/machines/1RB0LD_0RC---_0RD0RF_1LE0LA_1LF1LE_1RA0RD/notes.md · raw

W6-6 · 1RB0LD_0RC---_0RD0RF_1LE0LA_1LF1LE_1RA0RD (740 line 221)

Observe stage, 2026-10-14 (Wave 6). Sheet class: Unknown. Claimed in coord/claims.tsv (Wave 6 W6-6).

Checks

Halting condition

B1 is the only missing transition and B is entered only from A0 (1RB). A moving right is entered only from F0, and F moving right only from C1. Working the chain through: the machine halts iff it reaches C> 1001 (C on a 1 followed by 0, 0, 1), which runs C1 → F0 → A0 → B1. Never seen.

Simulations

Mechanism

1. Two fields and an interface glider

Left of the head lies a field of 11010100 (written W; other rotations of the same cyclic word 10101001 show up depending on alignment). Right of it lies a field of 11110001 / 11111000 (rotations of 11100011, written R). The head is a translated cycler between them:

GR:  11010100^(m+1) 100 D> 00 11111000^(n+k) 11 0^inf   ->   11010100^(m+k+1) 100 D> 00 11111000^n 11 0^inf    32k steps
GL:  1 11010100^(m+k) <E 11110001^n 1 0^inf             ->   1 11010100^m <E 11110001^(n+k) 1 0^inf            36k steps

Moving right it turns R blocks into W blocks (32 steps per block); moving left it turns W blocks into R blocks (36 steps per block). Both validated 200/200 on random m, n, k (scripts/rules.py, rules.json).

2. Bounces

The glider bounces between a wall on the left and the right end of the tape. Each bounce adds 2 cells at the right end. A tracker of turning points (scripts/turns.c) shows two alternating phases:

S1: l H 11010100^(b+2) D> 0^inf -> l Y H 11010100^b D> 0^inf 68b + 388 steps H = 0110 10101001^2 100^2 (26 cells), Y = 011001101010011010 (18 cells)

So each bounce leaves one 18-cell piece Y of "wake" behind and the field loses 2 blocks. Validated 200/200 random (a, b), the 4-bounce composition S4 (272b + 2368) 200/200, and 830/830 real bounces to 1.2e8 (scripts/realcheck2.py: tape window compared cell by cell). - Transition S → G: S stops with b = 0 or 1. Then one long sweep runs left through the whole wake to the junk and back. On the way it rewrites the Y pieces into 72-cell units V (4 Y's each). - Phase G (grow): the wall moves left 72 cells every 36 bounces (net 2 per bounce, in a fixed 36-bounce pattern with "probe" bounces that dip 14-42 cells into the next unit). One period, exact:

G36: l V^(a+1) Z 11010100^b D> 0^inf -> l V^a Z 11010100^(b+18) D> 0^inf 2448b + 26828 steps V = 10011010^2 10100110^2 10101001^2 10^4 01101010^2 (72 cells) Z = 10011010^2 0110^2 101001^2 10^4 0 (45 cells)

Validated 150/150 random (a in 0..8, b in 0..120) and 86/86 real periods to 1.2e8. This is one alignment of the G phase: in the 2e12 cycle log it matches in every large cycle with even b (b = 72, 408, 928, 2104, 4720, 10630, 121394; S ends with b = 0) and in none with odd b (173, 23959, 53939; S ends with b = 1), so odd cycles run G in a shifted alignment (same shape, different V/Z rotation; not yet written out). - Transition G → S: when the units are used up the wall reaches the junk. The probes then dig about 130-150 cells into the junk and rewrite it, and a new S phase starts at the junk's right end.

3. Cycle law (observed, not exact)

Let b_k be the field size (blocks) at the start of the k-th S phase (scripts/accel2.c, work/cycles_2e12.txt):

S start step b b mod 8 next b next b − 9b/4
3,311,129 173 5 408 +18.75
15,667,118 408 0 928 +10
78,104,903 928 0 2,104 +16
395,843,382 2,104 0 4,720 −14
2,007,488,939 4,720 0 10,630 +10
10,081,940,898 10,630 6 23,959 +41.5
51,081,997,453 23,959 7 53,939 +31.25
258,741,221,346 53,939 3 121,394 +31.25

Why 9/4: S runs floor(b/2) bounces and leaves floor(b/2) Y pieces (9b cells, b/8 units V); G turns each V into 18 blocks. So b' = 9b/4 + c, where the remainder b mod 8 picks the S→G branch (b mod 2: how S ends; floor(b/2) mod 4: the leftover Y pieces next to the junk) and c depends on the junk met at G → S (the last unit plus the probe digging added 33, 32, 38, 8, 32 and 59 blocks in six cycles). Cycle time grows about ×5, the right edge like sqrt(t).

4. The junk (the chaotic edge)

Left junk at each S start (scripts/sin_compress.py on work/accel_1e14.txt) is rewritten once per cycle and slowly eaten: - a counter (0011 1010011010^2 1001^3)^k: k = 6, 6, 4, 4, 3, 3, 1, then gone by 1.0e10; - then a 14-cell counter 10100110101001^k: 17, 14, 12, 10, 9, 7 (5.1e10 .. 3.4e13); - the left edge, fixed at -52 until 1e10, moved to -78, -91, -104, -104, -111; - the wall at S start drifts left: 577, 566, 451, 362, 285, 240, 215.

Nothing in it is periodic yet. When the 14-cell counter runs out (a few more cycles, around 1e14-1e16) the regime may change again.

Cryptid check

The cycle law is a ×9/4 map on b with an 8-way remainder split and a junk-dependent offset, and the junk is rewritten by whichever branch fires: pseudo-random arithmetic driving a chaotic edge (W6-3/W6-5 pattern). No halting branch is known (C> 1001 never appears; no halt to 4.2e13). Per the cryptid protocol: rules formalized above (GR, GL, S1, G36 validated; transitions observed), flagged, stopped.

Files