 the last and n mod 3 picks the next phase.

Upstream: The blank-start machine halts: PR_ChaoticBell4.v.TM2 ↗.
Status: Externally Solvedobserving · updated 2026-10-14Parked · Observe done (about 2 h). The 3 open questions are optional.
idle since Oct 14 16:43 (44 h ago) · status.json 2026-10-14
Class: Chaotic Bell Class 4ours: sheet Chaotic Bell Class 4 ≠ ours Layered Bell counter: budget phases with a x4/3, mod-3-branching layer law (cryptid-like) · med confidence
On the list: not on BB6_holdouts_663.txt (line 333 of the previous list) · historical 740 line 333 · observe.json rank #333
eqv ×6sim 1e14

Your calls on file 3

priority call (answered): Cryptid-like (pre-registered stop): the layer law is x4/3 and n mod 3 picks the next phase; no halting branch is known. Park it, or fund one 2 h stage for an exact phase-level accelerator (R1-R3 plus measured phase-end maps) and a census of the residue branches?
parked: Dennis 2026-10-14: park
2026-10-14 · park: W6-5's layer law is x4/3 with n mod 3 picking the next phase (the pre-registered stop): park it, or fund one 2 h stage?

Mechanism

How it works: 3 notes

Trip and phase level: three short trips cross the unary counter 1001^c, the fourth converts one budget block; the budget sum is conserved and c grows by 2 per cycle (R1-R3 validated 60/60, 40/40, 40/40).
Epoch level: at a phase end the counter (about 8n cells) becomes a layer of (4n+r)/3 blocks, and n mod 3 picks the next phase (0: H6 shift phase, 1: R1 phase at once, 2: re-eat an older layer).
To 1e11: layers 5803, 9996, 13333, 17774; the old 9996 layer is re-eaten at 4.8e10..8e10 and rebuilt; no halt (halting needs B> 111, never written).

Figures for Checkpoint A

Fig 1 · One cycle of rule R1Q1
Count the trips from the right edge: three turn near the counter, the fourth crawls left through 100001 blocks.

Fig 2 · Phases from blank to 6.6e9Q2
Each slanted boundary is a budget being eaten; each new band is a layer left by a phase end.

More figures (2)Fig 3–4: Default view, first 10,000 steps · Records to 2 million steps

Rules (4/4 validated)exact tape rewrites the proof will formalize, each re-checked by simulation

rule	from ⟶ to	cases	steps	checked
R1 (K6 eats H6)	0^∞ 1011 (110010)^a 1² 0⁴ 1101 (100001)^b+2 (1001)^c A> 0^∞ ⟶ 0^∞ 1011 (110010)^a+1 1² 0⁴ 1101 (100001)^b+1 (1001)^c+2 A> 0^∞	b+2 >= 2 (the last block, b+1 = 1, is the phase end)	—	✓60/60
R2 (1e8 hub)	0^∞ (1011)³ (001011)^a 0⁴ (110)² (000110)^b+2 (01)² 1 0⁴ (110010)^p+1 (110000)^q+3 1³ 01 (1001)^c A> 0^∞ ⟶ 0^∞ (1011)³ (001011)^a+1 0⁴ (110)² (000110)^b+1 (01)² 1 0⁴ (110010)^p+1 (110000)^q+3 1³ 01 (1001)^c+2 A> 0^∞	b+2 >= 2	—	✓40/40
R3 (5e8 hub, Y^2 -> X)	0^∞ (110)³ X^a (010110)² (000110)³ 110 Y^(b+3) (000110)^p+1 (01)² (100001)^q+1 (1001)^c A> 0^∞ ⟶ 0^∞ (110)³ X^(a+1) (010110)² (000110)³ 110 Y^(b+1) (000110)^p+1 (01)² (100001)^q+1 (1001)^c+2 A> 0^∞	X = 010110010110000110000110, Y = 010110000110; b+3 >= 3	—	✓40/40
E (phase end, budget n)	phase 6 with budget n = g+h (real 1.29e10 configuration, h varied) ⟶ new layer of (4n+r)/3 blocks; n = 0 mod 3: H6->H6 shift phase; 1 mod 3: R1 phase at once; 2 mod 3: re-eats the older 5803 layer	n mod 3 (r = 7 for residue 2, 5 for residue 1 at the measured snapshot)	—	✓6/6

Compressed historythe tape as phase 6 at the A record: 0^∞ L (110)² 0³ (110010)^g 1² 0⁴ 1101 (100001)^h (1001)^c A> 0^∞ at 3 moments: where the rules are read off

phase 6 at the A record: 0^∞ L (110)² 0³ (110010)^g 1² 0⁴ 1101 (100001)^h (1001)^c A> 0^∞

step	`g`	`h`	`c`
12,500,084,130	9,144	853	18,290
12,700,067,096	9,459	537	18,921
12,900,059,348	9,773	223	19,549

glast 9,773

hlast 223

clast 19,549

Template comparisonW5-3: partly applies · the nearest solved proof, what carries over, and the transitions that differ

	0	1
A	1RB	0LB
B	0LC	0RE
C	1LA	1LD
D	0LB	1LD
E	1RA	0RF
F	1RA	---

file: —
module: W5-3 (our kill)
machine: 1RB1RA_1LC1LE_1RF1LD_1RE0LD_0LB0RA_---0RC (10 transitions apart)
diff: no table within 5 transitions; architecture comparison only
note: Our W5-3 kill (machines/<W5-3>/ .v, read). R1-R3 are linear walk lemmas like W5-3's Wk/W2Q. W5-3 closes its eats with a binary counter and one size bound; here the phase ends feed a x4/3 layer law with a mod-3 branch, which no template covers.

Proof strategy & riskshow the formal proof will go · 3 risks to watch

Parked under the cryptid protocol. If funded: build an exact phase-level accelerator from R1-R3 plus measured phase-end maps, run it far past 1e11, and census the residue branches for a closed set of phase shapes.

▲The layer law n -> (4n+r)/3 with a mod-3 choice of successor phase is Collatz-like (Hydra-style x3/2 relatives); a closed invariant may not exist.
▲Phase ends were measured on 6 instances from one real configuration only; other phase types may have other offsets.
▲Phases reach back into older layers (9996 re-eaten at 4.8e10), so the state is a stack of layers, not one counter.

Stats & provenance10¹¹ steps simulated · 601,752 cells · the status in full · files

simulated: 10¹¹ steps
tape: 601,752 cells
growth: span about 1.9-2.0 x sqrt(steps): 19k at 1e8, 58k at 1e9, 204k at 1e10, 602k at 1e11
status now: Observe done (about 2 h). The tape is a stack of layers of periodic words (110000, 110010, 1100, 110 rotations). The head runs 4-trip cycles: three short trips over a unary counter 1001^c, one long trip that converts one block of the current budget region; per cycle the budget sum is conserved and c grows by 2 (rules R1-R3 validated 60/60, 40/40, 40/40 from random instances). When a budget n runs out, the counter (about 8n cells) becomes a new layer of (4n+r)/3 six-cell blocks, and n mod 3 selects one of three successor phases (measured on n = 9996..10001 from the real 1.29e10 configuration: residue 0 -> H6 shift phase, 1 -> R1 phase at once, 2 -> re-eat the older 5803 layer). That is the pre-registered W6-5 stop rule (x m/k law with a residue split), so the cryptid protocol applies: rules formalized in observe.json, flagged, stopped. Direct run to 1e11: no halt, span 601,752; layers 5803, 9996, 13333, 17774; the old 9996 layer was re-eaten at 4.8e10..8e10 and rebuilt. Halting needs B> 111, never seen. (status.json, 2026-10-14)
observer's note: Pre-registered W6-5 stop rule met: the epoch law is x4/3 with a mod-3 residue split (three successor phases, one re-eats older layers). R1-R3 validated; phase ends measured on 6 instances. No halt to 1e11.
files: observe.json · notes.md · status.json

Proof & checks

No proof work yet.

Files

machines/<tm>/: 7 entries · raw notes, status, scripts, images

name	size	changed
notes.md ↓	6.7 KB	2026-10-14 14:25
status.json ↓	2.1 KB	2026-10-14 16:43
observe.json ↓	7.7 KB	2026-10-14 14:26
decisions/	1 item	2026-10-14 16:43
img/	4 items	2026-10-14 14:24
scripts/	6 items	2026-10-14 14:24
work/	7 items	2026-10-14 14:24

status.json in full

{
 "tm": "1RB0LB_0LC0RE_1LA1LD_0LB1LD_1RA0RF_1RA---",
 "label": "W6-5",
 "status": "CRYPTID_CANDIDATE",
 "stage": "observe",
 "updated": "2026-10-14",
 "confidence": "med",
 "holdout_line_740": 333,
 "reason": "Observe done (about 2 h). The tape is a stack of layers of periodic words (110000, 110010, 1100, 110 rotations). The head runs 4-trip cycles: three short trips over a unary counter 1001^c, one long trip that converts one block of the current budget region; per cycle the budget sum is conserved and c grows by 2 (rules R1-R3 validated 60/60, 40/40, 40/40 from random instances). When a budget n runs out, the counter (about 8n cells) becomes a new layer of (4n+r)/3 six-cell blocks, and n mod 3 selects one of three successor phases (measured on n = 9996..10001 from the real 1.29e10 configuration: residue 0 -> H6 shift phase, 1 -> R1 phase at once, 2 -> re-eat the older 5803 layer). That is the pre-registered W6-5 stop rule (x m/k law with a residue split), so the cryptid protocol applies: rules formalized in observe.json, flagged, stopped. Direct run to 1e11: no halt, span 601,752; layers 5803, 9996, 13333, 17774; the old 9996 layer was re-eaten at 4.8e10..8e10 and rebuilt. Halting needs B> 111, never seen.",
 "siblings": [],
 "sibling_note": "No other start or mirror of this table is on the 740/778 lists (canon from all 6 starts). Starts C, E, F are eqv_1590 lines 122, 128, 132 (276's equivalence group). In the critic's family only 479 and 145 share a table (145 = 479 from B); 333, 683 and 276 each have their own table. The time-shifted record-twin claim for 479/683 was not re-checked.",
 "upstream": "No upstream proof; sheet Results row: class only, note 'Possible bouncer'; discarded-machines tab: 'unanalysed'. No Discord hit.",
 "priority_call_answered": "Cryptid-like (pre-registered stop): the layer law is x4/3 and n mod 3 picks the next phase; no halting branch is known. Park it, or fund one 2 h stage for an exact phase-level accelerator (R1-R3 plus measured phase-end maps) and a census of the residue branches?",
 "parked": "Dennis 2026-10-14: park"
}

Rendered 2026-10-16 13:29 by tools/machinepage.py from status.json, observe.json (the card) and the dashboard records · rebuild: python3 -B tools/card.py 1RB0LB_0LC0RE_1LA1LD_0LB1LD_1RA0RF_1RA---