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 / R4

`1RB0RE_1LC0RD_1LD0LD_1RA0LC_1RA1RF_1RA---`

R4Cryptid candidateSkelet 1-like Class 2bbchallenge ↗Explorer

Where it stands

Cryptid candidate, parked at the observation

Class 2 close-out stage 3 of 3 (2026-10-12), joint with #32 (write-up in #32's notes.md): flagged CRYPTID_CANDIDATE, proof work stops. Halting is decided by modular conditions on fuel values at a hierarchy of exhaustions.

Read the full status

A regime-I top halts exactly when its fuel N runs out at N = 2 (mod 5) (N = 0..44 from #32's I(N,360): only 2, 7, 12, 17, 22 halt by 1e80). A lower digit that runs out first switches that outcome irregularly (N = 12: 14 of 24 small u1 values halt, 10 do not; N = 11, 13: 0 of 50). Wide-integer simulator c2s3_tsim.c (validated byte for byte against stage 2 to 1e37): R4 no halt to 1e80, first 40 defects frozen from 4.8e17 to 1e80; its top cycle started at N = 27 = 2 (mod 5) and waits behind deep levels. No invariant. Heuristic (random residues) leans to an astronomically late halt, not non-halting. decision.json: stop_cryptid (recommended) / recursive_model / formalize_rules. Stage-2 re-run (2026-10-12): replay of an already-run stage, no new proof work (cryptid protocol, decision pending). Kept simulators reproduce R4's stage-3 dump to 1e80 byte for byte (no halt). New probe on #32's base (same table): the second lower digit also switches the halting outcome, non-monotonically; N = 11/13 0 of 42 halts. Still CRYPTID_CANDIDATE; decision.json unchanged.

Observe

Deepen

Informal proof

Rocq

Waiting on you: 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?

See the question →

Overview

Needs you

your call 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?

In one sentence

#32's table, D-start: #11's counter plus nested walls whose fuel drops 1 per lower overflow; no proof idea yet.

Status: Cryptid candidateobserving · updated 2026-10-12Waiting on you · 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?
idle since Oct 12 23:02 · status.json 2026-10-12
Class: Skelet 1-like Class 2ours: sheet Skelet 1-like Class 2 ≠ ours hierarchical binary counter: #33/#11's counter whose u=1 digits freeze into fossil-K walls with decrementing fuel (= #32's table, D-start) · low confidence
On the list: line 506 of BB6_holdouts_663.txt · historical 740 line 561
R4eqv ×1sim 1e15

Your calls on file 6

priority call (open): 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?
priority call (answered): R4 and #32 share one table and one hierarchical-counter mechanism. Invest in a joint #32/R4 recursive invariant, 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.
funded: option: class2_closeout · date: 2026-10-12
2026-10-10 · park_both: R4 and #32 are one table with one open mechanism: a hierarchical counter whose fossil-K walls lose one unit of fuel per lower overflow. Invest in a joint #32/R4 recursive invariant, or park both? (Dennis: go with all recommendations (2026-10-10))
2026-10-12 · stop_cryptid: R4 and #32 are flagged CRYPTID_CANDIDATE (halting decided by fuel residues at nested exhaustions, no invariant): stop here, or fund a recursive abstract model to follow R4's real orbit, whose top already has the halting residue? (Dennis 2026-10-12: 'go with recommendations')

Mechanism

How it works: 3 notes

Level 1 is #33's / kill #11's binary counter (carry M_k, same formula, 12,350/12,350 exact to 3e8). One cell differs (B1 0RD vs 0RE): a carry reaching a bit-1 digit with u = 1 turns back and does a partial overflow P (#32's rule, exact).
P leaves misaligned text that acts as a fossil K-block wall (01)^w 000 (01)^x with a slow level-2 counter behind it. Each level-1 overflow lowers the wall gap by exactly 1 (217 at 1.8e7, 179 at 2.8e8, 151 at 2e10); a far wall (gap 52-53) sits at the end. Halting needs A> 111.
Fuel cut to 9 or 5 in a real config: the wall dissolves, the far wall keeps burning, new walls form with fresh fuel (109, 164); no halt to 2e8. 54 of 12,438 macro steps to 3e8 still have no rule (far-end terminators, the wall's v = 1 shape, Z3 junctions), as for #32.

Figures for Checkpoint A

Fig 1 · Whole tape, steps 0..3e7 (phase view)Q1
Each band is half a digit. Compare the bands right of the pinch near row 600 with those above.

Fig 2 · Right end, steps 0..1e9 (phase view)
Inner wall: the thin line near x = 640 px. To its right: level-2 digits, then the far end.

Fig 3 · R4 at a u = 1 digit (constructed)Q2
Start K: block, LSB digit (u=1, v=4), bit-0 digit (4,0,3), 1001. Watch where the first rightward sweep turns.

More figures (2)Fig 4–5: First 10,000 steps (site view) · #33 from the same start

Rules (3/4 validated)exact tape rewrites the proof will formalize, each re-checked by simulation

rule	from ⟶ to	cases	steps	checked
M_k carry (= #33's M_k)	0^∞ <C (01)^b 000 (01)^a [(10)^vj (01)^uj]_{j=m..j+1} (10)^v 00 (01)^u S ⟶ 0^∞ <C (01)^b+2 000 (01)^a+1 [(10)^vj-1 00 (01)^uj]_{j=m..j+1} (10)^v-1 (01)^u+1 S	needs a >= 1, v >= 1, every trailing digit uj >= 2 and vj >= 1; S never read. v = 1: the digit drops (fuses). 300 random (k = 0..5, sizes to 300) + all 12,350 M steps of the real run to 3e8. Control: one trailing uj = 1 -> formula fails 60/60	32+8a+8b+4v+sum_j(8uj+4vj)	✓12650/12650
P partial overflow at the first u = 1 digit (#32's P, mirrored)	0^∞ <C (01)^b 000 (01)^a [(10)^vi (01)^ui]_{i=m..p+1} (10)^vp 01 S ⟶ 0^∞ <C 01 000 (01)^b+3 (10)^a (01)^vm [(10)^u(i+1) 00 (01)^vi-1]_{i=m-1..p+1} (10)^u(p+1) 00 (01)^vp-1 10 S'	k = m-p+1 digits, up = 1, ui >= 2 (i > p), a >= 1, S starts with 1 and S' = S minus that 1; p = m: ... (01)^vm 10 S'. 300 random (k = 1..5) + all 34 P steps of the real run to 3e8	77-4k+8a+20b+4sum_{i>=p}ui+8sum_{i>=p}vi	✓334/334
O full overflow (= #33's O), all u >= 2, bare 1001 end	0^∞ <C (01)^b 000 (01)^a [(10)^vj (01)^uj]_{j=m..1} 1001 0^∞ ⟶ 0^∞ <C 01 000 (01)^b+3 (10)^a (01)^vm [(10)^uj 00 (01)^v(j-1)-1]_{j=m..2} (10)^u1 00 1001 0^∞	a >= 1, all uj >= 2. Never fires from blank to 3e8 (the far end is never the bare 1001). Control: one uj = 1 -> fails 200/200 (P happens instead)	89-4m+8a+20b+4sum(u)+8sum(v)	✓200/200
wall fuel law (empirical, real run only)	reset that ends at the inner wall W(L), shape Z2 0 O2 \| O2 0 Z2 \| Z3 ⟶ inner wall W'(L-1), next shape in the cycle	all 38 resets from 1.8e7 to 2.84e8 (L 217 -> 179); 2e10 sample L = 151. Not a formula yet; not tested on random instances	—	–untested

Compressed historythe tape as pre-reset K: 0^∞ <C (01)^b 000 (01)^a [level-1 digits] W1 [level-2 digits] W2 0^∞ (W = wall shape + gap) at 40 moments: where the rules are read off

pre-reset K: 0^∞ <C (01)^b 000 (01)^a [level-1 digits] W1 [level-2 digits] W2 0^∞ (W = wall shape + gap)

step	`b`	`a`	`hi`	`inner wall W1`	`far wall W2`
70	1	3	4	-	-
809	5	12	16	-	-
2,407	1	12	22	-	-
8,306	13	22	28	-	-
15,544	13	14	37	-	-
40,950	37	50	43	-	-
61,193	29	73	52	-	-
97,511	13	54	58	-	-
207,074	61	94	64	-	O2 0 Z2 66
261,200	29	30	67	-	O2 0 Z2 67
378,922	61	94	73	-	Z3 64
615,221	125	205	76	-	Z2 0 O2 62
1,128,940	125	190	76	-	O2 0 Z2 59
2,271,498	253	190	76	-	Z3 58
4,427,656	509	382	79	-	Z3 59
11,159,235	509	766	82	-	Z2 0 O2 56
18,115,616	885	954	85	Z3 218	Z3 54
18,388,227	29	921	85	Z2 0 O2 216	Z2 0 O2 53
18,695,766	29	46	85	O2 0 Z2 213	Z2 0 O2 53
19,204,521	125	126	85	Z2 0 O2 210	Z2 0 O2 53
19,804,212	61	158	85	O2 0 Z2 207	Z2 0 O2 53
21,032,655	253	254	85	Z2 0 O2 204	Z2 0 O2 53
23,053,530	253	382	85	O2 0 Z2 201	Z2 0 O2 53
29,254,917	509	510	85	Z2 0 O2 198	Z2 0 O2 53
43,094,560	253	1,150	85	O2 0 Z2 195	Z2 0 O2 53
61,261,763	1,021	1,022	85	Z2 0 O2 192	Z2 0 O2 53
124,890,854	1,021	2,558	85	O2 0 Z2 189	Z2 0 O2 53
181,235,665	509	510	85	Z2 0 O2 186	Z2 0 O2 53
202,004,399	253	1,150	85	Z2 0 O2 183	O2 0 Z2 52
264,408,730	2,045	1,534	85	Z3 180	O2 0 Z2 52
2,000,000,000	-	-	85	O2 0 Z2 166	O2 0 Z2 52
4,000,000,000	-	-	85	O2 0 Z2 162	O2 0 Z2 52
6,000,000,000	-	-	85	O2 0 Z2 158	O2 0 Z2 52
8,000,000,000	-	-	85	Z2 0 O2 157	O2 0 Z2 52
10,000,000,000	-	-	85	O2 0 Z2 156	O2 0 Z2 52
12,000,000,000	-	-	85	Z2 0 O2 155	O2 0 Z2 52
14,000,000,000	-	-	85	O2 0 Z2 152	O2 0 Z2 52
16,000,000,000	-	-	88	Z3 153	Z3 53
18,000,000,000	-	-	88	O2 0 Z2 151	Z3 53
20,000,000,000	-	-	88	Z3 151	Z3 53

blast -

alast -

hilast 88

inner wall W1last Z3 151

not plottable

far wall W2last Z3 53

not plottable

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

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

differs from the template

file: —
module: our kill #11 (machines/1RB0LE_1RC0RC_1LD0RB_1LA0LE_1LD1LF_1LD---/, check_kill PASS); same table as pool #32 (OPEN)
machine: 1RB0LE_1RC0RC_1LD0RB_1LA0LE_1LD1LF_1LD--- (9 transitions apart)
diff: 1 transition after mirror + renaming (#11's A,B,C,D,E,F = R4's B,C,D,A,E,F): #11 A1 0LE vs 0LC here (= R4's B1 0RE vs 0RD). With that change the table is exactly #32's; R4 starts in #32's D
note: M and O carry over verbatim when every digit has u >= 2. #11's INV does not survive: u = 1 digits appear right away (O's new MSB digit (0,0,u1) flips to u = 1), P replaces O, and the fossil walls are outside #11's family. #32 hit the same wall (notes there). SBCv6 TM21 / TCv3 are loose relatives only.

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

Joint with #32 (same table). Model one level as K-block + digits + fossil K-block, get exact rules for the 3 open event types and the fuel law, then find a recursive invariant (each level a counter whose wall fuel is refilled when a new wall forms). Constructed small-fuel runs first.

▲Recursive structure: walls form, burn fuel and dissolve; a proof needs a multi-level invariant, which is far beyond a delta of #11.
▲54 of 12,438 macro steps (3 event types) have no rule yet; #32 hit the same ones.
▲The long-run regime is unobservable: inner-wall fuel 151 at 2e10, burning at slowing rate.

Stats & provenance2·10¹⁰ steps simulated · 87,460 cells · the status in full · files

simulated: 2·10¹⁰ steps
tape: 87,460 cells · 43,726 nonzeros
growth: left edge ~2.8 t^0.5 at 1e9 (-87,374), -398,788 at 2e10; right edge 85 from 1.8e7 to 1.4e10, 88 after the level-2 overflow (~1.5e10). cells/nonzeros are at 1e9
status now: Class 2 close-out stage 3 of 3 (2026-10-12), joint with #32 (write-up in #32's notes.md): flagged CRYPTID_CANDIDATE, proof work stops. Halting is decided by modular conditions on fuel values at a hierarchy of exhaustions. A regime-I top halts exactly when its fuel N runs out at N = 2 (mod 5) (N = 0..44 from #32's I(N,360): only 2, 7, 12, 17, 22 halt by 1e80). A lower digit that runs out first switches that outcome irregularly (N = 12: 14 of 24 small u1 values halt, 10 do not; N = 11, 13: 0 of 50). Wide-integer simulator c2s3_tsim.c (validated byte for byte against stage 2 to 1e37): R4 no halt to 1e80, first 40 defects frozen from 4.8e17 to 1e80; its top cycle started at N = 27 = 2 (mod 5) and waits behind deep levels. No invariant. Heuristic (random residues) leans to an astronomically late halt, not non-halting. decision.json: stop_cryptid (recommended) / recursive_model / formalize_rules. Stage-2 re-run (2026-10-12): replay of an already-run stage, no new proof work (cryptid protocol, decision pending). Kept simulators reproduce R4's stage-3 dump to 1e80 byte for byte (no halt). New probe on #32's base (same table): the second lower digit also switches the halting outcome, non-monotonically; N = 11/13 0 of 42 halts. Still CRYPTID_CANDIDATE; decision.json unchanged. (status.json, 2026-10-12)
observer's note: Mechanism partly understood (M, P, O validated; nested fossil-K walls observed); 54/12,438 macro steps to 3e8 uncovered and no non-halting argument. Confidence low: waits on Dennis's priority call.
files: observe.json · notes.md · status.json

Proof & checks

No proof work yet.

Files

machines/<tm>/: 10 entries · raw notes, status, scripts, images

name	size	changed
notes.md ↓	17 KB	2026-10-12 21:04
status.json ↓	2.0 KB	2026-10-12 23:02
observe.json ↓	14 KB	2026-10-10 10:36
decisions/	2 items	2026-10-12 23:02
img/	6 items	2026-10-10 10:30
scripts/	21 items	2026-10-10 10:36
qsim.err ↓	0 B	2026-10-10 10:00
qsim.jsonl ↓	6.3 KB	2026-10-10 10:00
sim_1e9.err ↓	0 B	2026-10-10 10:00
sim_records_1e9.jsonl ↓	8.4 MB	2026-10-10 10:00

status.json in full

{
 "tm": "1RB0RE_1LC0RD_1LD0LD_1RA0LC_1RA1RF_1RA---",
 "status": "CRYPTID_CANDIDATE",
 "stage": "observe",
 "updated": "2026-10-12",
 "reason": "Class 2 close-out stage 3 of 3 (2026-10-12), joint with #32 (write-up in #32's notes.md): flagged CRYPTID_CANDIDATE, proof work stops. Halting is decided by modular conditions on fuel values at a hierarchy of exhaustions. A regime-I top halts exactly when its fuel N runs out at N = 2 (mod 5) (N = 0..44 from #32's I(N,360): only 2, 7, 12, 17, 22 halt by 1e80). A lower digit that runs out first switches that outcome irregularly (N = 12: 14 of 24 small u1 values halt, 10 do not; N = 11, 13: 0 of 50). Wide-integer simulator c2s3_tsim.c (validated byte for byte against stage 2 to 1e37): R4 no halt to 1e80, first 40 defects frozen from 4.8e17 to 1e80; its top cycle started at N = 27 = 2 (mod 5) and waits behind deep levels. No invariant. Heuristic (random residues) leans to an astronomically late halt, not non-halting. decision.json: stop_cryptid (recommended) / recursive_model / formalize_rules. Stage-2 re-run (2026-10-12): replay of an already-run stage, no new proof work (cryptid protocol, decision pending). Kept simulators reproduce R4's stage-3 dump to 1e80 byte for byte (no halt). New probe on #32's base (same table): the second lower digit also switches the halting outcome, non-monotonically; N = 11/13 0 of 42 halts. Still CRYPTID_CANDIDATE; decision.json unchanged.",
 "priority_call_answered": "R4 and #32 share one table and one hierarchical-counter mechanism. Invest in a joint #32/R4 recursive invariant, or park both?",
 "funded": {
  "option": "class2_closeout",
  "date": "2026-10-12"
 },
 "confidence": "med",
 "priority_call": "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?",
 "parked": "Stopped by Dennis 2026-10-12 (decision queue: go with recommendations: stop_cryptid): kept as CRYPTID_CANDIDATE, rules written up, no more compute."
}

observe.json contract (tools/README-card.md):

1 contract warning

rank: not an int

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 1RB0RE_1LC0RD_1LD0LD_1RA0LC_1RA1RF_1RA---