{
 "tm": "1RB0LC_1RC0RA_1RD0RF_0LE---_1LB1LA_1LD1RA",
 "rank": 16,
 "class_sheet": "Chaotic Fractal Others",
 "class_guess": "Fractal: Jacobsthal transfer staircase (right) + bouncer (left), chaotic segment list",
 "confidence": "med",
 "summary": "Self-similar Jacobsthal transfer staircase + (010)-eating bouncer; middle phase not yet closed-form",
 "mechanism": [
  "Right phase: transfers (01)^(T+c) (011)^T -> (011)^(T+c) (01)^T (c = 3 if T even, 2 if odd), nested as domes.",
  "Left phase: a plain bouncer eats (010)^d, left edge +2 per bounce; one right sweep then starts the next right phase.",
  "Between them, a record-free middle phase rebuilds the left part; its segment sizes are irregular (the open part)."
 ],
 "diagrams": [
  {
   "mode": "blaze",
   "png": "img/blaze_1e8.png",
   "html": null,
   "steps": 100000000,
   "caption": "Left bouncer domes plus self-similar right staircases, 1e8 steps",
   "title": "Blaze view, 100 million steps",
   "why": "Blaze view to 1e8 steps. Compare the domes on the left with the domes on the right.",
   "primary": true,
   "start": "blank",
   "rows": "Blaze time blocks of 131,072 steps (763 rows, each averaged), stretched to 500 px (1 px ~ 200,000 steps)",
   "window": "cells -6,064..8,159, 1 px = 17.8 cells (each px shows one 16-cell block)",
   "legend": "white = 0, orange = 1; pale orange = a mix (the fine 01/011/010 stripes average out over each pixel's cells and time block)",
   "style": "bbchallenge-blaze"
  },
  {
   "mode": "blaze",
   "png": "img/blaze_rightphase_x1400.png",
   "html": null,
   "steps": 4200000,
   "caption": "From (10)^24 (101)^24 (01)^1400 1 C>: nested transfer domes",
   "title": "One right phase, from a built tape",
   "why": "One right phase from a built tape. Look to the right of each big dome.",
   "primary": true,
   "start": "constructed: 0^inf (10)^24 (101)^24 (01)^1400 1 C> 0^inf",
   "rows": "Blaze time blocks of 8,192 steps (513 rows, each averaged), steps 0..4,200,000, stretched to 500 px",
   "window": "cells -3,308..1,367, 1 px = 5.8 cells (each px shows one 4-cell block; cell 0 = the start head cell)",
   "legend": "white = 0, orange = 1; pale orange = a mix (the fine 01/011/010 stripes average out over each pixel's cells and time block)",
   "style": "bbchallenge-blaze"
  },
  {
   "mode": "records",
   "png": "img/records_1e8.png",
   "html": "img/viewer.html",
   "steps": 9618857,
   "caption": "Records to 9.6e6 steps: right staircases alternate with left bouncer phases",
   "title": "Edge records to 9.6 million steps",
   "why": "Edge records to 9.6M steps. Track which edge moves, row by row, and how far.",
   "primary": true,
   "start": "blank",
   "rows": "the start, then one per new leftmost or rightmost cell: 5,000 rows (row cap hit), steps 0..9,618,857 only; not evenly spaced in time",
   "window": "cells -2,309..2,690, 1 px = 1 cell",
   "legend": "white = 1, black = 0, green/red = head at a new left/right edge; zoomed out, the 1-cell stripes blur to greys (lighter = more 1s)",
   "style": "bbchallenge-default"
  },
  {
   "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, first 10,000 steps",
   "why": "For orientation: the start of the run as bbchallenge.org shows it.",
   "primary": false,
   "start": "blank",
   "rows": "10,000 steps squeezed into 500 px rows (1 px row = 20 steps; the site blends steps 20y+9 and 20y+10)",
   "window": "cells -200..199, 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 (10)^p (101)^q (01)^x (011)^T 1 C> 0^inf",
  "vars": [
   "p",
   "q",
   "x",
   "T"
  ],
  "rows": [
   {
    "step": 14526001,
    "values": [
     1348,
     77,
     1420,
     0
    ]
   },
   {
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    "values": [
     1348,
     77,
     1417,
     3
    ]
   },
   {
    "step": 14526169,
    "values": [
     1348,
     77,
     1412,
     8
    ]
   },
   {
    "step": 14526894,
    "values": [
     1348,
     77,
     1401,
     19
    ]
   },
   {
    "step": 14529753,
    "values": [
     1348,
     77,
     1380,
     40
    ]
   },
   {
    "step": 14541326,
    "values": [
     1348,
     77,
     1337,
     83
    ]
   },
   {
    "step": 14586457,
    "values": [
     1348,
     77,
     1252,
     168
    ]
   },
   {
    "step": 14765710,
    "values": [
     1348,
     77,
     1081,
     339
    ]
   },
   {
    "step": 15474265,
    "values": [
     1348,
     77,
     740,
     680
    ]
   },
   {
    "step": 18295950,
    "values": [
     1348,
     77,
     57,
     1363
    ]
   },
   {
    "step": 479669602,
    "values": [
     4142,
     3895,
     5780,
     0
    ]
   },
   {
    "step": 479669623,
    "values": [
     4142,
     3895,
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     3
    ]
   },
   {
    "step": 479669770,
    "values": [
     4142,
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    ]
   },
   {
    "step": 479670495,
    "values": [
     4142,
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     19
    ]
   },
   {
    "step": 479673354,
    "values": [
     4142,
     3895,
     5740,
     40
    ]
   },
   {
    "step": 479684927,
    "values": [
     4142,
     3895,
     5697,
     83
    ]
   },
   {
    "step": 479730058,
    "values": [
     4142,
     3895,
     5612,
     168
    ]
   },
   {
    "step": 479909311,
    "values": [
     4142,
     3895,
     5441,
     339
    ]
   },
   {
    "step": 480617866,
    "values": [
     4142,
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     680
    ]
   },
   {
    "step": 483439551,
    "values": [
     4142,
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     1363
    ]
   },
   {
    "step": 494677386,
    "values": [
     4142,
     3895,
     3052,
     2728
    ]
   },
   {
    "step": 539548607,
    "values": [
     4142,
     3895,
     321,
     5459
    ]
   }
  ]
 },
 "rules": [
  {
   "name": "Transfer_even",
   "from": "l (01)^(x+T+3) (011)^T 1 C> 0^inf",
   "to": "l (01)^x (011)^(T+3) (01)^T 1 C> 0^inf",
   "steps": "4T^2+35T+21",
   "cases": "T even, x>=0; l = 0^inf (10)^p (101)^q or 0^inf (10)^p (011)^a",
   "validated": {
    "instances": 56,
    "passed": 56
   },
   "source": "manual"
  },
  {
   "name": "Transfer_odd",
   "from": "l (01)^(x+T+2) (011)^T 1 C> 0^inf",
   "to": "l (01)^x (011)^(T+2) (01)^T 1 C> 0^inf",
   "steps": "4T^2+27T+9",
   "cases": "T odd, x>=0; same l as Transfer_even",
   "validated": {
    "instances": 56,
    "passed": 56
   },
   "source": "manual"
  },
  {
   "name": "Conv",
   "from": "l (01)^(x+S_k) 1 C> 0^inf",
   "to": "l (01)^x (011)^(S_k) 1 C> 0^inf",
   "steps": null,
   "cases": "S_0=0, S_(k+1)=2S_k+3 (S_k even) or +2 (odd): 0,3,8,19,40,83,168,339,...; = Transfer iterated",
   "validated": {
    "instances": 12,
    "passed": 12
   },
   "source": "manual"
  },
  {
   "name": "Bounce_C",
   "from": "0^inf <C (01)^a (001101)^b (01)^c (001)^(d+2) 0^inf",
   "to": "0^inf <C (01)^(a+2) (001101)^b (01)^(c+2) (001)^d 0^inf",
   "steps": "6a+20b+6c+16",
   "cases": "also holds with middle (001101)^b (01)^e (001101)^f (20/20)",
   "validated": {
    "instances": 56,
    "passed": 56
   },
   "source": "rulefit"
  },
  {
   "name": "Bounce_A",
   "from": "0^inf <A (10)^a (011010)^b (10)^c (010)^(d+2) 0^inf",
   "to": "0^inf <A (10)^(a+2) (011010)^b (10)^(c+2) (010)^d 0^inf",
   "steps": null,
   "cases": "same phase as Bounce_C, seen at the A-record; d even ends in hub (d=0)",
   "validated": {
    "instances": 36,
    "passed": 36
   },
   "source": "rulefit"
  },
  {
   "name": "BounceEnd_odd",
   "from": "0^inf <A (10)^a (011010)^b (10)^c 010 0^inf",
   "to": "0^inf <A (10)^(a+2) (011010)^b (10)^(c+1) 0^inf",
   "steps": null,
   "cases": "d odd: last half-bounce lands in the hub",
   "validated": {
    "instances": 12,
    "passed": 12
   },
   "source": "manual"
  },
  {
   "name": "Sweep1",
   "from": "0^inf <A (10)^(a+1) (011010)^b (10)^c 0^inf",
   "to": "0^inf (10)^a (101)^(2b+1) (01)^c 1 C> 0^inf",
   "steps": null,
   "cases": "b,c>=1: hub -> right phase start (Conv on (01)^c)",
   "validated": {
    "instances": 36,
    "passed": 36
   },
   "source": "manual"
  },
  {
   "name": "Sweep2",
   "from": "0^inf <A (10)^(a+1) (011010)^b (10)^(c+1) (011010)^d (10)^e 0^inf",
   "to": "0^inf (10)^a (101)^(2b+1) (01)^c (011)^(2d) (01)^(e+1) 1 C> 0^inf",
   "steps": null,
   "cases": "5-segment hub; (011)^(2d) acts as a wall for Conv on (01)^(e+1)",
   "validated": {
    "instances": 36,
    "passed": 36
   },
   "source": "manual"
  }
 ],
 "template": {
  "file": "vendor/busycoq/verify/FractalType7v4.v",
  "module": "TM20",
  "machine": "1RB0LF_1RC0RA_0RD0RB_1LE0RF_1LB0LE_1LE---",
  "diff": "7/11 defined transitions differ (TM20 with D<->F): A1 C0 C1 D0 E1 F0 F1; same A0 B0 B1 E0. All 19 FractalMisc modules: >=8",
  "applies": "partly",
  "note": "Rules/shapes do not carry over: TM20 Inc from S1 0/8, FractalMisc TM1 Inc1 0/8 on this machine.\nReusable: architecture (P-call recursion, inductive Good invariant with inequalities, chunked native_compute init)."
 },
 "strategy": "FractalType7v4 architecture: es/ind lemmas for Transfer (T even/odd) and Bounce, Conv by induction on k, Sweep by chain steps.\nThen an inductive Good invariant on the segment list with inequality bounds (no exact values) + progress_nonhalt, like Inv_step.\nFirst: close the middle (underflow) phase as rules; init via chunked multistep_c + native_compute.",
 "risks": [
  "Middle (underflow) phase has no closed form: result splits on parities of p, q, b; 63/63 probes reach the left edge, rule table unknown",
  "Segment list grows (3->5 segments by 1e9); the inequalities a Good invariant needs are not known yet",
  "No template within 7 transitions: new-mechanism proof, likely 20-40 KB"
 ],
 "checkpoint_questions": [
  {
   "text": "Fig 1: do the big domes on the left look smooth and plain (no nested copies), unlike the stepped domes on the right?",
   "figs": [
    0
   ]
  },
  {
   "text": "Fig 2: does each dome have smaller copies of the same dome pattern nested to its right?",
   "figs": [
    1
   ]
  },
  {
   "text": "Fig 3: do right-edge staircases and left-edge growth phases strictly take turns, each bigger than the last?",
   "figs": [
    2
   ]
  }
 ],
 "discord_check": null,
 "stats": {
  "simulated_steps": 1000000000,
  "cells": 47345,
  "nonzeros": 21900,
  "growth": "span ~t^0.48 (5,086 cells at 1e7, 47,345 at 1e9); right-phase record counts are Jacobsthal numbers (85, 1365, 5461)"
 },
 "status": "CHECKPOINT_A",
 "status_reason": "Not a cryptid: parity splits are deterministic (T alternates along the staircase); 300 random hub configs x 5e7 steps: 0 halts"
}