{
 "tm": "1RB0LD_0RC---_0RD0RF_1LE0LA_1LF1LE_1RA0RD",
 "rank": 221,
 "class_sheet": "Unknown",
 "class_guess": "Chaotic Bell (bouncer type): glider between two 8-cell fields, x9/4 cycles, chaotic junk edge on the left",
 "confidence": "med",
 "summary": "Glider bounces between two 8-cell fields; field grows x9/4 per cycle; a chaotic junk edge sets the remainder",
 "mechanism": [
  "Two fields of 8-cell blocks, W = 11010100 left of the head and R = 11110001 right of it. The head is a glider between them: moving right it turns R into W (32 steps per block, GR), moving left W into R (36 steps per block, GL). It bounces between a wall on the left and the tape end, which grows 2 cells per bounce.",
  "Phase S: the wall moves right 18 cells per bounce, leaving an 18-cell wake piece Y (rule S1, exact, 830/830 real bounces). Then one sweep rewrites the wake into 72-cell units V. Phase G: the wall moves back left one unit per 36 bounces while the field gains 18 blocks per unit (rule G36, exact, 86/86 real periods). So the field at the next S start is b' = 9b/4 + c.",
  "The remainder b mod 8 picks the S->G branch (b mod 2 picks the G alignment) and c (-14..+42 seen) comes from the junk left of the wake, which each G->S transition digs into and rewrites: counters inside it are eaten (6,4,3,1,0, then 17,14,12,10,9,7) and the left edge moved from -52 to -111 after 1e10. Halting needs C> 1001; no halt to 4.2e13 (exact accelerated run)."
 ],
 "diagrams": [
  {
   "mode": "default",
   "png": "img/default_site.png",
   "html": "img/viewer.html",
   "steps": 10000,
   "caption": "Site Default view, 10,000 steps from blank",
   "title": "bbchallenge Default view",
   "why": "The standard site picture: a block field whose right edge grows in steps.",
   "primary": true,
   "start": "blank",
   "rows": "10,000 steps squeezed into 500 rows (site view, about 20 steps per row)",
   "window": "cells -200..199, 1 px = 1 cell",
   "legend": "white = 1, black = 0 or unvisited, red/green = head after a move R/L",
   "style": "bbchallenge-default"
  },
  {
   "mode": "every:200000",
   "png": "img/every2e5_1e8.png",
   "html": null,
   "steps": 100000000,
   "caption": "One row every 200,000 steps to 1e8, every 8th cell",
   "title": "Three cycles to 1e8",
   "why": "Vertical stripes: frozen wake and junk. Flat rows: the 8-cell fields. Follow the boundary between them down the picture.",
   "primary": true,
   "start": "blank",
   "rows": "every 200,000 steps, 501 rows to step 1e8",
   "window": "cells -52..10002, 1 px = 8 cells (every 8th cell sampled)",
   "legend": "white = 1, black = 0 or unvisited; with one sample per 8 cells a period-8 field is one flat colour in each row, while the wake (a phase defect every 18 or 72 cells) and the junk show as vertical stripes",
   "style": "bbchallenge-default"
  },
  {
   "mode": "every:4",
   "png": "img/s_bounces.png",
   "html": null,
   "steps": 4000,
   "caption": "Four phase-S bounces (rule S1) from a constructed start",
   "title": "Phase S: four bounces",
   "why": "Green zigzags: the glider going left; red diagonals: going right. Compare where each left turn lands.",
   "primary": true,
   "start": "constructed: 0^inf 10011010^4 011001101010011010^2 0110 10101001^2 100^2 11010100^14 D> 0^inf",
   "rows": "every 4 steps, steps 0..4,000 (bounces end at steps 1,204, 2,272, 3,204 and 4,000); 2 px per row",
   "window": "cells -206..8, 1 px = 0.5 cells (scale 2; cell 0 = the head's start cell)",
   "legend": "white = 1, black = 0 or unvisited, red/green = head after a move R/L",
   "style": "bbchallenge-default"
  },
  {
   "mode": "records:R",
   "png": "img/g_records.png",
   "html": null,
   "steps": 410864,
   "caption": "Phase G: four 36-bounce periods (rule G36), one row per edge cell",
   "title": "Phase G: four unit periods",
   "why": "Left: wake units (vertical stripes). Right: the field, whose stripes slant because it is anchored to the growing right end.",
   "primary": false,
   "start": "constructed: 0^inf 01101010^4 (10011010^2 10100110^2 10101001^2 10^4 01101010^2)^5 10011010^2 0110^2 101001^2 10^4 0 11010100^4 D> 0^inf",
   "rows": "one row per new rightmost cell (2 per bounce), 289 rows, steps 0..410,864 = four G36 periods",
   "window": "cells -469..288, 1 px = 0.5 cells (scale 2; cell 0 = the head's start cell)",
   "legend": "white = 1, black = 0 or unvisited, red/green = head after a move R/L",
   "style": "bbchallenge-default"
  },
  {
   "mode": "every:4",
   "png": "img/g_bounces.png",
   "html": null,
   "steps": 4400,
   "caption": "First bounces of a G period: probes dig into the units",
   "title": "Phase G close-up: probe bounces",
   "why": "Left turns alternate between shallow and deep: the deep ones are the probes into the next unit.",
   "primary": false,
   "start": "constructed: 0^inf 01101010^4 (10011010^2 10100110^2 10101001^2 10^4 01101010^2)^2 10011010^2 0110^2 101001^2 10^4 0 11010100^4 D> 0^inf",
   "rows": "every 4 steps, steps 0..4,400; 2 px per row",
   "window": "cells -253..16, 1 px = 0.5 cells (scale 2; cell 0 = the head's start cell)",
   "legend": "white = 1, black = 0 or unvisited, red/green = head after a move R/L",
   "style": "bbchallenge-default"
  }
 ],
 "history": {
  "skeleton": "phase-S start: l 0110 10101001^2 100^2 11010100^b D> 0^inf (l = junk, lo = left edge)",
  "vars": [
   "b (field blocks at S start)",
   "b mod 8",
   "lo (left edge)"
  ],
  "rows": [
   {
    "step": 3311129,
    "values": [
     173,
     5,
     -52
    ]
   },
   {
    "step": 15667118,
    "values": [
     408,
     0,
     -52
    ]
   },
   {
    "step": 78104903,
    "values": [
     928,
     0,
     -52
    ]
   },
   {
    "step": 395843382,
    "values": [
     2104,
     0,
     -52
    ]
   },
   {
    "step": 2007488939,
    "values": [
     4720,
     0,
     -52
    ]
   },
   {
    "step": 10081940898,
    "values": [
     10630,
     6,
     -52
    ]
   },
   {
    "step": 51081997453,
    "values": [
     23959,
     7,
     -78
    ]
   },
   {
    "step": 258741221346,
    "values": [
     53939,
     3,
     -91
    ]
   },
   {
    "step": 1310468894087,
    "values": [
     121394,
     2,
     -104
    ]
   }
  ]
 },
 "rules": [
  {
   "name": "GR (glider right)",
   "from": "11010100^(m+1) 100 D> 00 11111000^(n+k) 11 0^inf",
   "to": "11010100^(m+k+1) 100 D> 00 11111000^n 11 0^inf",
   "steps": "32k",
   "cases": "m, n, k >= 0; left context never read",
   "validated": {
    "instances": 200,
    "passed": 200
   },
   "source": "manual"
  },
  {
   "name": "GL (glider left)",
   "from": "1 11010100^(m+k) <E 11110001^n 1 0^inf",
   "to": "1 11010100^m <E 11110001^(n+k) 1 0^inf",
   "steps": "36k",
   "cases": "m, n, k >= 0",
   "validated": {
    "instances": 200,
    "passed": 200
   },
   "source": "manual"
  },
  {
   "name": "S1 (one phase-S bounce)",
   "from": "l 0110 10101001^2 100^2 11010100^(b+2) D> 0^inf",
   "to": "l 011001101010011010 0110 10101001^2 100^2 11010100^b D> 0^inf",
   "steps": "68b+388",
   "cases": "b >= 0; wall +18 cells, edge +2; plus 830/830 real bounces to 1.2e8",
   "validated": {
    "instances": 200,
    "passed": 200
   },
   "source": "manual"
  },
  {
   "name": "S4 (four S bounces, = qsim's rule)",
   "from": "l 0110 10101001^2 100^2 11010100^(b+8) D> 0^inf",
   "to": "l 011001101010011010^4 0110 10101001^2 100^2 11010100^b D> 0^inf",
   "steps": "272b+2368",
   "cases": "b >= 0",
   "validated": {
    "instances": 200,
    "passed": 200
   },
   "source": "qsim"
  },
  {
   "name": "G36 (one phase-G unit, 36 bounces)",
   "from": "l (10011010^2 10100110^2 10101001^2 10^4 01101010^2)^(a+1) 10011010^2 0110^2 101001^2 10^4 0 11010100^b D> 0^inf",
   "to": "l (10011010^2 10100110^2 10101001^2 10^4 01101010^2)^a 10011010^2 0110^2 101001^2 10^4 0 11010100^(b+18) D> 0^inf",
   "steps": "2448b+26828",
   "cases": "a, b >= 0; alignment of even-b cycles; plus 86/86 real periods to 1.2e8",
   "validated": {
    "instances": 150,
    "passed": 150
   },
   "source": "manual"
  },
  {
   "name": "Cycle law (observed)",
   "from": "l 0110 10101001^2 100^2 11010100^b D> 0^inf (S start)",
   "to": "l' 0110 10101001^2 100^2 11010100^(9b/4 + c) D> 0^inf (next S start)",
   "steps": null,
   "cases": "b mod 8 picks the S->G branch; c = -14..+42 depends on the junk l, which is rewritten (l -> l'); 9 cycles to 1.3e12 fit",
   "validated": {
    "instances": 0,
    "passed": 0
   },
   "source": "manual"
  }
 ],
 "template": {
  "file": null,
  "module": null,
  "machine": "1RB---_1LC0LA_1LD0LC_1RE0LB_1RF0RE_1LC0RD",
  "diff": "7 transitions (nearest proved table, W4-3c); nothing within 5",
  "applies": "no",
  "note": "W4-3c (our kill) is a base-3 odometer of flaws in a 0101 stripe; its visit lemmas share nothing with the glider/bounce rules here beyond the picture of defects in a periodic background. Upstream has this table only in Eqv_v2.v TM2413 (an equivalence with our start E), no proof."
 },
 "strategy": "Not a proof yet. Next: an exact cycle accelerator (GR, GL, S1, G36 plus measured S->G branches by b mod 8 and direct runs of G->S) to follow 100+ cycles and census the junk shapes. If they close up (finitely many shapes up to counters), write the branch table and an invariant; otherwise park as a cryptid.",
 "risks": [
  "The junk edge is rewritten every cycle by a branch chosen by b mod 8 under b' = 9b/4 + c: pseudo-random input, so the junk shapes may never close up.",
  "Two counters in the junk were eaten down (6 to 0, then 17 to 7); when the second runs out, around 1e14-1e16, the regime may change.",
  "The odd-b G alignment and the S->G and G->S transitions are observed only, not written as rules."
 ],
 "checkpoint_questions": [
  {
   "text": "Three cycles to 1e8: is the boundary between the vertically striped wake (left) and the flat field rows a slow diagonal moving left (phase G, rows ~95-390) followed by a fast sweep to the right (phase S, rows ~390-465)?",
   "figs": [
    1
   ],
   "kind": "check"
  },
  {
   "text": "Phase S: four bounces: does each left turn land further right (18 cells per bounce, rule S1)?",
   "figs": [
    2
   ],
   "kind": "check"
  },
  {
   "text": "Cryptid-like (cryptid protocol): the field grows as b' = 9b/4 + c, b mod 8 picks the branch and the junk sets c, and the junk is rewritten every cycle; no halting branch known, no halt to 4.2e13. Park it, or fund one 2 h stage for an exact cycle accelerator and a census of junk shapes?",
   "kind": "decision"
  }
 ],
 "discord_check": null,
 "stats": {
  "simulated_steps": 42000003008473,
  "cells": 6215534,
  "nonzeros": null,
  "growth": "right edge ~ sqrt(t); field x9/4 per cycle, cycle time about x5; direct C run to 1e9 (span -52..30411, 16,609 ones), exact accelerated run to 4.2e13 (span -111..6,215,422)"
 },
 "status": "CRYPTID_CANDIDATE",
 "status_reason": "Mechanism found and the phase rules are exact (GR, GL, S1, G36 validated on random and real instances), but the cycle law b' = 9b/4 + c branches on b mod 8 and on a junk edge that each cycle rewrites; cryptid protocol: rules formalized, flagged, stopped. No halting branch known (halting needs C> 1001)."
}