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Machines / #36

`1RB1RF_1LC0RF_1LE0LD_1RC0LB_---1RA_1LB1RA`

#36ParkedBouncer + Chaotic Edgebbchallenge ↗Explorer

Where it stands

Parked at the observation

Parked 2026-10-10 with #13 (auto-applied recommendation): same edge lemma (E'); an (E') proof would now pay #13, #34, #35, #36. Observe done.

Read the full status

The mechanism is exact and validated, and it is identical to parked #13 at the cycle level: the same bulk (1101101101)^a, the same 7 junction words, and the same tail orbit D_n (1,952/1,952 shared cycles; probe map equal on 217/217 tested D, 0 disagree). #35 is this table renamed. Edge map clean to 1.5e7 cycles (about 4.9e16 steps), but no non-halting argument exists for the chaotic tail (#13's open edge lemma E'). Confidence med, so proof work waits on Dennis (decision.json).

Observe

Deepen

Informal proof

Rocq

Overview

In one sentence

#13's twin: same period-10 bouncer, same 7 junction words, same chaotic tail D_n cycle for cycle. Tail = whole problem.

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 13:58 · status.json 2026-10-10
Class: Bouncer + Chaotic Edgeours: Bouncer + Chaotic Edge (sheet) · ours adds: twin of #13 at the cycle level (same bulk, junction and tail orbit D_n) · med confidence
On the list: line 552 of BB6_holdouts_663.txt · historical 740 line 615
#36eqv ×1sim 1e15UBRRBA

Your calls on file 3

priority call (answered): Park this machine with #13 (same edge lemma), or fund one family stage on that lemma for #13, #34, #35 and #36?
parked: Parked 2026-10-10 with #13 (auto-applied recommendation): same edge lemma (E'); an (E') proof would now pay #13, #34, #35, #36.
decision.json · answered 2026-10-10: park: Park this machine with #13 (same edge lemma), or fund one family stage on that lemma for #13, #34, #35 and #36? Decisions →

Mechanism

How it works: 3 notes

Bulk (1101101101)^a on a left wall moves 1 cell left per bounce (62a steps); the junction cycles through #13's 7 words; 1 bounce in 7 touches the tail D.
D_n equals #13's D_n in all 1,952 shared cycles, and the probe map P is #13's (217/217 tested, 0 disagree). #35 = this table renamed; #34 = #13 mirrored.
Halt only via B reading 0 with 00 on its left. Never seen: the edge map is clean to 1.5e7 cycles (about 4.9e16 steps). The tail has no proof.

Figures for Checkpoint A

Fig 1 · One row per bounce, first 1.1M stepsQ1 viewer ↗
Rows are bounces. Left: striped bulk; middle: diagonal seam; right: ragged part. Compare their widths, top vs bottom.

Fig 2 · Our tail vs #13's tail, per cycleQ2
One row per 7-bounce cycle. Compare left and middle panels row by row; the right panel shows differences in red.

Fig 3 · Right end only, 100 million stepsviewer ↗
Rows are shifted so the right edge stays put. Compare the ragged band's width at top and bottom.

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

Rules (9/9 validated)exact tape rewrites the proof will formalize, each re-checked by simulation

rule	from ⟶ to	cases	steps	checked
WALL	0^∞ <D 0 110110 r ⟶ 0^∞ 11101111 B> r	—	12	✓30/30
RS right sweep	B> (1101110110)ⁿ ⟶ (0110101111)ⁿ B>	—	12n	✓30/30
LS left sweep	(0111101101)ⁿ <D ⟶ <D (0110110111)ⁿ	—	50n	✓30/30
B_k bounce, k=1..5	0^∞ <D 0 (1101101101)^a X_k D 0^∞ ⟶ 0^∞ <D 0 (1101101101)^a+[k=5] X_(k+1) D 0^∞	any D (random and orbit); X_k = #13's junction words	62a+b_k, b = 13, 433, 55, 49, 73	✓200/200
B_6 cycle close	0^∞ <D 0 (1101101101)^a X6 D 0^∞ ⟶ 0^∞ <D 0 (1101101101)^a X0 D 0^∞	any D	62a+13	✓40/40
probe B_0	0^∞ <D 0 (1101101101)^a X0 D 0^∞ ⟶ 0^∞ <D 0 (1101101101)^a X1 P(D) 0^∞	P = #13's probe map: orbit D 120/120 same; random D 97 same + 103 break in both, 0 disagree	62a+c(D)	✓120/120
cycle	0^∞ <D 0 (1101101101)^a X0 D_n 0^∞ ⟶ 0^∞ <D 0 (1101101101)^a+1 X0 D_(n+1) 0^∞	D_n = #13's D_n; also 2,079/2,079 real cycles to 1e9	434a+698+c(D_n)	✓60/60
halt	00 B> 0 ⟶ halt	also 000 <B; the only way to halt (B0, C0, E0)	3	✓40/40
init	0^∞ A> 0^∞ ⟶ 0^∞ <D 0 (1101101101)⁵⁷ X1 D_0 0^∞	first cycle start C_0(58, D_0) at step 679,041	657139	✓1/1

Compressed historythe tape as 0^∞ <D 0 (1101101101)^a X0 D 0^∞ (X0 = 110111100110011101100100100111101100100110110111010011, #13's X0) at 20 moments: where the rules are read off

0^∞ <D 0 (1101101101)^a X0 D 0^∞ (X0 = 110111100110011101100100100111101100100110110111010011, #13's X0)

step	`a`	`\|D\|`	`D (first 24 cells)`
679,041	58	261	1.1·10²²
710,472	59	258	1.1·10²²
739,157	60	255	1.11·10²²
771,604	61	252	1·10²¹
801,867	62	249	1.1·10²²
833,752	63	246	1.11·10²²
864,985	64	243	1·10²¹
992,699	68	231	1.1·10²²
1,349,053	78	201	1.1·10²²
2,711,163	108	321	1·10²¹
5,831,403	158	321	1.11·10²²
15,317,035	258	291	1.11·10²²
29,137,475	358	351	1.1·10²²
69,822,111	558	351	1·10²¹
127,853,013	758	321	1.1·10²²
247,450,499	1,058	411	1·10²¹
406,142,429	1,358	291	1.11·10²²
603,885,785	1,658	321	1·10²¹
884,868,232	2,009	348	1.1·10²²
999,698,415	2,136	327	1.11·10²²

alast 2,136

|D|last 327

D (first 24 cells)last 1.11·10²²

Template comparisonBouncer_v3.v TM1: partly applies · the nearest solved proof, what carries over, and the transitions that differ

	0	1
A	1RB	1RF
B	1LC	0RF
C	1LE	0LD
D	1RC	0LB
E	---	1RA
F	1LB	1RA

file: Bouncer_v3.v:44
module: TM1
machine: 1LB1RA_0RA0RC_---1RD_1RE1RB_1LF0LE_0RD0LE (12 transitions apart)
diff: —
note: sideRLs: a fixed crossing protocol into a one-sided right part fits (ours: 14 fixed round trips 2 cells left of the X0|D cut), but TM1's RC i is an explicit word; our D is chaotic and needs a closed language (#13's lemma E'). The A-C neighbours in RWL_mod_v2.v / CPS_LRU_v1.v are decider certificates: same parameters give false here.

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

Everything except the edge is routine (Bouncer_v3/sideRLs shape; init by direct execution, 657,139 steps). A kill needs #13's edge lemma (E'): a closed language for D under P. It is shared by #13, #34, #35 and #36, so one lemma would mean 4 kills. Until then, park with #13.

▲Edge lemma open: #13 refuted SFT_k invariants for k <= 36 and plain n-gram CPS (n <= 26); no regular invariant is known.
▲mxdys listed the family on UBRRBA_TODO (a halting tool): a late break or halt is possible; edge map clean to 1.5e7 cycles (about 4.9e16 steps).
▲Even with (E'), this machine needs its own .v: same architecture, but the wall, the sweeps (62a) and the step constants differ from #13.

Stats & provenance10⁹ steps simulated · 21,745 cells · the status in full · files

simulated: 10⁹ steps
tape: 21,745 cells · 15,171 nonzeros
growth: both edges ~ sqrt(t): lo = -0.47 sqrt(t), hi = +0.22 sqrt(t) at 1e9
status now: Parked 2026-10-10 with #13 (auto-applied recommendation): same edge lemma (E'); an (E') proof would now pay #13, #34, #35, #36. Observe done. The mechanism is exact and validated, and it is identical to parked #13 at the cycle level: the same bulk (1101101101)^a, the same 7 junction words, and the same tail orbit D_n (1,952/1,952 shared cycles; probe map equal on 217/217 tested D, 0 disagree). #35 is this table renamed. Edge map clean to 1.5e7 cycles (about 4.9e16 steps), but no non-halting argument exists for the chaotic tail (#13's open edge lemma E'). Confidence med, so proof work waits on Dennis (decision.json). (status.json, 2026-10-10)
observer's note: Mechanism exact and validated, and identical to parked #13 at the cycle level; no non-halting argument for the chaotic tail D (shared edge lemma E'). Confidence med: proof work waits on Dennis (decision.json).
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 ↓	8.4 KB	2026-10-10 13:58
status.json ↓	1.0 KB	2026-10-10 13:58
observe.json ↓	12 KB	2026-10-10 13:56
decision.json ↓	2.8 KB	2026-10-10 13:58
img/	7 items	2026-10-10 13:40
scripts/	3 items	2026-10-10 13:44
work/	22 items	2026-10-10 13:47

status.json in full

{
 "tm": "1RB1RF_1LC0RF_1LE0LD_1RC0LB_---1RA_1LB1RA",
 "status": "STUCK",
 "stage": "observe",
 "updated": "2026-10-10",
 "confidence": "med",
 "reason": "Parked 2026-10-10 with #13 (auto-applied recommendation): same edge lemma (E'); an (E') proof would now pay #13, #34, #35, #36. Observe done. The mechanism is exact and validated, and it is identical to parked #13 at the cycle level: the same bulk (1101101101)^a, the same 7 junction words, and the same tail orbit D_n (1,952/1,952 shared cycles; probe map equal on 217/217 tested D, 0 disagree). #35 is this table renamed. Edge map clean to 1.5e7 cycles (about 4.9e16 steps), but no non-halting argument exists for the chaotic tail (#13's open edge lemma E'). Confidence med, so proof work waits on Dennis (decision.json).",
 "priority_call_answered": "Park this machine with #13 (same edge lemma), or fund one family stage on that lemma for #13, #34, #35 and #36?",
 "parked": "Parked 2026-10-10 with #13 (auto-applied recommendation): same edge lemma (E'); an (E') proof would now pay #13, #34, #35, #36."
}

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 1RB1RF_1LC0RF_1LE0LD_1RC0LB_---1RA_1LB1RA