{
 "tm": "1RB0LD_1RC0RE_1LD0RE_1LA0LA_1RB1RF_1RB---",
 "rank": 388,
 "class_sheet": "Skelet 1-like Class 2",
 "class_guess": "Binary counter with re-pairing overflow: kill #33's table renamed (BCDAEF, no mirror), started in #33's D",
 "confidence": "high",
 "summary": "Kill #33's table renamed, started in #33's D: same counter; a 687-step init lands in #33's proved invariant",
 "mechanism": [
  "Same table as kill #33 `1RB0RE_1LC0RE_1LD0LD_1RA0LC_1RA1RF_1RA---`: rename its states A,B,C,D -> B,C,D,A (E, F fixed), no mirror. This machine starts in #33's D (= kill #11's table mirrored, started in #11's C).",
  "Tape K = `0^inf <D (01)^b 000 (01)^a` + digits `(10)^v [00] (01)^u` + `1001`: #33's binary counter with head state D. M carries to the last 0-bit; O re-pairs every digit when all bits are 1.",
  "From blank, 687 steps reach K((1,1,9); 8, 1), class A of #33's invariant (#33: 215 steps to K((1,1,3); 4, 1)). Rules, INV and closure are #33's unchanged. Orbit = kill #11's with one top-digit exponent +3 from macro step 54 on (not a premise)."
 ],
 "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": "records:L",
   "png": "img/records_L_3e5.png",
   "html": null,
   "steps": 300000,
   "caption": "One row per new leftmost cell, to step 300,000",
   "title": "This machine at every left-edge visit",
   "why": "Each row is the whole tape at a new leftmost cell. Watch the vertical walls: where they creep and jump.",
   "primary": true,
   "start": "blank",
   "rows": "left records (each new leftmost cell): the start row plus 1,099 rows to step 300,000",
   "window": "cells -1099..59, 1 px = 1 cell",
   "legend": "white = 1, black = 0 or unvisited, red/green = head (last move right/left)",
   "style": "bbchallenge-default"
  },
  {
   "mode": "records:L",
   "png": "img/parent33_records_L_3e5.png",
   "html": null,
   "steps": 300000,
   "caption": "Parent #33 from its own blank start, same view",
   "title": "Parent #33, same view, for comparison",
   "why": "The same view of kill #33 itself. Compare the kind of walls with the previous figure, not their positions.",
   "primary": true,
   "start": "blank",
   "rows": "left records of kill #33 (1RB0RE_1LC0RE_1LD0LD_1RA0LC_1RA1RF_1RA---, its own start A): the start row plus 1,059 rows to step 300,000",
   "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"
  }
 ],
 "history": {
  "skeleton": "0^inf <D (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; abstract model, equal to the real run to 1e9)",
  "vars": [
   "m",
   "u_1..u_m",
   "v_1..v_m",
   "a",
   "b",
   "INV class"
  ],
  "rows": [
   {
    "step": 687,
    "values": [
     1,
     "1",
     "9",
     8,
     1,
     "A"
    ]
   },
   {
    "step": 1236,
    "values": [
     1,
     "11",
     "6",
     6,
     5,
     "C"
    ]
   },
   {
    "step": 1929,
    "values": [
     2,
     "1,7",
     "10,4",
     10,
     5,
     "A"
    ]
   },
   {
    "step": 3774,
    "values": [
     2,
     "12,7",
     "4,4",
     14,
     13,
     "C"
    ]
   },
   {
    "step": 6283,
    "values": [
     3,
     "1,5,7",
     "11,4,8",
     22,
     13,
     "A"
    ]
   },
   {
    "step": 13424,
    "values": [
     2,
     "13,22",
     "2,8",
     30,
     29,
     "C"
    ]
   },
   {
    "step": 17877,
    "values": [
     3,
     "1,3,11",
     "12,19,24",
     38,
     13,
     "A"
    ]
   },
   {
    "step": 27658,
    "values": [
     2,
     "36,31",
     "4,24",
     30,
     29,
     "C"
    ]
   },
   {
    "step": 32983,
    "values": [
     3,
     "1,5,27",
     "35,28,24",
     38,
     13,
     "A"
    ]
   },
   {
    "step": 43964,
    "values": [
     3,
     "37,31,31",
     "2,20,24",
     30,
     29,
     "C"
    ]
   },
   {
    "step": 56593,
    "values": [
     4,
     "1,3,23,31",
     "36,28,24,16",
     46,
     29,
     "A"
    ]
   },
   {
    "step": 89062,
    "values": [
     3,
     "69,31,31",
     "16,16,16",
     62,
     61,
     "C"
    ]
   },
   {
    "step": 107803,
    "values": [
     4,
     "1,17,19,23",
     "68,28,24,48",
     78,
     29,
     "A"
    ]
   },
   {
    "step": 148560,
    "values": [
     4,
     "70,31,31,63",
     "14,12,8,48",
     62,
     61,
     "C"
    ]
   },
   {
    "step": 196909,
    "values": [
     5,
     "1,15,15,15,63",
     "69,28,24,48,32",
     94,
     61,
     "A"
    ]
   },
   {
    "step": 324306,
    "values": [
     4,
     "71,31,94,63",
     "12,8,32,32",
     126,
     125,
     "C"
    ]
   },
   {
    "step": 398839,
    "values": [
     5,
     "1,13,11,39,47",
     "70,28,87,48,96",
     158,
     61,
     "A"
    ]
   },
   {
    "step": 562380,
    "values": [
     5,
     "72,31,94,63,127",
     "10,4,24,16,96",
     126,
     125,
     "C"
    ]
   },
   {
    "step": 756185,
    "values": [
     6,
     "1,11,7,31,31,127",
     "71,28,87,48,96,64",
     190,
     125,
     "A"
    ]
   },
   {
    "step": 1267742,
    "values": [
     4,
     "73,125,190,127",
     "8,16,64,64",
     254,
     253,
     "C"
    ]
   },
   {
    "step": 1406963,
    "values": [
     5,
     "1,9,19,71,79",
     "72,122,183,112,224",
     286,
     61,
     "A"
    ]
   },
   {
    "step": 1659752,
    "values": [
     5,
     "74,125,190,127,255",
     "6,12,56,48,224",
     126,
     125,
     "C"
    ]
   },
   {
    "step": 1917733,
    "values": [
     6,
     "1,7,15,63,63,255",
     "73,122,183,112,224,64",
     190,
     125,
     "A"
    ]
   },
   {
    "step": 2518538,
    "values": [
     6,
     "75,125,190,127,255,127",
     "4,8,48,32,192,64",
     254,
     253,
     "C"
    ]
   },
   {
    "step": 3255855,
    "values": [
     7,
     "1,5,11,55,47,223,127",
     "74,122,183,112,224,64,128",
     382,
     253,
     "A"
    ]
   },
   {
    "step": 5251716,
    "values": [
     6,
     "76,125,190,127,255,382",
     "2,4,40,16,160,128",
     510,
     509,
     "C"
    ]
   },
   {
    "step": 6470417,
    "values": [
     7,
     "1,3,7,47,31,191,191",
     "75,122,183,112,224,319,384",
     638,
     253,
     "A"
    ]
   },
   {
    "step": 9142998,
    "values": [
     4,
     "392,382,382,511",
     "32,128,64,384",
     510,
     509,
     "C"
    ]
   },
   {
    "step": 9463859,
    "values": [
     5,
     "1,33,131,71,399",
     "391,379,375,496,480",
     542,
     61,
     "A"
    ]
   },
   {
    "step": 9967416,
    "values": [
     5,
     "393,382,382,511,511",
     "30,124,56,368,480",
     126,
     125,
     "C"
    ]
   },
   {
    "step": 14422148,
    "values": [
     6,
     "395,382,382,511,511,382",
     "26,116,40,336,416,128",
     510,
     509,
     "C"
    ]
   },
   {
    "step": 30572592,
    "values": [
     7,
     "397,382,382,511,511,893,511",
     "22,108,24,304,352,256,256",
     1022,
     1021,
     "C"
    ]
   },
   {
    "step": 92222268,
    "values": [
     8,
     "399,382,382,511,511,893,1534,1023",
     "18,100,8,272,288,128,512,512",
     2046,
     2045,
     "C"
    ]
   },
   {
    "step": 222617416,
    "values": [
     9,
     "401,382,893,511,893,1534,1023,2047,2047",
     "14,92,248,240,32,320,128,1280,1536",
     2046,
     2045,
     "C"
    ]
   },
   {
    "step": 513032532,
    "values": [
     9,
     "403,382,893,511,2427,3070,2047,2047,4095",
     "10,84,232,208,224,960,896,768,3584",
     2046,
     2045,
     "C"
    ]
   },
   {
    "step": 924603323,
    "values": [
     11,
     "1,9,83,231,207,223,959,895,767,3583,2047",
     "403,379,886,496,2396,3007,1920,1792,3584,1024,2048",
     6142,
     4093,
     "A"
    ]
   }
  ]
 },
 "rules": [
  {
   "name": "init (blank -> first INV state)",
   "from": "0^inf A> 0^inf",
   "to": "0^inf <D 01 000 (01)^8 (10)^9 01 1001 0^inf",
   "steps": "687",
   "cases": "= K((1,1,9); a=8, b=1), class A. Passes K-configs at 101, 234, 326, 426 (none in INV). Exact by direct simulation; Rocq solve_init in rocq/delta_check.v",
   "validated": {
    "instances": 1,
    "passed": 1
   },
   "source": "manual"
  },
  {
   "name": "M_k carry (k = trailing 1-bits)",
   "from": "0^inf <D (01)^b 000 (01)^a [(10)^v_j (01)^u_j]_{j=m..j*+1} (10)^v 00 (01)^u X",
   "to": "0^inf <D (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) X",
   "steps": "32+8a+8b+4v+sum(8u_j+4v_j)",
   "cases": "#33's M with <C read as <D; v=1: the flipped digit drops (fuses with the next). check_proof A: 700 random; H: 37,220 link-by-link chains on this table",
   "validated": {
    "instances": 37920,
    "passed": 37920
   },
   "source": "manual"
  },
  {
   "name": "O overflow (all bits 1)",
   "from": "0^inf <D (01)^b 000 (01)^a [(10)^v_j (01)^u_j]_{j=m..1} 1001 0^inf",
   "to": "0^inf <D 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+4sum(u)+8sum(v)",
   "cases": "#33's O with <C read as <D; m>=1, all u,v>=1, a>=1. check_proof A: 350 random; H: 9,996 link-by-link chains (m=0 incl.)",
   "validated": {
    "instances": 10346,
    "passed": 10346
   },
   "source": "manual"
  }
 ],
 "template": {
  "file": null,
  "module": "our kill #33 (machines/1RB0RE_1LC0RE_1LD0LD_1RA0LC_1RA1RF_1RA---/, check_kill PASS)",
  "machine": "1RB0RE_1LC0RE_1LD0LD_1RA0LC_1RA1RF_1RA---",
  "diff": "0 transitions after renaming #33's A,B,C,D,E,F -> B,C,D,A,E,F (no mirror); only the start differs (#33's D)",
  "applies": "yes",
  "note": "Same table, so #33's window lemmas, M, O and INV (proved in Rocq) apply verbatim with the K head state C -> D. Only init changes: 687 steps to K [d1 1 9] 8 1. The renamed .v compiles as a scratch file (rocq/delta_check.v, closed); check_kill not run yet."
 },
 "strategy": "Delta proof (proof.md): Lemma R (renaming) + #33's rules and invariant verbatim + a new 687-step init to K((1,1,9);8,1), class A. Formal: #33's .v with {{X}} renamed by sigma, new init/base (rocq/delta_check.v compiles in 8.8 s). Next: copy it to the kill path and run check_kill.",
 "risks": [
  "Duplicate work: unclaimed in the sheet and our Discord lists, but Discord #bb6 was not searched for this string.",
  "Same family as kills #11 and #33 (and hipparcos's line 541): post them together so the twins paragraphs agree.",
  "Little math risk: the base is in class A and every INV clause there is a lower bound."
 ],
 "checkpoint_questions": [
  {
   "text": "Fig 2 vs Fig 3: is this the same kind of picture as #33's (a dense alternating band with near-vertical walls that creep and then all jump at once), only with the walls in other places?",
   "figs": [
    1,
    2
   ],
   "kind": "check"
  },
  {
   "text": "proof.md is a delta proof: same table up to renaming, a new 687-step init, the invariant unchanged. Accept it as the informal proof for the submission (with #33's proof.md attached), or restate the parent proof in full?",
   "kind": "decision"
  }
 ],
 "discord_check": null,
 "stats": {
  "simulated_steps": 1000000000,
  "cells": 77691,
  "nonzeros": 38839,
  "growth": "left edge ~2.45 t^0.5 (77,517 cells left of the start by 1e9); right edge 173 (+3 cells per overflow, 53 overflows by 1e9)"
 },
 "status": "CHECKPOINT_A",
 "status_reason": "Same table as kill #33 (renaming BCDAEF, no mirror, D-start). Rules and INV unchanged; 687-step init to class A; closure exact on the real run. Delta proof.md written (CHECKPOINT_B in status.json)."
}