/machines/1RB1LC_1LA1RF_0RD1RD_0RA0LE_1LA0LE_0RC---/notes.md · raw

W6-3: 1RB1LC_1LA1RF_0RD1RD_0RA0LE_1LA0LE_0RC--- (740 line 291)

Observe stage, 2026-10-14 (Claude). Outcome: CRYPTID_CANDIDATE under the pre-registered 45-minute go/no-go (reports/wave6/ranking.md, W6-3: "if the reset law divides a field and branches on its residue, apply the cryptid protocol"). Visit-level rules are exact and validated; the epoch (reset) law is a 2-D piecewise-affine map with residue-selected branches, fitted only.

Claim and list checks

Halting condition (exact, from the table)

F1 is the only halt. F is entered only from B1 (moving right), B only from A0 (moving right). If A arrives moving left (from E0 or B0) the cell to its right was just written and the chain cannot reach F reading 1. So the machine halts iff D moving right reads the first 0 of 0011: D> 0 0 1 1 halts 4 steps later (checked: 0^inf 110^5 D> 0011 110^4 0^inf halts at step 4). The 0011 defect is exactly the wall the head bounces off, always reached from the right. A proof must show D never meets a defect from its left side.

Mechanism

The tape is almost all 110 blocks (3-periodic fields), with a few defects.

  1. Defect walk (one trip = one block). The head shuttles between a 0011 defect (left wall) and a counter at the right end. The leftward pass erases the field to 100/001 blocks, the rightward pass restores 110; each round trip moves the defect one block right. Fig visit_close shows it.
  2. Right counter. Each 8 trips add 2 blocks to the counter field 110^c (unary). A "visit" (6 record skeletons, 1 cycle of the right-end junk) = 8 trips in the main field.
  3. Three exact visit rules (validated 25/25 each from random instances, scripts/validate.py): - R1 (P1, main walk): 0^inf 110^a 0011 110^b 1^6 110^c 11011110^2 1^6 0^2 D> 0^inf -> (a+8, b-8, c+2), b >= 8. - R2 (Q1, walk that eats the second field): 0^inf 110^x 0011 110^y 1011 110^z 11011110^2 1^6 0^2 D> 0^inf -> (x+16, y-8, z-6), y >= 8, z >= 6. - R3 (Q3, the same walk one level down, inside the second field): 0^inf 110^p 0011 110^q 1^6 011^2 0^3 1^6 110^a 0011 110^b 11011110^2 1^6 0^2 D> 0^inf -> (a+4, b-2), b >= 2.
  4. Epochs. When the active defect reaches the junk in front of the counter, the head runs to the left edge (two left-record pairs, 2 cells each), sweeping the whole tape (<E (001)^N J word^M R). The next epoch is one of: Q1 (R2) then P1 (R1), or a Q3 sub-walk (R3) in the second field first. Which one is chosen depends on the junk J and the right-end phase R left by the residues. Seen J kinds: 01, (01)^2, 010, 0^4 1 0^6 (10)^2 0, ... 0^2, ... 0^3, ... 0 (001)^2 0^7/0^8.

Reset law (fitted, not exact)

22 resets from 2e6 to 1.63e10 (work/leftrec_2e10.txt; N = main field, M = second field at the reset):

N' ~ 0.999 N + 1.221 M + 92   (residuals up to +-550)
M' ~ 0.296 N - 0.577 M - 38   (residuals up to +-330)
eigenvalues 1.20 and -0.78

Heuristic reason: Q1 eats the second field at 6 blocks per visit while the defect moves 16, so the defect ends near 8M/3; P1 then walks the rest at 8 per visit and grows the new counter by 2 per visit; R3 doubles a field (a + 2b is conserved). Every phase ends on a remainder (z mod 6, b mod 8, b mod 2), and the remainders pick J and R, which pick the next branch. M/N stays in 0.06..0.25 (needs < 3/8 for Q1 to fit); late values 0.15..0.18. Late resets (N, M): (10511,1551) (12585,2113) (15405,2440) (18671,3037) (22725,3655) (26702,4690). Growth ~1.2 per epoch, so 10^73975 steps is ~5e5 epochs: geometric, not tetrational (qsim's "tetration-scale" label comes from its recursive rule acceleration).

Cryptid check

The epoch map divides fields (by 6, 8, 2) and branches on the remainders: the pre-registered stop rule fires. Unlike H-4's lottery, no branch is known to halt; halting would need D to reach a 0011 from the left, which no observed branch does. ~5e5 epochs (Alistaire) with no halt suggest every branch that occurs is safe. A proof would need (a) a finite, closed set of branch shapes (J x R x phase), each an exact rule chain, and (b) a 2-D invariant band such as 0.05 N <= M <= 0.3 N kept by the map with its bounded residue perturbations. Neither is established. The shape census (work/shapes_1e8.json, 185 raw visit shapes at 1e8, mostly sampling-phase noise) was not canonicalized in this stage.

Template check

Nearest proved neighbour: W5-3 (our kill, 1RB1RA_1LC1LE_1RF1LD_1RE0LD_0LB0RA_---0RC, BECv5.v TM1 architecture). Shared: a defect walking through a periodic word while a right counter counts trips; an eat/sweep at the left edge; nonhalting = the bad transition is never read. Different: W5-3 has one level, a binary counter with 5 residue cases and a 1-D invariant (1 <= N <= 2p). Here the counter is unary, the same walk runs at two levels (R1, R3), and the epoch map is 2-D with a -0.78 eigenvalue, so the invariant must be a 2-D band plus a closed branch census. No transition-level overlap (not within 4 transitions). Applies: architecture only.

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