{
 "tm": "1RB1LC_1RC1LB_1LD0RB_0LE1RD_---0LF_0LA1LF",
 "rank": 12,
 "class_sheet": "Counter Class 4",
 "class_guess": "Counter Class 4: recursive run-length counter (self-similar epochs, time doubles per epoch)",
 "confidence": "med",
 "summary": "Run-length counter: epochs double in time, 2 passenger marker 1s; 9 rules validated, inner invariant open",
 "mechanism": [
  "Tape = runs of 1s. R1: pointer A moves one run right; a 1 moves from its old run to the run past the 00 gap.",
  "R2: A on a lone 1 merges it left and jumps 2 runs back; R3 grows the left edge. Halt needs 0^inf 1 <A: never seen.",
  "Epochs: short (40k+288 steps), then long (~1260*2^k): run 1 counts 2k+1 -> 1, each tick a doubling mini-epoch."
 ],
 "diagrams": [
  {
   "mode": "blaze",
   "png": "img/blaze_1e7.png",
   "html": null,
   "steps": 10000000,
   "caption": "Blaze 1e7: each epoch twice as long",
   "title": "Blaze view, 10 million steps",
   "why": "Blaze view, time runs down. Find each row where the left edge steps out, and compare the gaps between them.",
   "primary": true,
   "start": "blank",
   "rows": "Blaze time blocks of 16,384 steps (611 rows, each averaged), stretched to 500 px (1 px ~ 20,000 steps); epochs start near y = 32, 64, 129, 258 px",
   "window": "cells -58..33, 1 px = 0.115 cells (1 cell = 8.7 px)",
   "legend": "white = 0, orange = 1; pale orange = a cell that is 1 for part of its time block",
   "style": "bbchallenge-blaze"
  },
  {
   "mode": "blaze",
   "png": "img/blaze_long_epoch_k8.png",
   "html": null,
   "steps": 321732,
   "caption": "Real k=8 long epoch: r1 counts 17 to 1, waits doubling",
   "title": "Zoom: one long epoch (k = 8)",
   "why": "One long epoch (k = 8), time runs down. Find each step where the long left block (run 1) shrinks.",
   "primary": true,
   "start": "mid-run: step 320,794, Fl(8,10) = 0^inf <A 0 1^3 0^2 1^17 0^2 1^19 0^2 1 0^10 1 0^6 1 0^inf (head at cell -42)",
   "rows": "Blaze time blocks of 512 steps (629 rows, each averaged), steps 320,794..642,526 (ends at Fs(9,4)), stretched to 500 px; r1 loses cells near y = 31, 62, 125, 250, 499 px",
   "window": "cells -43..27, 1 px = 0.089 cells (1 cell = 11.3 px)",
   "legend": "white = 0, orange = 1; pale orange = a cell that is 1 for part of its time block",
   "style": "bbchallenge-blaze"
  },
  {
   "mode": "records",
   "png": "img/records_1e9.png",
   "html": null,
   "steps": 1000000000,
   "caption": "Row per new edge cell to 1e9; right: two lone marker 1s",
   "title": "Edge records to 1 billion steps",
   "why": "Edge records to 1e9 (only 134 rows). Look at the two thin white lines in the black right half.",
   "primary": true,
   "start": "blank",
   "rows": "the start, then one per new leftmost or rightmost cell (134 rows, steps 0..660,597,554; no new cell from there to 1e9); not evenly spaced in time",
   "window": "cells -86..47, 1 px = 0.25 cells (1 cell = 4 px)",
   "legend": "white = 1, black = 0, green/red = head at a new left/right edge; right-edge rows catch the tape mid-epoch (the long white bars)",
   "style": "bbchallenge-default"
  },
  {
   "mode": "default",
   "png": "img/default_site.png",
   "html": "img/viewer.html",
   "steps": 10000,
   "caption": "Site view: zig-zag sweeps over runs of 1s",
   "title": "bbchallenge Default view, first 10,000 steps",
   "why": "For orientation: zig-zag sweeps over runs of 1s, as bbchallenge.org shows them.",
   "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 <A 0 1^3 0^2 1^2 0^2 1^(2k) 0^2 1^(2k+1) 0^P 1 0^Q 1 0^inf",
  "vars": [
   "k",
   "P",
   "Q"
  ],
  "rows": [
   {
    "step": 1590,
    "values": [
     1,
     "D",
     "D"
    ]
   },
   {
    "step": 4090,
    "values": [
     2,
     2,
     2
    ]
   },
   {
    "step": 8806,
    "values": [
     3,
     "D",
     "D"
    ]
   },
   {
    "step": 18826,
    "values": [
     4,
     2,
     6
    ]
   },
   {
    "step": 38730,
    "values": [
     5,
     6,
     4
    ]
   },
   {
    "step": 78838,
    "values": [
     6,
     4,
     8
    ]
   },
   {
    "step": 159230,
    "values": [
     7,
     4,
     10
    ]
   },
   {
    "step": 320186,
    "values": [
     8,
     10,
     6
    ]
   },
   {
    "step": 642526,
    "values": [
     9,
     4,
     14
    ]
   },
   {
    "step": 1287310,
    "values": [
     10,
     8,
     12
    ]
   },
   {
    "step": 2577198,
    "values": [
     11,
     12,
     10
    ]
   },
   {
    "step": 5157430,
    "values": [
     12,
     4,
     20
    ]
   },
   {
    "step": 10317966,
    "values": [
     13,
     12,
     14
    ]
   },
   {
    "step": 20639446,
    "values": [
     14,
     20,
     8
    ]
   },
   {
    "step": 41282870,
    "values": [
     15,
     24,
     6
    ]
   },
   {
    "step": 82570218,
    "values": [
     16,
     18,
     14
    ]
   },
   {
    "step": 165145050,
    "values": [
     17,
     30,
     4
    ]
   },
   {
    "step": 330295486,
    "values": [
     18,
     16,
     20
    ]
   },
   {
    "step": 660596506,
    "values": [
     19,
     14,
     24
    ]
   },
   {
    "step": 1321198810,
    "values": [
     20,
     26,
     14
    ]
   },
   {
    "step": 2642404258,
    "values": [
     21,
     10,
     32
    ]
   },
   {
    "step": 5284815110,
    "values": [
     22,
     28,
     16
    ]
   },
   {
    "step": 10569637546,
    "values": [
     23,
     38,
     8
    ]
   },
   {
    "step": 21139283246,
    "values": [
     24,
     24,
     24
    ]
   },
   {
    "step": 42278575038,
    "values": [
     25,
     "D",
     "D"
    ]
   },
   {
    "step": 84557158858,
    "values": [
     26,
     2,
     50
    ]
   }
  ]
 },
 "rules": [
  {
   "name": "R1 pointer right",
   "from": "1^(n+2) <A 0 1^(m+1) 0^2 1^x 0",
   "to": "1^(n+1) 0 1^(m+1) <A 0 1^(x+1) 0^2",
   "steps": "3m+2x+15",
   "cases": "n,m,x>=0; x=0 covers 0^3 and 0^inf after the 00",
   "validated": {
    "instances": 60,
    "passed": 60
   },
   "source": "manual"
  },
  {
   "name": "R2 lone 1 merges, jump back",
   "from": "1^(j+1) 0 1^(k+1) 0 1 <A 0",
   "to": "1^(j+1) <A 0 1^(k+2) 0^2",
   "steps": "k+10",
   "cases": "j,k>=0",
   "validated": {
    "instances": 60,
    "passed": 60
   },
   "source": "manual"
  },
  {
   "name": "R2e jump to edge",
   "from": "0^inf 1^(k+1) 0 1 <A 0",
   "to": "0^inf <A 0 1^(k+2) 0^2",
   "steps": "k+10",
   "cases": "k>=0",
   "validated": {
    "instances": 60,
    "passed": 60
   },
   "source": "manual"
  },
  {
   "name": "R3 edge refill",
   "from": "0^inf <A 0 1^(k+1) 0^2 1^m 0",
   "to": "0^inf 1^(k+2) <A 0 1^(m+1) 0^2",
   "steps": "3k+2m+11",
   "cases": "k,m>=0",
   "validated": {
    "instances": 60,
    "passed": 60
   },
   "source": "manual"
  },
  {
   "name": "HALT",
   "from": "0^3 1 <A 0",
   "to": "halt",
   "steps": "4 (incl. halting transition)",
   "cases": "only halting route; needs a lone 1 at the far left",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "short epoch",
   "from": "Fs(k,P) = 0^inf <A 0 1^3 0^2 1^2 0^2 1^(2k) 0^2 1^(2k+1) 0^P 1 0^Q 1 0^inf, P+Q=2k",
   "to": "Fl(k,P) = 0^inf <A 0 1^3 0^2 1^(2k+1) 0^2 1^(2k+3) 0^2 1 0^P 1 0^Q 1 0^inf",
   "steps": "40k+288",
   "cases": "P,Q even >=2 (k up to 200 tested)",
   "validated": {
    "instances": 24,
    "passed": 24
   },
   "source": "manual"
  },
  {
   "name": "long epoch",
   "from": "Fl(k,P)",
   "to": "Fs(k+1,P') with P' even, 2<=P'<=2k; or D(k+1)",
   "steps": "~1260*2^k (+-200, depends on P)",
   "cases": "P' irregular in (k,P), e.g. k=11: P 2,4,6,8,10,12 -> 6,8,10,16,D,4. Macro model: every even P for k<=13 closes with no halt",
   "validated": {
    "instances": 22,
    "passed": 22
   },
   "source": "manual"
  },
  {
   "name": "degenerate D",
   "from": "D(k) = 0^inf <A 0 1^3 0^2 1^2 0^2 1^(2k+2) 0^2 1^(2k+1) 0^inf",
   "to": "E(k) = 0^inf <A 0 1^3 0^2 1^(2k+3) 0^2 1^(2k+3) 0^2 1 0^inf",
   "steps": "40k+312",
   "cases": "k>=3",
   "validated": {
    "instances": 8,
    "passed": 8
   },
   "source": "manual"
  },
  {
   "name": "E back to family",
   "from": "E(k)",
   "to": "Fs(k+1,2)",
   "steps": "~1260*2^k",
   "cases": "k=3..10; the real orbit takes D at k=25 (step 4.2e10), then E, then Fs(26,2)",
   "validated": {
    "instances": 8,
    "passed": 8
   },
   "source": "manual"
  }
 ],
 "template": {
  "file": "verify/CounterClass2v1.v",
  "module": null,
  "machine": "1RB1RD_1LC---_1LE0LD_0RE1LC_1RA1RF_1RE0LF",
  "diff": "10/12 transitions differ (best renaming+mirror); CounterClass3v2 8/12, closest CounterClass1 machine 8/12",
  "applies": "no",
  "note": "No rules or shapes carry over: 7 of 16 CC2v1 starting shapes (SkelE/Be) halt on this machine. What does carry over is the proof skeleton: an Inductive Side type, a Good invariant and progress_nonhalt_cond."
 },
 "strategy": "Level 1: prove R1/R2/R2e/R3 with es plus shift rules (C> 1^n, D>, <F sweeps) and induction on run lengths. Level 2: copy the CounterClass2v1 pattern, with epoch starts Fs/Fl/D/E as an Inductive state with P existential, a Good invariant and progress_nonhalt_cond. Open: an invariant for the long epoch's right side that does not depend on P.",
 "risks": [
  "The inner invariant for the long epoch is not found yet. The right side is a recursive mini-counter, likely CC2v1-sized (~100 KB).",
  "The P->P' marker map is irregular, so the proof must work for every even P, plus the degenerate D branch.",
  "Untouched class with no Counter Class 4 precedent. The twin (6 transitions away) needs its own instance."
 ],
 "checkpoint_questions": [
  {
   "text": "Fig 1: does each epoch (between two outward steps of the left edge) last about twice as long as the one before?",
   "figs": [
    0
   ]
  },
  {
   "text": "Fig 2: does the long left block shrink in steps whose spacing doubles each time (one countdown tick per doubling inner epoch)?",
   "figs": [
    1
   ]
  },
  {
   "text": "Fig 3: are the two thin white lines in the black right half just passengers: lone 1s that move but never grow?",
   "figs": [
    2
   ]
  }
 ],
 "discord_check": "see reports/discord-drafts.md message 1",
 "stats": {
  "simulated_steps": 100000000000,
  "cells": 176,
  "nonzeros": 116,
  "growth": "log: span ~ 4*log2(t) (+4 cells per epoch pair, epoch time x2); 134 cells at 1e9, 176 at 1e11"
 },
 "status": "CHECKPOINT_A",
 "status_reason": "Mechanism found at two levels with 9 validated rules. No sign that anyone is working on it (sheet status blank, no Discord mention). Halting does not depend on the irregular marker positions (every even P tested closes), so this is not a cryptid."
}