{
 "tm": "1RB1LC_1RC---_1LD1LC_1RE0LC_1RF0RE_1RA0RD",
 "rank": 6,
 "class_sheet": "Structural counter + chaotic edge",
 "class_guess": "Structural counter + chaotic edge: drifting defect groups (hierarchical counter) fed by a chaotic right edge",
 "confidence": "med",
 "summary": "Defect groups drift left at 1, 3/4, 1/2, 3/8.. cells/bounce: exact 16-bounce counter on left, chaotic edge on right",
 "mechanism": [
  "Tape: (01)^n runs split by single defects (11, 00, 1111); the head zig-zags between them; the wall grows 2 cells/bounce.",
  "Defect groups drift left from the right edge at exact speeds 1, 3/4, 1/2, 3/8...; left block repeats every 16 bounces.",
  "The right edge is chaotic (hi ~ 20·sqrt(L)). Halting needs E to sweep an odd (10) run ending in 00: unseen to 1e11."
 ],
 "diagrams": [
  {
   "mode": "records:L",
   "png": "img/recordsL_abs_stride4.png",
   "html": null,
   "steps": 25015029,
   "caption": "2 rows per wall bounce: defect groups fan out in straight lines",
   "title": "Left records, every 4th cell",
   "why": "2 rows per wall bounce, every 4th cell; each white/black edge is a defect. Follow the edges downward.",
   "primary": true,
   "start": "blank",
   "rows": "the start, then one per new leftmost cell = 2 per wall bounce (5,000 rows, steps 0..25,015,029; stopped at the 5,000-row cap); not evenly spaced in time",
   "window": "cells -4,999..1,476, 1 px = 4 cells (only the first cell of each 4 is drawn)",
   "legend": "white = 1, black = 0 or never visited (top-left), green line = head at the wall. Only every 4th cell is drawn, so a `0101...` run shows as solid white or solid black (its phase), and every white/black edge inside the tape is a defect (`00`, `11` or `1111`)",
   "style": "bbchallenge-default"
  },
  {
   "mode": "records:R defects",
   "png": "img/defects_recordsR_right_1e9.png",
   "html": null,
   "steps": 1000000000,
   "caption": "Right edge pinned: defects are born at the edge and drift left",
   "title": "Right edge pinned, defects only",
   "why": "Right edge pinned, defects only (black). Compare the dense band at the right edge with the slanted lines leaving it.",
   "primary": true,
   "start": "blank",
   "rows": "the start, then one per new rightmost cell (2,819 rows, steps 0..969,848,428; no new right cell from then to 1e9); not evenly spaced in time",
   "window": "cells -1,599..0, 1 px = 2 cells, counted from the right edge (each row's rightmost visited cell is 0, pinned to the last column; it is absolute cell 2,818 in the last row)",
   "legend": "custom: black = at least one defect (`00` or `11`) among the pixel's 2 cells; white = clean `0101...` run; grey = not yet visited; head not drawn. Each slanted line = a defect drifting left, away from the edge; the dense band at the right = the chaotic edge zone",
   "style": "custom"
  },
  {
   "mode": "every:500k defects",
   "png": "img/defects_every500k_left_1e9.png",
   "html": null,
   "steps": 1000000000,
   "caption": "To 1e9, wall pinned at left: defect groups drift away from it",
   "title": "Defects to 1e9, left wall pinned",
   "why": "Defect groups drift away from the wall; lines curve only because rows are equal in steps, not bounces.",
   "start": "blank",
   "rows": "every 500,000 steps: steps 0, 500,000, ..., 1,000,000,000 (2,001 rows), so consecutive rows are 500,000 steps apart",
   "window": "cells 0..36,470, 1 px = 8 cells, counted from the wall (each row's leftmost visited cell is 0, pinned to column 0; it is absolute cell -33,652 in the last row)",
   "legend": "custom: black = at least one defect (two equal neighbours, `00` or `11`) among the pixel's 8 cells; white = clean `0101...` run; grey = not yet visited; head not drawn. Isolated dots = the head's own working cells at that moment. Lines curve because rows are evenly spaced in steps, not in bounces",
   "style": "custom"
  },
  {
   "mode": "blaze",
   "png": "img/blaze_1e8.png",
   "html": null,
   "steps": 100000000,
   "caption": "bbchallenge Blaze: sqrt-growing wall, ragged near-static right edge",
   "title": "Blaze, 100M steps",
   "why": "The wall grows like sqrt(t); the right edge stays ragged and almost still.",
   "start": "blank",
   "rows": "time blocks of 131,072 steps, averaged (763 blocks, steps 0..100,000,000), stretched to 500 px: 1 px ~ 200,000 steps",
   "window": "cells -10,360..1,751, 1 px = ~15 cells (Blaze averages 8 cells per column; its 1,514 columns are stretched to 800 px)",
   "legend": "white = 0, orange = 1, in-between shades = both mixed inside the pixel's block (averaged); no head",
   "style": "bbchallenge-blaze"
  },
  {
   "mode": "default",
   "png": "img/default_site_1e4.png",
   "html": "img/viewer.html",
   "steps": 10000,
   "caption": "bbchallenge Default: zig-zag bouncer between defects",
   "title": "bbchallenge default view, first 10,000 steps",
   "why": "The site's view of the first 10,000 steps: zig-zag bounces between defects.",
   "start": "blank",
   "rows": "every step: steps 0..9,999 squeezed into 500 px rows as on bbchallenge.org (each px row blends steps 20y+9 and 20y+10, so 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 colours = blended by the squeeze)",
   "style": "bbchallenge-default"
  }
 ],
 "history": {
  "skeleton": "0^inf <D 11 01^14 10^a 1^4 01^3 1^2 10^8 01^b 10^12 1 10^c 1^3 10^6 01^18 0 01^d 1^3 01^6 r",
  "vars": [
   "a",
   "b",
   "c",
   "d",
   "L (=-lo)",
   "hi",
   "defects"
  ],
  "rows": [
   {
    "step": 1074148,
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     261,
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    ]
   },
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   },
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    ]
   },
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    ]
   },
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    ]
   },
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    ]
   },
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    ]
   },
   {
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    "values": [
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    ]
   },
   {
    "step": 13434250,
    "values": [
     949,
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    ]
   },
   {
    "step": 18237176,
    "values": [
     1109,
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     260,
     131,
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     119
    ]
   },
   {
    "step": 23714088,
    "values": [
     1269,
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     152
    ]
   },
   {
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    "values": [
     1477,
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    ]
   },
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    "values": [
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    ]
   },
   {
    "step": 56264118,
    "values": [
     1973,
     478,
     476,
     239,
     7674,
     1641,
     150
    ]
   },
   {
    "step": 75566108,
    "values": [
     2293,
     558,
     556,
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     171
    ]
   },
   {
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    "values": [
     2645,
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    ]
   },
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    "values": [
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    ]
   },
   {
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    "values": [
     3541,
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    ]
   },
   {
    "step": 237710744,
    "values": [
     4101,
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    ]
   },
   {
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    "values": [
     4741,
     1170,
     1168,
     585,
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     1960,
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    ]
   },
   {
    "step": 423685322,
    "values": [
     5493,
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     679,
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    ]
   },
   {
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    "values": [
     6341,
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    ]
   },
   {
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   },
   {
    "step": 1000348998,
    "values": [
     8469,
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   }
  ]
 },
 "rules": [
  {
   "name": "G16 left block (16 bounces)",
   "from": "0^inf <D 11 01^14 10^a 1^4 01^3 1^2 10^8 01^b 10^12 1 10^c 1^3 10^6 01^18 0 01^2 r",
   "to": "0^inf <D 11 01^14 10^(a+8) 1^4 01^3 1^2 10^8 01^(b+2) 10^12 1 10^(c+2) 1^3 10^6 01^18 0 01^2 r'",
   "steps": null,
   "cases": "a odd >= 1, b even >= 4, c even >= 2, independent; r = real right part (4 tapes, 1e7..1e9). Other parity classes: 0/12 pass (wrong guess killed). [Notation fixed at assembly: was '<D 011 ...', which puts an extra 0 left of the 11; re-checked 30/30 in sim notation.]",
   "validated": {
    "instances": 32,
    "passed": 32
   },
   "source": "manual"
  },
  {
   "name": "orbit lock",
   "from": "c0 (blank tape)",
   "to": "G16 skeleton with (a,b,c,d) = (8n+61, 2n, 2n-2, n), L = 32n+26, at every 16th wall visit",
   "steps": null,
   "cases": "observed on the orbit (25 snapshots, n = 25..1051), not a random-parameter test",
   "validated": {
    "instances": 25,
    "passed": 25
   },
   "source": "manual"
  },
  {
   "name": "H halt trigger",
   "from": "E> 10^(2n+1) 001",
   "to": "halt (B reads 1)",
   "steps": "4n+5 (busycoq halts_in 4n+4)",
   "cases": "sibling E> 10^(2n) 001 -> 01^(2n) 1 1 <C 1 in 4n+3 (safe turn), 40/40",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "left sweep",
   "from": "10^n <C",
   "to": "<C 01^n",
   "steps": "2n",
   "cases": null,
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "right sweep, even",
   "from": "E> 01^(2n)",
   "to": "10^(2n) E>",
   "steps": "4n",
   "cases": "also E> 10^(2n) -> 01^(2n) E> in 4n",
   "validated": {
    "instances": 80,
    "passed": 80
   },
   "source": "manual"
  },
  {
   "name": "right sweep, odd",
   "from": "E> 01^(2n+1)",
   "to": "10^(2n+1) D>",
   "steps": "4n+2",
   "cases": "also E> 10^(2n+1) -> 01^(2n+1) F> in 4n+2 (F then reads the next cell: 0 0 1 there = halt)",
   "validated": {
    "instances": 80,
    "passed": 80
   },
   "source": "manual"
  },
  {
   "name": "wall bounce",
   "from": "0^inf <C",
   "to": "0^inf 1 0 E>",
   "steps": "3",
   "cases": null,
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "edge extension",
   "from": "E> 0^inf",
   "to": "1 <C 1101 0^inf",
   "steps": "8",
   "cases": "the only place B is entered in 1e9 steps (512 times); B always reads 0 there",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  }
 ],
 "template": {
  "file": "vendor/busycoq/verify/BLv3.v",
  "module": "TM1 (TM2 shares it)",
  "machine": "1RB0RA_1LC0RD_0LD0LB_1RA1LE_0LC1LF_0LA---",
  "diff": "8 of 11 transitions differ under best relabeling (A0 A1 B0 C1 D0 E0 E1 F1); BLv3 TM2 8, BLv2 TM1-3 8-9, Bouncer_v4 9",
  "applies": "partly",
  "note": "Method carries: columns (01)^n+defect, head passes as a signal stream, per-column transducer + quadRect closure. Lemmas don't: we add 1111 columns, our edge grows, and BLv3's own cut tape halts on our machine at sim step 20,175."
 },
 "strategy": "BLv3-style. 1) es/ind for sweep/wall/edge rules; 2) the 16-bounce left-block rule with a odd, b,c even (multistep_nonhalt + progress_nonhalt_cond on n);\n3) the hard part: a closed (regular) set for the edge region that excludes 'E> 10^odd 001' (LongN/InfiniteRect quadRect, or a CTL-style language search first).",
 "risks": [
  "Edge is chaotic and growing (hi ~ 20*sqrt(L), 56 groups at 1e9): a finite closed set may not exist -> STUCK at step 3.",
  "Halting is a parity event (odd (10) run before a 00 defect); a late halt like BLv2's 3 kills is possible. None to 1e11.",
  "On mxdys's UBRRBA_TODO list (Dennis: fair game); twin #27 is this exact table started in state E, so one proof should cover both."
 ],
 "checkpoint_questions": [
  {
   "text": "Fig 1: do the defect lines fan out from the top as straight lines (exact speeds), i.e. a clean counter?",
   "figs": [
    0
   ]
  },
  {
   "text": "Fig 2: does the dense band at the right edge look like a bounded zone that emits defects, rather than chaos that spreads left?",
   "figs": [
    1
   ]
  }
 ],
 "discord_check": null,
 "stats": {
  "simulated_steps": 100000000000,
  "cells": 352865,
  "nonzeros": 177158,
  "growth": "wall L ~ 1.08*sqrt(t) (2 cells/bounce); right edge hi ~ 20*sqrt(L) ~ t^0.25; defects 99 -> 275 (1e6 -> 1e9)"
 },
 "status": "CHECKPOINT_A",
 "status_reason": "Left counter found and validated; edge chaotic but no Collatz-like arithmetic (gaps grow linearly). Needs Dennis's call on the edge approach."
}