{
 "tm": "1RB1RC_1LC1LE_1RD0RA_1LB0RA_0LD1LF_1LD---",
 "rank": 75,
 "class_sheet": "Skelet 1-like Class 1",
 "class_guess": "Skelet 1-like: binary counter whose digits are field parities, with re-pairing bounces",
 "confidence": "high",
 "summary": "Binary counter on budget fields (10)^f 1; parities are the digits; dead fields re-pair; no halt to 2.37e14.",
 "mechanism": [
  "At every D:R event the tape is a list of fields [f]=(10)^f 1 joined by separators | (00), + (11) or # (000); the last field L is the growing end.",
  "Each half-cycle the head walks left over even fields to the first odd field (or a + or #), takes 1 from the field just left of it and adds 3 to L: the field parities are the digits of a binary counter (ruler sequence).",
  "A field that reaches 0 becomes a # separator; the next carry into it is a uniform re-pairing bounce (+2 to the field right of it, +1 to the rest, all separators +, new L = 1). A carry past the far end is the same bounce for the whole tape. Exact simulator: no halt to 2.367e14; the 4 starts share every event and differ only in the first field."
 ],
 "diagrams": [
  {
   "mode": "default",
   "png": "img/default_site_1e4.png",
   "html": null,
   "steps": 10000,
   "caption": "bbchallenge default view, first 10,000 steps",
   "title": "Default view, first 10,000 steps",
   "why": "The site's picture: striped (10) fields; the far-left resets of the first 10^4 steps settle into right-end growth.",
   "primary": false,
   "start": "blank",
   "rows": "every step; 10,000 steps squeezed into 500 rows (site canvas)",
   "window": "cells -200..199, 1 px = 1 cell",
   "legend": "white = 1, black = 0, red/green = head moving R/L",
   "style": "bbchallenge-default"
  },
  {
   "mode": "custom",
   "png": "img/counter_parity_3e8.png",
   "html": null,
   "steps": 128,
   "caption": "128 half-cycles of the field counter at 3e8",
   "title": "The field counter, 128 half-cycles",
   "why": "One row per half-cycle; columns are the 14 fields. Follow one column: when does it change colour?",
   "primary": true,
   "start": "mid-run: step 300,021,233 (token list of line 75 at a D:R event)",
   "rows": "one 3 px row per half-cycle (D:R to next D:R), 128 half-cycles",
   "window": "cells 1..14, 1 px = 0.083 cells (a 'cell' here is one field f_i, 12 px wide; not tape cells)",
   "legend": "grey = odd field, white = even field, red = field that loses 1 this half-cycle, green = last field L (+3 each row), black = | separator, blue = + separator",
   "style": "custom"
  },
  {
   "mode": "default",
   "png": "img/rule_odd_constructed.png",
   "html": null,
   "steps": 1040,
   "caption": "Seven half-cycles from fields 9|6|5|8|4",
   "title": "Seven half-cycles, constructed fields",
   "why": "Each V is one half-cycle: the head turns just past the first odd field; the right edge grows.",
   "primary": false,
   "start": "constructed: 0^inf (10)^9 1 00 (10)^6 1 00 (10)^5 1 00 (10)^8 1 00 (10)^4 1 00 11 D> 0^inf",
   "rows": "every step, 1,040 steps (7 half-cycles: 9|6|5|8|4 -> 8|5|3|5|25)",
   "window": "cells -94..15, 1 px = 1 cell",
   "legend": "white = 1, black = 0, red/green = head moving R/L",
   "style": "bbchallenge-default"
  },
  {
   "mode": "default",
   "png": "img/death_repair_constructed.png",
   "html": null,
   "steps": 722,
   "caption": "A 0-field dies, then the re-pairing bounce",
   "title": "Death and re-pairing, constructed",
   "why": "Watch the third field (0): its gap widens, its left neighbour shrinks once, then one long V.",
   "primary": true,
   "start": "constructed: 0^inf (10)^7 1 00 (10)^6 1 00 1 00 (10)^5 1 00 (10)^4 1 00 11 D> 0^inf",
   "rows": "every step, 722 steps (7|6|0|5|4 -> 7|6#5|7 -> .. -> 7|5+5+17|1 -> 7|5+3|16|7)",
   "window": "cells -84..15, 1 px = 1 cell",
   "legend": "white = 1, black = 0, red/green = head moving R/L",
   "style": "bbchallenge-default"
  }
 ],
 "history": {
  "skeleton": "0^inf [f_1] s_1 [f_2] ... s_{k-1} [f_k] 00 11 D> 0^inf,  [f] = (10)^f 1,  s in {| = 00, + = 11-join, # = 000}",
  "vars": [
   "fields k",
   "far-end prefix + first field",
   "L = f_k",
   "max field",
   "cells"
  ],
  "rows": [
   {
    "step": 1000003379,
    "values": [
     13,
     "25",
     16639,
     16639,
     81673
    ]
   },
   {
    "step": 10000057453,
    "values": [
     16,
     "1 + 20",
     51508,
     51508,
     266748
    ]
   },
   {
    "step": 100000835151,
    "values": [
     19,
     "1 + 1 + 16",
     73819,
     132074,
     908321
    ]
   },
   {
    "step": 1000005709393,
    "values": [
     19,
     "1 + 10",
     231499,
     443941,
     2884505
    ]
   },
   {
    "step": 10000006342829,
    "values": [
     20,
     "8",
     174283,
     2072876,
     8834812
    ]
   },
   {
    "step": 100000020965165,
    "values": [
     24,
     "1 + 1 + 5",
     5027266,
     5027266,
     26899366
    ]
   },
   {
    "step": 236695882593413,
    "values": [
     24,
     "1 + 0 | 2",
     8737531,
     8737531,
     39300840
    ]
   }
  ]
 },
 "rules": [
  {
   "name": "ODD",
   "from": ".. f_d | f_j(odd) | e .. | L  (all fields right of f_j even)",
   "to": ".. (f_d - 1) | f_j | e .. | (L + 3)",
   "steps": "6S + 12n + 12 (S, n = sum, count of f_j..L)",
   "cases": "f_d >= 1 (1 -> 0 included); separator left of f_d is | or +",
   "validated": {
    "instances": 665,
    "passed": 665
   },
   "source": "manual"
  },
  {
   "name": "PLUS",
   "from": ".. f + e_j | e .. | L  (e = even)",
   "to": ".. (f - 2) | e_j | e .. | (L + 3)",
   "steps": "6S + 12n + 10",
   "cases": "f >= 3",
   "validated": {
    "instances": 300,
    "passed": 300
   },
   "source": "manual"
  },
  {
   "name": "death",
   "from": "a | 0 | b(odd) | e ..",
   "to": "a # b | e .. (L + 3)",
   "steps": "6S + 12n + 12",
   "cases": null,
   "validated": {
    "instances": 150,
    "passed": 150
   },
   "source": "manual"
  },
  {
   "name": "death-merge",
   "from": "a + 0 | b(odd) | e ..",
   "to": "(a + b + 1) | e .. (L + 3)",
   "steps": "6S + 12n + 12",
   "cases": null,
   "validated": {
    "instances": 150,
    "passed": 150
   },
   "source": "manual"
  },
  {
   "name": "hash-odd",
   "from": "a # e | .. | L",
   "to": "(a - 1) # e | .. | (L + 3)",
   "steps": "6S + 12n + 18",
   "cases": null,
   "validated": {
    "instances": 150,
    "passed": 150
   },
   "source": "manual"
  },
  {
   "name": "hash-bounce (re-pairing + birth)",
   "from": "a # b(odd) | e_1 | .. | e_m",
   "to": "a + (b+2) + (e_1+1) + .. + (e_m+1) | 1",
   "steps": "6S + 6n + 28",
   "cases": null,
   "validated": {
    "instances": 150,
    "passed": 150
   },
   "source": "manual"
  },
  {
   "name": "overflow-even (far end)",
   "from": "e_1 | .. | e_m  (all even)",
   "to": "1 + (e_1+1) + .. + (e_m+1) | 1",
   "steps": "6S + 6n + 28",
   "cases": null,
   "validated": {
    "instances": 150,
    "passed": 150
   },
   "source": "manual"
  },
  {
   "name": "overflow-odd (far end)",
   "from": "o | e_2 | .. | e_m",
   "to": "(o+2) + (e_2+1) + .. + (e_m+1) | 1",
   "steps": "6S + 6n + 28",
   "cases": null,
   "validated": {
    "instances": 150,
    "passed": 150
   },
   "source": "manual"
  },
  {
   "name": "ODD-across-plus",
   "from": "d + j(odd) | e ..",
   "to": "(d - 1) | (j - 1) | e .. (L + 3)",
   "steps": "6S + 12n + 8",
   "cases": "d >= 2 (d = 1 at the far end: 1 + j -> 0 | j-1)",
   "validated": {
    "instances": 150,
    "passed": 150
   },
   "source": "manual"
  }
 ],
 "template": {
  "file": "machines/1RB0LD_1RC0RA_1RD1RF_1LA0LE_1RE1LD_0RB---/1RB0LD_1RC0RA_1RD1RF_1LA0LE_1RE1LD_0RB---.v",
  "module": null,
  "machine": "1RB0LD_1RC0RA_1RD1RF_1LA0LE_1RE1LD_0RB---",
  "diff": "#3: explicit digit blocks s(d) on (10)^p (01)^q pairs; here the digits are field parities, 3 separator kinds (| + #), far-end prefixes, births at every bounce",
  "applies": "partly",
  "note": "Our kill #3 (Skelet 1-like Class 2): same architecture (one macro rule per decrement, merges, re-pairing overflow, per-step invariant J). Upstream Sk1Machines.v / Sk1like_TC_v*.v (mxdys) use other digit words: not templates."
 },
 "strategy": "Prove a token-level invariant INV (allowed local patterns, budgets of the fields next to # and +, far-end prefix set) closed under the 9 validated rules plus the far-end table; nonhalting follows. One argument for the table; 179/265/597 are #24-style deltas (own base segment into the same family, first field as a parameter).",
 "risks": [
  "The global invariant is open: 255 of 4,000 random tiny token lists halt, so INV must exclude bad local patterns for all field values.",
  "Far-end prefix set looks small (about 10 shapes in 35 x 12 hand-built deaths) but is not shown closed; line 75's natural far-end death is due just after 2.4e14.",
  "The case table (9 rules plus far-end variants) is larger than #3's; the formal stage may exceed 1 agent-day."
 ],
 "checkpoint_questions": [
  {
   "text": "Counter figure: in every row exactly one non-green column is red, and each column switches grey/white only in its red rows (so field parity = counter digit)?",
   "figs": [
    1
   ],
   "kind": "check"
  },
  {
   "text": "Death figure: the 0-field's gap widens into one wider gap, the field left of it shrinks once, and then one long V re-groups every field to its right and starts a new short field at the right end?",
   "figs": [
    3
   ],
   "kind": "check"
  },
  {
   "text": "Before proof.md on #3's route, should we spend 2 h on an abstract closure search (fields as {0,1,2,>=3} x parity, separators | + #, far-end prefixes)? If it closes, it is the invariant and a regular-certificate attempt for all 4 lines.",
   "figs": [],
   "kind": "decision"
  }
 ],
 "discord_check": null,
 "stats": {
  "simulated_steps": 236695882593413,
  "cells": 39300840,
  "nonzeros": null,
  "growth": "span 82k at 1e9, 267k at 1e10, 2.9M at 1e12, 8.8M at 1e13, 39M at 2.4e14 (exact accelerated simulator); direct C runs to 1e10 on all 4 strings"
 },
 "status": "CHECKPOINT_A",
 "status_reason": "Mechanism found and validated; not a cryptid stop (affine events, parity = binary-counter digit). Stage 1 continues: invariant / closure for proof.md."
}