{
 "tm": "1RB0RE_1LC0RE_1LD0LD_1RA0LC_1RA1RF_1RA---",
 "rank": 33,
 "class_sheet": "Skelet 1-like Class 2",
 "class_guess": "Binary counter with re-pairing overflow: kill #11's table, mirrored and started in #11's D",
 "confidence": "high",
 "summary": "Kill #11's table mirrored, started in D: same binary counter; a 215-step init lands in #11's proved invariant",
 "mechanism": [
  "Same table as our kill #11 `1RB0LE_1RC0RC_1LD0RB_1LA0LE_1LD1LF_1LD---`: mirror it and rename A,B,C,D -> B,C,D,A (E, F fixed). This machine starts in #11's D.",
  "Tape K = `0^inf <C (01)^b 000 (01)^a` + digits `(10)^v [00] (01)^u` + `1001`: a binary counter. M_k carries to the last 0-bit (ruler depths); O re-pairs every digit when all bits are 1.",
  "From blank, 215 steps reach K((1,1,3); 4, 1), class A of #11's invariant. The real run equals M_k/O exactly for all 18,976 macro steps to 1e9, every K in INV."
 ],
 "diagrams": [
  {
   "mode": "default",
   "png": "img/default_site.png",
   "html": "img/viewer.html",
   "steps": 10000,
   "caption": "bbchallenge Default view, first 10,000 steps",
   "title": "First 10,000 steps (site view)",
   "why": "The site's own picture. The tape grows to the left; the right end barely moves.",
   "primary": true,
   "start": "blank",
   "rows": "every step, steps 0..10,000 squeezed into 500 rows (site canvas, bilinear: about 20 steps per row)",
   "window": "cells -200..199, 1 px = 1 cell (cell 0 = start cell, at column 200)",
   "legend": "white = 1, black = 0 or unvisited, red/green = head (last move right/left)",
   "style": "bbchallenge-default"
  },
  {
   "mode": "every:20",
   "png": "img/cycle_10050.png",
   "html": null,
   "steps": 8100,
   "caption": "One counter cycle: 14 carries, then one overflow",
   "title": "One counter cycle from step 10,050",
   "why": "Rows every 20 steps; each phase-shift diagonal is one head sweep. Compare how far right each sweep gets.",
   "primary": true,
   "start": "mid-run: step 10,050 (the K-config right after an overflow: 0^inf <C 01 000 (01)^16 (10)^22 (01)^8 (10)^15 00 (01)^11 (10)^3 00 (01)^12 10 00 1001 0^inf, file img/cycle_from_10050_start.txt)",
   "rows": "every 20 steps, steps 0..8,100 after the start (406 rows, 2 px each). Carries M1 M0 M2 M0 M1 M0 M3 M0 M1 M0 M2 M0 M1 M0, then the overflow O at steps 6,800..8,009 after the start (run steps 16,850..18,059)",
   "window": "cells -66..194, 1 px = 1/2 cell (each cell 2x2 px); cell 0 = the head's start cell (left edge of the tape)",
   "legend": "white = 1, black = 0 or unvisited, red/green = head (last move right/left); thick black bars = 00 walls (bit-0 digits)",
   "style": "bbchallenge-default"
  },
  {
   "mode": "records:L",
   "png": "img/records_L_3e5.png",
   "html": null,
   "steps": 300000,
   "caption": "One row per new leftmost cell, to step 300,000",
   "title": "Tape at every left-edge visit",
   "why": "Each row is the whole tape at a new left-edge cell. Watch the vertical walls and where they jump.",
   "primary": true,
   "start": "blank",
   "rows": "left records (each new leftmost cell): 1,060 rows to step 300,000; a visit to the left edge makes 2 records, a counter increment 4",
   "window": "cells -1059..55, 1 px = 1 cell",
   "legend": "white = 1, black = 0 or unvisited, red/green = head (last move right/left)",
   "style": "bbchallenge-default"
  },
  {
   "mode": "blaze",
   "png": "img/blaze_1e7.png",
   "html": null,
   "steps": 10000000,
   "caption": "Blaze overview to 10 million steps",
   "title": "Ten million steps (Blaze)",
   "why": "Shape over a long run: left edge on a square-root curve, fixed right end, wall lines between.",
   "primary": false,
   "start": "blank",
   "rows": "Blaze time blocks of 16,384 steps (611 rows, averaged), stretched to 500 px",
   "window": "cells -7272..104, 1 px = 8 cells (922 px stretched to 800 px)",
   "legend": "white = 0, orange = 1 (shade = fraction of time the cell held 1); no head",
   "style": "bbchallenge-blaze"
  }
 ],
 "history": {
  "skeleton": "0^inf <C (01)^b 000 (01)^a [(10)^v_j (01)^u_j]_{j=m..1} 1001 0^inf  (all bits 1: the K just before each overflow)",
  "vars": [
   "m",
   "u_1..u_m",
   "v_1..v_m",
   "a",
   "b",
   "INV class"
  ],
  "rows": [
   {
    "step": 215,
    "values": [
     1,
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     "3",
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   },
   {
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    ]
   },
   {
    "step": 2870,
    "values": [
     1,
     "13",
     "4",
     14,
     13,
     "C"
    ]
   },
   {
    "step": 3963,
    "values": [
     2,
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     "12,12",
     18,
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    ]
   },
   {
    "step": 6320,
    "values": [
     2,
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     "2,12",
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    ]
   },
   {
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     22,
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    ]
   },
   {
    "step": 16850,
    "values": [
     2,
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     30,
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    ]
   },
   {
    "step": 21423,
    "values": [
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     "1,9,11",
     "29,12,24",
     38,
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    ]
   },
   {
    "step": 31348,
    "values": [
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     30,
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    ]
   },
   {
    "step": 43225,
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     46,
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    ]
   },
   {
    "step": 74638,
    "values": [
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     "4,16,16",
     62,
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    ]
   },
   {
    "step": 93131,
    "values": [
     4,
     "1,5,19,23",
     "31,43,24,48",
     78,
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   },
   {
    "step": 133584,
    "values": [
     4,
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     "2,12,8,48",
     62,
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    ]
   },
   {
    "step": 181685,
    "values": [
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     "32,43,24,48,32",
     94,
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   },
   {
    "step": 308778,
    "values": [
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     "8,32,32",
     126,
     125,
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   },
   {
    "step": 343591,
    "values": [
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     "79,91,56,112",
     142,
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   },
   {
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     "177,187,183,240,224",
     286,
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   {
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    "values": [
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     "179,190,190,255,255",
     "14,60,24,176,224",
     126,
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    ]
   },
   {
    "step": 3010153,
    "values": [
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     "178,187,183,240,224,64",
     190,
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   {
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    "values": [
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     "12,56,16,160,192,64",
     254,
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   },
   {
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    "values": [
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     "179,187,183,240,224,64,128",
     382,
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   },
   {
    "step": 6442496,
    "values": [
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     "10,52,8,144,160,128",
     510,
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   },
   {
    "step": 421432981,
    "values": [
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     "1,27,87,47,159,63,383,255,1535,1535",
     "378,442,248,878,480,1471,896,1792,2559,3072",
     5118,
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   {
    "step": 592819210,
    "values": [
     8,
     "380,445,255,893,2045,3070,3070,4095",
     "24,80,32,128,256,1024,512,3072",
     4094,
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     "C"
    ]
   },
   {
    "step": 635100567,
    "values": [
     9,
     "1,25,83,39,143,287,1087,639,3327",
     "379,442,248,878,2014,3007,2943,3840,3584",
     4606,
     1021,
     "A"
    ]
   },
   {
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    "values": [
     9,
     "381,445,255,893,2045,3070,3070,4095,4095",
     "22,76,24,112,224,960,384,2816,3584",
     2046,
     2045,
     "C"
    ]
   },
   {
    "step": 782428529,
    "values": [
     10,
     "1,23,79,31,127,255,1023,511,3071,4095",
     "380,442,248,878,2014,3007,2943,3840,3584,1024",
     3070,
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    ]
   },
   {
    "step": 946193350,
    "values": [
     10,
     "382,445,255,893,2045,3070,3070,4095,4095,2047",
     "20,72,16,96,192,896,256,2560,3072,1024",
     4094,
     4093,
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    ]
   }
  ]
 },
 "rules": [
  {
   "name": "init (blank -> first INV state)",
   "from": "0^inf A> 0^inf",
   "to": "0^inf <C 01 000 (01)^4 (10)^3 01 1001 0^inf",
   "steps": "215",
   "cases": "= K((1,1,3); a=4, b=1), class A. Passes K(; 3, 1) at step 82 (no digits, not in INV). Exact on #33 by direct simulation",
   "validated": {
    "instances": 2,
    "passed": 2
   },
   "source": "manual"
  },
  {
   "name": "M_k carry (k = trailing 1-bits)",
   "from": "0^inf <C (01)^b 000 (01)^a [(10)^v_j (01)^u_j]_{j=m..j*+1} (10)^v 00 (01)^u P 1001 0^inf",
   "to": "0^inf <C (01)^(b+2) 000 (01)^(a+1) [(10)^(v_j-1) 00 (01)^u_j]_{j=m..j*+1} (10)^(v-1) (01)^(u+1) P 1001 0^inf",
   "steps": "32 + 8a + 8b + 4v + sum_{j>j*} (8u_j + 4v_j)",
   "cases": "j* = last bit-0 digit, k = m - j*; k = 0..5 tested, 61 of them with v = 1 (the digit drops: same string, re-read). Needs v >= 1, u_j, v_j >= 1 for j > j*, a, b >= 0",
   "validated": {
    "instances": 240,
    "passed": 240
   },
   "source": "manual"
  },
  {
   "name": "O overflow (all bits 1)",
   "from": "0^inf <C (01)^b 000 (01)^a [(10)^v_j (01)^u_j]_{j=m..1} 1001 0^inf",
   "to": "0^inf <C 01 000 (01)^(b+3) (10)^a (01)^v_m [(10)^u_j 00 (01)^(v_(j-1)-1)]_{j=m..2} (10)^u_1 00 1001 0^inf",
   "steps": "89 - 4m + 8a + 20b + 4 sum u_j + 8 sum v_j",
   "cases": "m = 1..7 tested; needs m >= 1, all u_j, v_j >= 1, a >= 1. New digits (#11 notation): (0,0,u_1), (v_(j-1)-1, 0, u_j), (v_m, 1, a)",
   "validated": {
    "instances": 120,
    "passed": 120
   },
   "source": "manual"
  },
  {
   "name": "window lemmas (#11's S1-S6, T1-T14, mirrored)",
   "from": "20 windows, e.g. S1m 10 <C, S3m A> 10, T9m E> 1001000, T12m 00011 <D",
   "to": "S1m <C 01, S3m 01 A>, T9m <C 0001001, T12m 10110 E> (full list in notes.md)",
   "steps": "2-13 each",
   "cases": "Exact window check on #33's table (head never reads outside the window); F entered only in T4m, T9m, T13m, always reading 0. M and O are #11's chains of these, mirrored",
   "validated": {
    "instances": 20,
    "passed": 20
   },
   "source": "manual"
  }
 ],
 "template": {
  "file": null,
  "module": "our kill #11 (machines/1RB0LE_1RC0RC_1LD0RB_1LA0LE_1LD1LF_1LD---/, check_kill PASS)",
  "machine": "1RB0LE_1RC0RC_1LD0RB_1LA0LE_1LD1LF_1LD---",
  "diff": "0 transitions after mirroring + renaming (#11's A,B,C,D,E,F = this machine's B,C,D,A,E,F); only the start state differs (#11's D)",
  "applies": "yes",
  "note": "Same table, so #11's rules (M, O, the 20 window lemmas) and its Rocq-checked invariant INV = Common and (A or B or C) carry over unchanged. Only the init is new: 215 steps to K((1,1,3);4,1), class A. SBCv6 TM21 / TCv3 (targeting.md) are only loose relatives."
 },
 "strategy": "Reuse kill #11 wholesale: copy its .v and mirror it (states A,B,C,D -> B,C,D,A; tape sides swapped). Replace init (483 steps to K [d1 1 2] 8 5) with 215 steps to K [d1 1 3] 4 1, check INV there by computation, keep the closure proof verbatim. Alternative: keep tm11's lemmas and transport with busycoq's Flip.v + Permute.v.",
 "risks": [
  "Mirroring 692 lines by hand is error-prone; script it (swap <*/*>, {{X}}>/<{{X}}, rename states) and let Rocq check. Flip/Permute route adds a second TM_from_str (check_kill warns).",
  "Duplicate work: hipparcos's Level-1 machine is the B-start of this table (same open question as #11).",
  "Proof size is small (init + INV check on top of #11), so the main cost is the mechanical port."
 ],
 "checkpoint_questions": [
  {
   "text": "Fig 2: going down, do the sweeps reach right in a ruler pattern (shallow, deeper, shallow, deepest, ...) and end in one sweep to the right end that moves every wall?",
   "figs": [
    1
   ],
   "kind": "check"
  },
  {
   "text": "Fig 3: between band breaks, do the walls only creep, and at each break do all walls jump at once, with nothing new appearing?",
   "figs": [
    2
   ],
   "kind": "check"
  },
  {
   "text": "This is kill #11's table mirrored and started in D. Port #11's .v by a scripted mirror with the new 215-step init, or transport #11 with busycoq's Flip/Permute?",
   "figs": [],
   "kind": "decision"
  }
 ],
 "discord_check": "Is anyone working on `1RB0RE_1LC0RE_1LD0LD_1RA0LC_1RA1RF_1RA---`? It has the same table as @hipparcos's `1RB0RB_1LC0RA_1LE0LD_1LC1LF_1RA0LD_1LC---` (mirrored, started in another state). Four holdouts share this table; for one of them, `1RB0LE_1RC0RC_1LD0RB_1LA0LE_1LD1LF_1LD---`, we have a Rocq proof (not posted yet): a binary counter over `(10)^u [00] (01)^v` blocks with a re-pairing overflow. This start state reaches the same invariant after 215 steps, so we would like to do it next unless someone already has it.",
 "stats": {
  "simulated_steps": 1000000000,
  "cells": 76245,
  "nonzeros": 38119,
  "growth": "left edge ~2.4 t^0.5 (76,078 cells left of the start by 1e9); right edge +3 cells per overflow (52 overflows by 1e9; rules-only model: 103 by 2.4e13)"
 },
 "status": "CHECKPOINT_A",
 "status_reason": "Same table as kill #11 (mirror, D-start). M_k/O 360/360 random instances; real run = rules for all 18,976 macro steps to 1e9; INV holds from step 215. Not a cryptid."
}