{
 "tm": "1RB1LC_1LA1RF_0RD1RD_0RA0LE_1LA0LE_0RC---",
 "rank": 291,
 "class_sheet": "Unknown",
 "class_guess": "Nested defect-walk counter (budget + round counter at two levels); 2-D residue-branching epoch map: cryptid-like",
 "confidence": "med",
 "summary": "A 0011 defect walks through 110 fields off a right counter; epochs reset via a 2-D map that branches on remainders",
 "mechanism": [
  "Trips: the head shuttles between a 0011 defect (left wall) and a unary counter at the right end; each round trip moves the defect one 110 block right, and every 8 trips add 2 blocks to the counter (rule R1).",
  "Two levels: the same walk also eats the second field (R2: x+16, y-8, z-6) and runs inside it (R3: a+4, b-2). When the active defect reaches the junk before the counter, the head sweeps to the left edge and a new epoch starts.",
  "Epoch law (fitted, 22 resets to 1.6e10): N' ~ N + 1.22M, M' ~ 0.30N - 0.58M (eigenvalues 1.20, -0.78); phases end on remainders (mod 6, 8, 2) that pick the junk and the next branch. Halting needs D to read 0011 from its left; never seen."
 ],
 "diagrams": [
  {
   "mode": "default",
   "png": "img/default_site.png",
   "html": "img/viewer.html",
   "steps": 10000,
   "caption": "bbchallenge default view, first 10,000 steps",
   "title": "bbchallenge default view, 10,000 steps",
   "why": "The site's view. The striped area is the 110 field; the ragged right edge is the counter.",
   "primary": true,
   "start": "blank",
   "rows": "every step: steps 0..9,999 squeezed into 500 px rows as on bbchallenge.org (1 px row = 20 steps)",
   "window": "cells -200..199, 1 px = 1 cell",
   "legend": "white = 1, black = 0 or never visited, red/green = head after a right/left move (pale = blended by the squeeze)",
   "style": "bbchallenge-default"
  },
  {
   "mode": "every:8",
   "png": "img/visit_close.png",
   "html": null,
   "steps": 6000,
   "caption": "Trips between the defect and the right counter",
   "title": "One visit: trips off the defect",
   "why": "Each black wedge is one round trip. Follow the left tip of the wedges from row to row.",
   "primary": true,
   "start": "constructed: 0^inf 110^10 0011 110^40 1^6 110^6 11011110^2 1^6 0^2 D> 0^inf",
   "rows": "every 8 steps, 6,000 steps (751 rows)",
   "window": "cells -202..11, 1 px = 1 cell",
   "legend": "white = 1, black = 0 or never visited, red/green = head after a right/left move; black wedges = the field erased to 100/001 on the leftward pass",
   "style": "bbchallenge-default"
  },
  {
   "mode": "every:3000",
   "png": "img/every3000_3e6.png",
   "html": null,
   "steps": 3000000,
   "caption": "Epochs: defect diagonals and left-edge resets to 3e6",
   "title": "Epochs to 3 million steps",
   "why": "Thin diagonals are defects crossing the field; each new diagonal from the left edge is a reset.",
   "primary": true,
   "start": "blank",
   "rows": "every 3,000 steps, 3,000,000 steps (1,001 rows)",
   "window": "cells -66..1248, 1 px = 1 cell",
   "legend": "white = 1, black = 0 or never visited, red/green = head after a right/left move",
   "style": "bbchallenge-default"
  },
  {
   "mode": "records:R",
   "png": "img/records_3e6.png",
   "html": null,
   "steps": 3000000,
   "caption": "Right records to 3e6 steps",
   "title": "Right records, 3 million steps",
   "why": "One row per new rightmost cell. The vertical streaks are the defect paths seen at record times.",
   "primary": false,
   "start": "blank",
   "rows": "right records only (one row per new rightmost cell), 3,000,000 steps",
   "window": "cells -66..1248, 1 px = 1 cell",
   "legend": "white = 1, black = 0 or never visited, red/green = head after a right/left move",
   "style": "bbchallenge-default"
  }
 ],
 "history": {
  "skeleton": "0^inf <E 001^N J word^M R 0^inf",
  "vars": [
   "N",
   "M"
  ],
  "rows": [
   {
    "step": 2032991,
    "values": [
     319,
     72
    ]
   },
   {
    "step": 3168091,
    "values": [
     416,
     28
    ]
   },
   {
    "step": 4681947,
    "values": [
     458,
     43
    ]
   },
   {
    "step": 7679013,
    "values": [
     682,
     70
    ]
   },
   {
    "step": 12185873,
    "values": [
     783,
     147
    ]
   },
   {
    "step": 18852531,
    "values": [
     985,
     149
    ]
   },
   {
    "step": 28624657,
    "values": [
     1202,
     93
    ]
   },
   {
    "step": 44343831,
    "values": [
     1408,
     341
    ]
   },
   {
    "step": 66995761,
    "values": [
     1894,
     113
    ]
   },
   {
    "step": 97482007,
    "values": [
     2072,
     213
    ]
   },
   {
    "step": 147640349,
    "values": [
     2506,
     623
    ]
   },
   {
    "step": 218584065,
    "values": [
     3241,
     473
    ]
   },
   {
    "step": 323194717,
    "values": [
     3801,
     695
    ]
   },
   {
    "step": 472935407,
    "values": [
     4751,
     355
    ]
   },
   {
    "step": 710419407,
    "values": [
     5471,
     1366
    ]
   },
   {
    "step": 1057265263,
    "values": [
     7298,
     909
    ]
   },
   {
    "step": 1570250057,
    "values": [
     8353,
     1615
    ]
   },
   {
    "step": 2324688333,
    "values": [
     10511,
     1551
    ]
   },
   {
    "step": 3447311415,
    "values": [
     12585,
     2113
    ]
   },
   {
    "step": 5102449077,
    "values": [
     15405,
     2440
    ]
   },
   {
    "step": 7551201897,
    "values": [
     18671,
     3037
    ]
   },
   {
    "step": 11167615143,
    "values": [
     22725,
     3655
    ]
   },
   {
    "step": 16295935265,
    "values": [
     26702,
     4690
    ]
   }
  ]
 },
 "rules": [
  {
   "name": "R1 main walk (P1)",
   "from": "0^inf 110^a 0011 110^b 1^6 110^c 11011110^2 1^6 0^2 D> 0^inf",
   "to": "0^inf 110^(a+8) 0011 110^(b-8) 1^6 110^(c+2) 11011110^2 1^6 0^2 D> 0^inf",
   "steps": "measured per instance (e.g. 5,966 at (41,27,50)); not fitted",
   "cases": "b >= 8; 8 trips of one block each",
   "validated": {
    "instances": 25,
    "passed": 25
   },
   "source": "manual"
  },
  {
   "name": "R2 walk eating the second field (Q1)",
   "from": "0^inf 110^x 0011 110^y 1011 110^z 11011110^2 1^6 0^2 D> 0^inf",
   "to": "0^inf 110^(x+16) 0011 110^(y-8) 1011 110^(z-6) 11011110^2 1^6 0^2 D> 0^inf",
   "steps": "measured per instance (e.g. 17,086 at (118,66,52)); not fitted",
   "cases": "y >= 8, z >= 6",
   "validated": {
    "instances": 25,
    "passed": 25
   },
   "source": "manual"
  },
  {
   "name": "R3 walk inside the second field (Q3)",
   "from": "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",
   "to": "0^inf 110^p 0011 110^q 1^6 011^2 0^3 1^6 110^(a+4) 0011 110^(b-2) 11011110^2 1^6 0^2 D> 0^inf",
   "steps": "measured per instance; not fitted",
   "cases": "b >= 2; a + 2b conserved",
   "validated": {
    "instances": 25,
    "passed": 25
   },
   "source": "manual"
  },
  {
   "name": "halting pattern",
   "from": "0^inf 110^5 D> 0011 110^4 0^inf",
   "to": "halt",
   "steps": "4",
   "cases": "the only way to halt: D moving right reads the first 0 of 0011 (A0, B1, F1)",
   "validated": {
    "instances": 1,
    "passed": 1
   },
   "source": "manual"
  },
  {
   "name": "epoch law (reset to reset), fitted",
   "from": "0^inf <E 001^N J word^M R 0^inf",
   "to": "0^inf <E 001^N' J' word^M' R' 0^inf, N' ~ N + 1.22M + 92, M' ~ 0.30N - 0.58M - 38",
   "steps": null,
   "cases": "residues of the phase ends (mod 6, 8, 2) pick J', R' and the next branch (Q1 then P1, or Q3 first); residuals up to +-550 / +-330",
   "validated": {
    "instances": 0,
    "passed": 0
   },
   "source": "manual"
  }
 ],
 "template": {
  "file": "BECv5.v",
  "module": "TM1",
  "machine": "1RB1RA_1LC1LE_1RF1LD_1RE0LD_0LB0RA_---0RC",
  "diff": "architecture only (no shared transitions)",
  "applies": "partly",
  "note": "W5-3 (our kill, BECv5 TM1 architecture): a defect walks through a periodic word while a right counter counts trips, plus a left-edge eat; one level, a binary counter, 5 residue cases, 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 eigenvalues 1.20 and -0.78, so a proof needs a 2-D band (e.g. 0.05N <= M <= 0.3N) plus a closed census of branch shapes. No upstream proof of this table; 291 is only in Eqv lemmas (Eqv.v TM44, Eqv_v3.v TM437)."
 },
 "strategy": "Pre-registered stop: the epoch law divides fields and branches on remainders, so park as a cryptid candidate. If funded: build an exact epoch accelerator from R1-R3 and the reset branches, check it against direct runs to 2e10, then census the branch shapes far out to see whether they close.",
 "risks": [
  "The branch set (J x R x phase, plus interleaved two-defect visits) may be large or not closed; 185 raw visit shapes by 1e8 (uncanonicalized).",
  "The 2-D invariant band must survive residue perturbations; the -0.78 eigenvalue makes M/N oscillate (0.06..0.25 seen).",
  "152 is only Eqv-linked (not the same table): a 291 proof transfers only through upstream Eqv lemmas resting on BBinf (two .v files)."
 ],
 "checkpoint_questions": [
  {
   "text": "One visit: each black wedge is a round trip from the right counter to the 0011 defect. Does the wedges' left tip move right by one 3-cell block per trip?",
   "figs": [
    1
   ],
   "kind": "check"
  },
  {
   "text": "Epochs: each new diagonal from the left edge starts an epoch. Do the epochs look like the same process repeating at a larger size each time?",
   "figs": [
    2
   ],
   "kind": "check"
  },
  {
   "text": "Priority call (pre-registered 45-min go/no-go): the epoch law is a 2-D map that branches on remainders, though no branch is known to halt. Park it as a cryptid candidate, or fund one 2 h stage to build an exact epoch accelerator and census its branch shapes for closure?",
   "figs": [],
   "kind": "decision"
  }
 ],
 "discord_check": null,
 "stats": {
  "simulated_steps": 20000000000,
  "cells": 94226,
  "nonzeros": null,
  "growth": "epochs grow ~1.20x (fitted eigenvalue); span 94,226 at 1.63e10; 23 resets to 1.63e10, no halt"
 },
 "status": "CRYPTID_CANDIDATE",
 "status_reason": "Visit rules R1-R3 exact and validated (25/25 each). The epoch law is a 2-D piecewise-affine map (eigenvalues 1.20, -0.78) whose branches are picked by remainders mod 6/8/2: the pre-registered W6-3 stop rule. No halting branch is known; closure of the branch set is unproved."
}