{
 "tm": "1RB0RD_0LC0RA_1LA1LC_1RE0LF_0RA1RF_1LB---",
 "rank": 274,
 "class_sheet": "Skelet 1-like Class 1",
 "class_guess": "Base-4 counter: fixed 4-phase digit words in a 100 sea; births at the right end, a zero-field cluster at the left wall",
 "confidence": "high",
 "summary": "Exact base-4 counter on fixed digit words in a 100 sea; both starts follow one rule set; no halt to 1e16.",
 "mechanism": [
  "At every D-record the tape is 0^inf [1100] P(p1) s^f1 ... P(pk) s^R 100 D> 0^inf, s = 100, digit words P0 = 11001100, P1 = 110000, P2 = 1001100, P3 = 10000. One sweep adds 1 from the right: 3s wrap to 0 (moving 2 cells left), the first lower digit steps up in place. Fields follow from positions; R grows 6 per 4 sweeps.",
  "Fields shrink 2 per cycle of their left digit and die; a digit whose field is 0 is pushed one word right instead of overlapping, so the oldest digits form a zero-field cluster at the left and keep counting. Overflows alternate the wall 1100 / none; every other one gives birth to a new digit P3 at the right end.",
  "Lines 274 and 514 (start F, mirrored) enter the same language by step 108 / 792 and differ only in one field (+4). Exact sweep simulator (rules + step formula) = C core at 1e11 on both; no halt to 1e16 on either."
 ],
 "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 own picture: a striped 100 sea growing to the right, head bouncing at the right edge.",
   "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": "every:2",
   "png": "img/sweeps_carry_closeup.png",
   "html": null,
   "steps": 950,
   "caption": "five counter sweeps; the first and last carry",
   "title": "Five counter sweeps, two carries",
   "why": "Each zigzag from the right edge is one sweep. Compare how far left each one turns before going back.",
   "primary": true,
   "start": "constructed: 0^inf 1100 110000 (100)^3 10000 (100)^4 10000 (100)^8 100 D> 0^inf",
   "rows": "every 2 steps, steps 0..950 (sweeps end at steps 300, 404, 568, 696, 916)",
   "window": "cells -68..23, 1 px = 1 cell (drawn at 3x)",
   "legend": "white = 1, black = 0, red/green = head moving R/L",
   "style": "bbchallenge-default"
  },
  {
   "mode": "custom:digitmap",
   "png": "img/digit_worldlines_1e9.png",
   "html": null,
   "steps": 1000000000,
   "caption": "digits as white lines, one row per 46 sweeps",
   "title": "Digit worldlines from blank to 1e9",
   "why": "Each white line is one digit. Find where new lines start at the right edge; follow them left.",
   "primary": true,
   "start": "blank",
   "rows": "every 46th D-record (sweep), sweeps 0..18,410, steps 108..998,798,918 (401 rows; time is linear in sweeps, not steps)",
   "window": "cells -40..73720, 1 px = 128 cells",
   "legend": "black = not yet visited, dark grey = 100 sea, white = digit word, orange = wall 1100, red = head at the right end",
   "style": "custom"
  },
  {
   "mode": "records:R",
   "png": "img/overflows_right_records.png",
   "html": null,
   "steps": 125000,
   "caption": "right-edge records, first 125,000 steps: two births",
   "title": "Births at the right edge",
   "why": "Rows are new rightmost cells (4 per sweep). Look for dark lines starting at the right edge.",
   "primary": true,
   "start": "blank",
   "rows": "right records (new rightmost cell, 4 per sweep), steps 0..125,000 (681 rows)",
   "window": "cells -18..680, 1 px = 1 cell",
   "legend": "white = 1, black = 0, red/green = head moving R/L",
   "style": "bbchallenge-default"
  },
  {
   "mode": "default",
   "png": "img/default_site_1e4_514.png",
   "html": null,
   "steps": 10000,
   "caption": "line 514 (start F): the mirror image",
   "title": "Line 514, default view",
   "why": "The same table started from F grows to the left: compare with Fig 1 mirrored.",
   "primary": false,
   "start": "blank",
   "rows": "every step; 10,000 steps squeezed into 500 rows (site canvas); machine 1RB---_0RC0LD_1RD1RC_1LB0LE_1LF0RA_0LD1LA",
   "window": "cells -200..199, 1 px = 1 cell",
   "legend": "white = 1, black = 0, red/green = head moving R/L",
   "style": "bbchallenge-default"
  }
 ],
 "history": {
  "skeleton": "overflow outputs: 0^inf [wall] P(p1) s^f1 ... P(pk) s^R 100 D> 0^inf (274, exact sweep simulator)",
  "vars": [
   "event",
   "digits",
   "wall",
   "cluster digits",
   "nonzero inner fields",
   "R"
  ],
  "rows": [
   {
    "step": 477,
    "values": [
     "O2",
     2,
     "1100",
     1,
     "3",
     2
    ]
   },
   {
    "step": 2529,
    "values": [
     "O1",
     2,
     "none",
     1,
     "1",
     21
    ]
   },
   {
    "step": 7910,
    "values": [
     "O2",
     3,
     "1100",
     2,
     "41",
     2
    ]
   },
   {
    "step": 39426,
    "values": [
     "O1",
     3,
     "none",
     2,
     "31",
     93
    ]
   },
   {
    "step": 119447,
    "values": [
     "O2",
     4,
     "1100",
     2,
     "20 187",
     2
    ]
   },
   {
    "step": 611635,
    "values": [
     "O1",
     4,
     "none",
     2,
     "10 155",
     381
    ]
   },
   {
    "step": 1874600,
    "values": [
     "O2",
     5,
     "1100",
     3,
     "122 763",
     2
    ]
   },
   {
    "step": 9688076,
    "values": [
     "O1",
     5,
     "none",
     3,
     "80 635",
     1533
    ]
   },
   {
    "step": 29808277,
    "values": [
     "O2",
     6,
     "1100",
     3,
     "37 507 3067",
     2
    ]
   },
   {
    "step": 154568141,
    "values": [
     "O1",
     6,
     "none",
     4,
     "374 2555",
     6141
    ]
   },
   {
    "step": 476169214,
    "values": [
     "O2",
     7,
     "1100",
     4,
     "203 2043 12283",
     2
    ]
   },
   {
    "step": 2471212970,
    "values": [
     "O1",
     7,
     "none",
     4,
     "33 1531 10235",
     24573
    ]
   },
   {
    "step": 7615621471,
    "values": [
     "O2",
     8,
     "1100",
     5,
     "881 8187 49147",
     2
    ]
   },
   {
    "step": 39531956819,
    "values": [
     "O1",
     8,
     "none",
     5,
     "199 6139 40955",
     98301
    ]
   },
   {
    "step": 121837780040,
    "values": [
     "O2",
     9,
     "1100",
     6,
     "3607 32763 196603",
     2
    ]
   },
   {
    "step": 632482087556,
    "values": [
     "O1",
     9,
     "none",
     6,
     "877 24571 163835",
     393213
    ]
   },
   {
    "step": 1949357337161,
    "values": [
     "O2",
     10,
     "1100",
     7,
     "14525 131067 786427",
     2
    ]
   },
   {
    "step": 10119599654349,
    "values": [
     "O1",
     10,
     "none",
     7,
     "3603 98299 655355",
     1572861
    ]
   },
   {
    "step": 31189536436514,
    "values": [
     "O2",
     11,
     "1100",
     8,
     "58211 524283 3145723",
     2
    ]
   },
   {
    "step": 161913153642990,
    "values": [
     "O1",
     11,
     "none",
     8,
     "14521 393211 2621435",
     6291453
    ]
   },
   {
    "step": 499031892364995,
    "values": [
     "O2",
     12,
     "1100",
     9,
     "232969 2097147 12582907",
     2
    ]
   },
   {
    "step": 2590608754398423,
    "values": [
     "O1",
     12,
     "none",
     9,
     "58207 1572859 10485755",
     25165821
    ]
   },
   {
    "step": 7984507652620524,
    "values": [
     "O2",
     13,
     "1100",
     10,
     "932015 8388603 50331643",
     2
    ]
   }
  ]
 },
 "rules": [
  {
   "name": "R1 increment",
   "from": "P(p) s^R 100 D>  (p = 0, 1, 2)",
   "to": "P(p+1) s^(R+2) 100 D>  (R+1 for p = 1)",
   "steps": "8R + 32 (p = 0, 2) or 8R + 76 (p = 1)",
   "cases": "p = 0, 1, 2; the digit stays in place",
   "validated": {
    "instances": 215658,
    "passed": 215658
   },
   "source": "manual"
  },
  {
   "name": "R2 carry",
   "from": "P(q) s^f P(3)^j-chain s^R 100 D>  (q < 3)",
   "to": "P(q+1) s^(f - [q=1]) P(0)^j-chain s^(R+1) 100 D>",
   "steps": "8(R + fields crossed) + 52 per wrapping digit + 32 or 76 (stop digit q = 1) + 20 per push word",
   "cases": "each wrapped digit moves 2 cells left and its right field loses 1; q = 1 also costs its right field 1",
   "validated": {
    "instances": 72019,
    "passed": 72019
   },
   "source": "manual"
  },
  {
   "name": "PUSH (zero field)",
   "from": "P(a) s^0 P(b) with the field due to go to -1",
   "to": "P(a') s^0 P(b') with P(b') one word further right; its right field pays 1",
   "steps": "+20 per pushed word",
   "cases": "cascades through runs of zero fields",
   "validated": {
    "instances": 3156,
    "passed": 3156
   },
   "source": "manual"
  },
  {
   "name": "O1 overflow, wall leaves",
   "from": "0^inf 1100 P(3)...P(3) s^R 100 D>",
   "to": "0^inf P(0)...P(0) s^(R+1) 100 D>  (after pushes)",
   "steps": "8(R + all fields) + 52k + 32 + 20 per push word",
   "cases": "k digits, any fields",
   "validated": {
    "instances": 2858,
    "passed": 2858
   },
   "source": "manual"
  },
  {
   "name": "O2 overflow, wall + birth",
   "from": "0^inf P(3)...P(3) s^R 100 D>  (R >= 2k+2)",
   "to": "0^inf 1100 P(0)...P(0) s^R' P(3) s^2 100 D>  (every digit 2 more cells left)",
   "steps": "10(R + all fields) + 50k + 101 + 20 per push word",
   "cases": "k digits, any fields; R' = R + 1 - push words",
   "validated": {
    "instances": 2315,
    "passed": 2315
   },
   "source": "manual"
  }
 ],
 "template": {
  "file": "Sk1Machines.v",
  "module": "Sk1Counter / Sk1CounterMixed",
  "machine": null,
  "diff": "W = 100 here; digit words of 8/6/7/5 cells; wraps shift 2 cells; zero-field pushes; O2 extra pass",
  "applies": "partly",
  "note": "Same take/give/carry digit-counter shape with fixed-size digit words, but the 2-cell wrap shift needs a re-cut of the words, the Sk1 batch rule excludes zero-field pushes, and the O2 overflow adds a full extra pass. Closest own kills: #30/#7 counter route; W7-4 shares the sea and the wall/birth cycle but not the digit law."
 },
 "strategy": "One closed-language proof: sea-crossing lemmas, 4-phase digit lemmas (stop/wrap), a push lemma by induction over zero-field runs, the two overflow lemmas, and an invariant giving R >= 2k+2 at every O2; then entry lemmas for 274 (108 steps) and 514 (792 steps).",
 "risks": [
  "The push cascade and O2's extra pass need inductive segment lemmas; that is new formal work beyond Sk1CounterMixed.",
  "The domain condition (room at O2) counts, so a pure regular-language certificate is unlikely without extra structure.",
  "Scoop risk: Skelet 1-like Class 1 is mxdys's mined class (Sk1Machines.v TM1..TM105 list)."
 ],
 "checkpoint_questions": [
  {
   "text": "Close-up: does each zigzag stop at the first digit that is not at its last phase, and do the two long ones carry? (sweeps_carry_closeup.png)",
   "figs": [
    1
   ],
   "kind": "check"
  },
  {
   "text": "Worldlines: do new digits start only at the right edge, about every other overflow, and drift left until they join the cluster? (digit_worldlines_1e9.png)",
   "figs": [
    2
   ],
   "kind": "check"
  }
 ],
 "discord_check": null,
 "stats": {
  "simulated_steps": 10000000405212800,
  "cells": 642934,
  "nonzeros": 214315,
  "growth": "direct C core: span 73,697 at 1e9 and 642,933 at 1e11 (274); exact sweep simulator: no halt to 1e16 on 274 and 514 (56.4 million sweeps, 13 digits, span 225,496,005); one new digit per two overflows"
 },
 "status": "CHECKPOINT_A",
 "status_reason": "Observe done: exact base-4 counter, rules validated (real 36.8k sweeps, 12k random, exhaustive small), sweep simulator = C core at 1e11 on both starts, no halt to 1e16. Stage 1 waits on the W7-5 stop rule (decision.json)."
}