{
 "tm": "1RB1RA_1LC0RE_1LE0LD_0LB1LB_1RA0LF_1LD---",
 "rank": null,
 "class_sheet": "Unknown",
 "class_guess": "Fossil bouncer: one bounce per cycle over a sea of u = 01001111 with seams; the wall leaves 1-deposits that later fossilize",
 "confidence": "low",
 "summary": "Bouncer over a 01001111 sea: quiet epochs (rule Q) validated; epoch changes are irregular and not closed yet.",
 "mechanism": [
  "The tape is a sea of u = 01001111 (any rotation) with short seams. Each cycle the head sweeps right (RS: 20 steps per block), turns at a wall and sweeps back (LS: 40 per block); the left turn LT adds 3 cells.",
  "Quiet epoch (rule Q): the left reservoir u^a gains a block, the wall eats one block of u^b and leaves 111 behind (1^c +3), and the active sea shifts +5 cells. 248 consecutive cycles from 9.5e7 to 1.1e8 match Q exactly.",
  "Epochs end when b runs out or a seam (riding right at +5 cells per cycle) reaches the wall; the 1-deposit then fossilizes and at irregular cycles u^a freezes into a new segment (22 freezes to 2e9, a = 9 ... 2535). No closed epoch grammar yet."
 ],
 "diagrams": [
  {
   "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": "The site's view. The left edge grows; the stripes are the 01001111 sea, rewritten on every pass.",
   "primary": true,
   "start": "blank",
   "rows": "10,000 steps squeezed into 500 px rows (1 px row = 20 steps; the site blends neighbouring 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",
   "style": "bbchallenge-default"
  },
  {
   "mode": "custom rows: every 10th left record, cells classified by block type",
   "png": "img/segmap_1e9.png",
   "html": null,
   "steps": 999707934,
   "caption": "Segment map to 1e9: sea, wall, deposits, fossils",
   "title": "Segment map to 1e9 steps",
   "why": "One row per 10 cycles. Follow the green turning point; compare grey wedges with the dark fossil blocks.",
   "primary": true,
   "start": "blank",
   "rows": "one per 10th left record in state B (1,021 rows, steps 971..999,707,934; not evenly spaced in time, cycles get longer)",
   "window": "cells -30654..1159, 1 px = 32 cells (majority class of the 32 cells)",
   "legend": "blue = u-sea (01001111 in any rotation), white = run of 6+ ones, yellow = (10) run, red = other cells (seams); bright = changed since the previous left record (active), dark = unchanged (fossil); green = this cycle's turning point; black = never visited",
   "style": "custom"
  },
  {
   "mode": "default, constructed start, every step",
   "png": "img/cycle_Q.png",
   "html": null,
   "steps": 1495,
   "caption": "One cycle of rule Q from a small instance",
   "title": "One cycle of the quiet-epoch rule Q",
   "why": "Rows are single steps. Find the turn near cell 196; check whether any cell right of it changes.",
   "primary": true,
   "start": "constructed: 0^inf <C (10100111)^6 1 (110100)^2 1^6 (10100111)^4 (010011111)^2 (11010011)^2 (10100111)^2 0100 1^10 (01001111)^3 1 (10100)^2 1^10 (10100111111)^2 (10100111)^3 0100 1^5 0^inf",
   "rows": "every step, steps 0..1,495 (one Q cycle is 60(a+b+d+e)+595 = 1,495 steps here; a=6, b=3, d=4, e=2)",
   "window": "cells -17..322, 1 px = 1 cell (the start configuration covers cells 0..263; head starts at cell 0)",
   "legend": "white = 1, black = 0 or never visited, red/green = head after a right/left move",
   "style": "bbchallenge-default"
  },
  {
   "mode": "custom rows: every left record, cells classified by block type",
   "png": "img/segmap_2e7.png",
   "html": null,
   "steps": 19999524,
   "caption": "Segment map to 2e7, every cycle",
   "title": "Segment map to 2e7 steps, every cycle",
   "why": "Same colours, one row per cycle. Red diagonals are seams riding right; watch them meet the green wall.",
   "start": "blank",
   "rows": "every left record in state B (1,344 rows, steps 17..19,999,524; not evenly spaced in time)",
   "window": "cells -4050..421, 1 px = 4 cells (majority class of the 4 cells)",
   "legend": "blue = u-sea (01001111 in any rotation), white = run of 6+ ones, yellow = (10) run, red = other cells (seams); bright = changed since the previous left record (active), dark = unchanged (fossil); green = this cycle's turning point; black = never visited",
   "style": "custom"
  },
  {
   "mode": "custom rows: every 30th cycle start, cells classified by block type (from the token file, no re-simulation)",
   "png": "img/segmap_1e10_right.png",
   "html": null,
   "steps": 9988875874,
   "caption": "Segment map to 1e10, right part: deposits, conversions and fossils",
   "title": "Segment map to 1e10, right part",
   "why": "Follow a grey wedge down to the row where it turns dark blue; compare the red seams left behind.",
   "primary": false,
   "start": "blank",
   "rows": "one per 30th left record in state C (1,101 rows, cycles 30..33,030, steps 9,432..9,988,875,874; not evenly spaced in time, cycles get longer)",
   "window": "cells -30000..1687, 1 px = 32 cells (majority class of the 32 cells)",
   "legend": "blue = u-sea (01001111 in any rotation, runs of 24+ cells), white = run of 12+ ones (6+ inside a seam), yellow = (10) run of 4+ repetitions, red = other seam cells; bright = at or left of this cycle's turning point, dark = right of it; green = turning point; black = outside the span",
   "style": "custom"
  }
 ],
 "history": {
  "skeleton": "0^inf <C (10100111)^a 1 (110100)^2 1^6 (10100111)^751 (010011111)^2 (11010011)^23 (10100111)^2 0100 1^10 (01001111)^b 1 (10100)^2 1^c (10100111111)^2 (10100111)^198 0100 1^5 0^inf",
  "vars": [
   "a",
   "b",
   "c"
  ],
  "rows": [
   {
    "step": 94875591,
    "values": [
     9,
     247,
     2
    ]
   },
   {
    "step": 95374751,
    "values": [
     17,
     239,
     26
    ]
   },
   {
    "step": 95873911,
    "values": [
     25,
     231,
     50
    ]
   },
   {
    "step": 96373071,
    "values": [
     33,
     223,
     74
    ]
   },
   {
    "step": 96872231,
    "values": [
     41,
     215,
     98
    ]
   },
   {
    "step": 97371391,
    "values": [
     49,
     207,
     122
    ]
   },
   {
    "step": 97870551,
    "values": [
     57,
     199,
     146
    ]
   },
   {
    "step": 98369711,
    "values": [
     65,
     191,
     170
    ]
   },
   {
    "step": 98868871,
    "values": [
     73,
     183,
     194
    ]
   },
   {
    "step": 99368031,
    "values": [
     81,
     175,
     218
    ]
   },
   {
    "step": 99867191,
    "values": [
     89,
     167,
     242
    ]
   },
   {
    "step": 100366351,
    "values": [
     97,
     159,
     266
    ]
   },
   {
    "step": 100865511,
    "values": [
     105,
     151,
     290
    ]
   },
   {
    "step": 101364671,
    "values": [
     113,
     143,
     314
    ]
   },
   {
    "step": 101863831,
    "values": [
     121,
     135,
     338
    ]
   },
   {
    "step": 102362991,
    "values": [
     129,
     127,
     362
    ]
   },
   {
    "step": 102862151,
    "values": [
     137,
     119,
     386
    ]
   },
   {
    "step": 103361311,
    "values": [
     145,
     111,
     410
    ]
   },
   {
    "step": 103860471,
    "values": [
     153,
     103,
     434
    ]
   },
   {
    "step": 104359631,
    "values": [
     161,
     95,
     458
    ]
   },
   {
    "step": 104858791,
    "values": [
     169,
     87,
     482
    ]
   },
   {
    "step": 105357951,
    "values": [
     177,
     79,
     506
    ]
   },
   {
    "step": 105857111,
    "values": [
     185,
     71,
     530
    ]
   },
   {
    "step": 106356271,
    "values": [
     193,
     63,
     554
    ]
   },
   {
    "step": 106855431,
    "values": [
     201,
     55,
     578
    ]
   },
   {
    "step": 107354591,
    "values": [
     209,
     47,
     602
    ]
   },
   {
    "step": 107853751,
    "values": [
     217,
     39,
     626
    ]
   },
   {
    "step": 108352911,
    "values": [
     225,
     31,
     650
    ]
   },
   {
    "step": 108852071,
    "values": [
     233,
     23,
     674
    ]
   },
   {
    "step": 109351231,
    "values": [
     241,
     15,
     698
    ]
   },
   {
    "step": 109850391,
    "values": [
     249,
     7,
     722
    ]
   },
   {
    "step": 110287156,
    "values": [
     256,
     0,
     743
    ]
   }
  ]
 },
 "rules": [
  {
   "name": "RS right sweep",
   "from": "111 A> (01001111)^n",
   "to": "111 (01110111)^n A>",
   "steps": "20n",
   "cases": "any left and right context (random words up to 12 cells), n = 0..40",
   "validated": {
    "instances": 80,
    "passed": 80
   },
   "source": "manual"
  },
  {
   "name": "LS left sweep",
   "from": "(01110111)^n 0 <B",
   "to": "0 <B (01001111)^n",
   "steps": "40n",
   "cases": "any context. RS leaves the blocks in place as (0111)^2, which is 4-periodic, and LS reads them back 4 cells off, so a full pass moves the sea by -3 cells (= +5 mod 8); seams move +5 cells per cycle",
   "validated": {
    "instances": 80,
    "passed": 80
   },
   "source": "manual"
  },
  {
   "name": "LT left turn",
   "from": "0^inf <B",
   "to": "0^inf 111 A>",
   "steps": "5",
   "cases": "any right context; the left edge gains 3 cells per cycle",
   "validated": {
    "instances": 80,
    "passed": 80
   },
   "source": "manual"
  },
  {
   "name": "RO ones",
   "from": "A> 1^n",
   "to": "1^n A>",
   "steps": "n",
   "cases": "A1 = 1RA; any context",
   "validated": {
    "instances": 80,
    "passed": 80
   },
   "source": "manual"
  },
  {
   "name": "Q quiet epoch",
   "from": "0^inf <C (10100111)^a 1 (110100)^2 1^6 (10100111)^d (010011111)^2 (11010011)^e (10100111)^2 0100 1^10 (01001111)^b 1 (10100)^2 1^c (10100111111)^2 (10100111)^f 0100 1^5 0^inf",
   "to": "same with a+1, b-1, c+3",
   "steps": "60(a+b+d+e)+595",
   "cases": "a, b, c, d, e, f >= 1 independent (random a <= 60, b <= 40, c <= 120, d <= 40, e <= 30, f <= 40); c and f are never read. Also 247/247 consecutive cycles from blank, 9.49e7..1.10e8 (d = 751, e = 23, f = 198), ending at b = 0",
   "validated": {
    "instances": 80,
    "passed": 80
   },
   "source": "manual"
  },
  {
   "name": "H halting pattern",
   "from": "11 0 <C",
   "to": "halt",
   "steps": "3",
   "cases": "the only halt: F1 is undefined, F is entered only by E1 (0LF), and E reads a 1 with a 1 to its left only after C0 (1LE). So the machine halts iff C reads 0 with 11 on its left",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  }
 ],
 "template": {
  "file": "Bouncer_v2.v",
  "module": "TM1",
  "machine": "1RB0LB_1RC0LC_1LD1RF_---1LE_0RC1LA_0RB1RA",
  "diff": null,
  "applies": "no",
  "note": "No proved neighbour within 3 transitions (any start); Bouncer_v2 is the nearest proof by class. It proves S1 n -> S1 (1+n) with one es' call after 4,760,139 steps: the tape becomes a fixed word list with two blocks repeated 1+n times. Ours never settles into one S1: seams and fossil segments keep appearing (22 freezes to 2e9). Q is the analogue of BigStep only inside one epoch."
 },
 "strategy": "Collect the seam words and their collisions (seam meets wall, b = 0, freeze), then look for a tape language (u-runs separated by seams from a finite set) that one cycle maps into itself and that excludes 11 0 <C. Prove it CTL-style, with RS/LS/Q as the inside-epoch lemmas.",
 "risks": [
  "The seam set may be infinite: distinct seam words between u-runs keep growing (170 at 1e6, 526 at 1e8, 800 at 1e9, 829 at 2e9; crude count).",
  "Freeze sizes look irregular (9, 20, 12, 41, ... 2483, 29, 2535); if they come from arithmetic on reservoir sizes, this is cryptid-like.",
  "61 and 704 share the table and the u-sea but run different orbits; one proof covers them only if it is a language-closure proof."
 ],
 "checkpoint_questions": [
  {
   "text": "Segment map: does it read as one bouncer whose wall (green) walks left leaving grey 1-deposits, with red seams riding right into it?",
   "figs": [
    1
   ],
   "kind": "check"
  },
  {
   "text": "One cycle of Q: a fast right sweep, a turn at the 1 (10100)^2 wall and a slower left sweep, with nothing right of the turn changed?",
   "figs": [
    2
   ],
   "kind": "check"
  },
  {
   "text": "Fund one stage to map the seam words and test a closed tape language, or park W4-8 as STUCK at observe?",
   "kind": "decision"
  }
 ],
 "discord_check": null,
 "stats": {
  "simulated_steps": 2000000000,
  "cells": 31819,
  "nonzeros": 22003,
  "growth": "left edge ~ t^0.5 (lo = -30659 at 1e9, -43525 at 1.9e9); right edge grows only in bursts (hi = 1159 at 1e9, 1219 at 1.9e9); no halt to 2e9"
 },
 "status": "CHECKPOINT_A",
 "status_reason": "Observe done at low confidence: quiet-epoch rule Q and the sweep rules are validated, but the epoch changes (seams meeting the wall, reservoir freezes) are not understood, so there is no non-halting argument yet."
}