{
 "tm": "1RB0LB_0LC0RE_1LA1LD_0LB1LD_1RA0RF_1RA---",
 "rank": 333,
 "class_sheet": "Chaotic Bell Class 4",
 "class_guess": "Layered Bell counter: budget phases with a x4/3, mod-3-branching layer law (cryptid-like)",
 "confidence": "med",
 "summary": "Phases convert one budget block per 4-trip cycle; each new layer is ~4/3 the last and n mod 3 picks the next phase.",
 "mechanism": [
  "Trip and phase level: three short trips cross the unary counter 1001^c, the fourth converts one budget block; the budget sum is conserved and c grows by 2 per cycle (R1-R3 validated 60/60, 40/40, 40/40).",
  "Epoch level: at a phase end the counter (about 8n cells) becomes a layer of (4n+r)/3 blocks, and n mod 3 picks the next phase (0: H6 shift phase, 1: R1 phase at once, 2: re-eat an older layer).",
  "To 1e11: layers 5803, 9996, 13333, 17774; the old 9996 layer is re-eaten at 4.8e10..8e10 and rebuilt; no halt (halting needs B> 111, never written)."
 ],
 "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 growing triangle of striped regions, head sweeping to the right end.",
   "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:1",
   "png": "img/cycle_closeup_P.png",
   "html": null,
   "steps": 1030,
   "caption": "one R1 cycle: three short trips, one long converting trip",
   "title": "One cycle of rule R1",
   "why": "Count the trips from the right edge: three turn near the counter, the fourth crawls left through 100001 blocks.",
   "primary": true,
   "start": "constructed: 0^inf 1011 110010^5 1^2 0^4 1101 100001^10 1001^12 A> 0^inf",
   "rows": "every step, steps 0..1030 (one cycle ends at step 1026)",
   "window": "cells -152..9, 1 px = 1 cell",
   "legend": "white = 1, black = 0, red/green = head moving R/L",
   "style": "bbchallenge-default"
  },
  {
   "mode": "every:10000000",
   "png": "img/every_1e7_to_1e10.png",
   "html": null,
   "steps": 6640000000,
   "caption": "phases as bands, one row per 10 million steps",
   "title": "Phases from blank to 6.6e9",
   "why": "Each slanted boundary is a budget being eaten; each new band is a layer left by a phase end.",
   "primary": true,
   "start": "blank",
   "rows": "every 10000000 steps, to step 6,640,000,000 (665 rows; stopped by the cell cap)",
   "window": "cells -17..156908, 1 px = 128 cells (sampled, so periodic words show as textures)",
   "legend": "white = 1, black = 0, red/green = head moving R/L",
   "style": "bbchallenge-default"
  },
  {
   "mode": "records",
   "png": "img/records_2e6.png",
   "html": null,
   "steps": 2000000,
   "caption": "records to 2e6: early phases and growing counter",
   "title": "Records to 2 million steps",
   "why": "One row per new record; the grey right band is the counter, diagonals are budget boundaries.",
   "start": "blank",
   "rows": "left/right records to step 2,000,000 (2,590 rows)",
   "window": "cells -17..2572, 1 px = 1 cell",
   "legend": "white = 1, black = 0, red/green = head moving R/L",
   "style": "bbchallenge-default"
  }
 ],
 "history": {
  "skeleton": "phase 6 at the A record: 0^inf L 110^2 0^3 110010^g 1^2 0^4 1101 100001^h 1001^c A> 0^inf",
  "vars": [
   "g",
   "h",
   "c"
  ],
  "rows": [
   {
    "step": 12500084130,
    "values": [
     9144,
     853,
     18290
    ]
   },
   {
    "step": 12700067096,
    "values": [
     9459,
     537,
     18921
    ]
   },
   {
    "step": 12900059348,
    "values": [
     9773,
     223,
     19549
    ]
   }
  ]
 },
 "rules": [
  {
   "name": "R1 (K6 eats H6)",
   "from": "0^inf 1011 110010^a 1^2 0^4 1101 100001^(b+2) 1001^c A> 0^inf",
   "to": "0^inf 1011 110010^(a+1) 1^2 0^4 1101 100001^(b+1) 1001^(c+2) A> 0^inf",
   "steps": null,
   "cases": "b+2 >= 2 (the last block, b+1 = 1, is the phase end)",
   "validated": {
    "instances": 60,
    "passed": 60
   },
   "source": "manual"
  },
  {
   "name": "R2 (1e8 hub)",
   "from": "0^inf 1011^3 001011^a 0^4 110^2 000110^(b+2) 01^2 1 0^4 110010^(p+1) 110000^(q+3) 1^3 01 1001^c A> 0^inf",
   "to": "0^inf 1011^3 001011^(a+1) 0^4 110^2 000110^(b+1) 01^2 1 0^4 110010^(p+1) 110000^(q+3) 1^3 01 1001^(c+2) A> 0^inf",
   "steps": null,
   "cases": "b+2 >= 2",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "rulefit"
  },
  {
   "name": "R3 (5e8 hub, Y^2 -> X)",
   "from": "0^inf 110^3 X^a 010110^2 000110^3 110 Y^(b+3) 000110^(p+1) 01^2 100001^(q+1) 1001^c A> 0^inf",
   "to": "0^inf 110^3 X^(a+1) 010110^2 000110^3 110 Y^(b+1) 000110^(p+1) 01^2 100001^(q+1) 1001^(c+2) A> 0^inf",
   "steps": null,
   "cases": "X = 010110010110000110000110, Y = 010110000110; b+3 >= 3",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "rulefit"
  },
  {
   "name": "E (phase end, budget n)",
   "from": "phase 6 with budget n = g+h (real 1.29e10 configuration, h varied)",
   "to": "new layer of (4n+r)/3 blocks; n = 0 mod 3: H6->H6 shift phase; 1 mod 3: R1 phase at once; 2 mod 3: re-eats the older 5803 layer",
   "steps": null,
   "cases": "n mod 3 (r = 7 for residue 2, 5 for residue 1 at the measured snapshot)",
   "validated": {
    "instances": 6,
    "passed": 6
   },
   "source": "manual"
  }
 ],
 "template": {
  "file": null,
  "module": "W5-3 (our kill)",
  "machine": "1RB1RA_1LC1LE_1RF1LD_1RE0LD_0LB0RA_---0RC",
  "diff": "no table within 5 transitions; architecture comparison only",
  "applies": "partly",
  "note": "Our W5-3 kill (machines/<W5-3>/ .v, read). R1-R3 are linear walk lemmas like W5-3's Wk/W2Q. W5-3 closes its eats with a binary counter and one size bound; here the phase ends feed a x4/3 layer law with a mod-3 branch, which no template covers."
 },
 "strategy": "Parked under the cryptid protocol. If funded: build an exact phase-level accelerator from R1-R3 plus measured phase-end maps, run it far past 1e11, and census the residue branches for a closed set of phase shapes.",
 "risks": [
  "The layer law n -> (4n+r)/3 with a mod-3 choice of successor phase is Collatz-like (Hydra-style x3/2 relatives); a closed invariant may not exist.",
  "Phase ends were measured on 6 instances from one real configuration only; other phase types may have other offsets.",
  "Phases reach back into older layers (9996 re-eaten at 4.8e10), so the state is a stack of layers, not one counter."
 ],
 "checkpoint_questions": [
  {
   "text": "cycle_closeup_P: do you see three short trips near the right edge and then one long trip that zig-zags left through the striped 100001 region before returning?",
   "figs": [
    1
   ],
   "kind": "check"
  },
  {
   "text": "every_1e7_to_1e10: do the slanted boundaries (budgets being eaten) and the new bands left at each phase end show up as separate stages?",
   "figs": [
    2
   ],
   "kind": "check"
  },
  {
   "text": "Cryptid-like (pre-registered stop): the layer law is x4/3 and n mod 3 picks the next phase. Park it, or fund one 2 h stage for an exact phase accelerator and a census of the residue branches?",
   "figs": [],
   "kind": "decision"
  }
 ],
 "discord_check": null,
 "stats": {
  "simulated_steps": 100000000000,
  "cells": 601752,
  "nonzeros": null,
  "growth": "span about 1.9-2.0 x sqrt(steps): 19k at 1e8, 58k at 1e9, 204k at 1e10, 602k at 1e11"
 },
 "status": "CRYPTID_CANDIDATE",
 "status_reason": "Pre-registered W6-5 stop rule met: the epoch law is x4/3 with a mod-3 residue split (three successor phases, one re-eats older layers). R1-R3 validated; phase ends measured on 6 instances. No halt to 1e11."
}