{
 "tm": "1RB0LE_1RC1RB_1LD0RE_1LA1LC_1RB0LF_0LC---",
 "rank": 412,
 "class_sheet": "Chaotic Bell Class 1",
 "class_guess": "Chaotic Bell Class 1: ChaoticBell1Halt.v TM13's table (renamed), started in TM13's D",
 "confidence": "med",
 "summary": "TM13's table (ChaoticBell1Halt.v) from TM13's D: CB1 bell; certified-executor port finds no halt in 16.5M ticks.",
 "mechanism": [
  "Same table as ChaoticBell1Halt.v TM13 (ours A,B,C,D,E,F = TM13 D,A,B,C,E,F; no mirror): our blank start is TM13 started in D. All TM13 lemmas hold verbatim; 26 rules + the halt window pass 40/40 random instances here.",
  "A bell over digits D n = 1^(2n+1) 00: B> 0100 sweeps right (D n -> S n = 1(01)^(n+1)), <C 1 sweeps back. Each 111 on the left is one call (sweep to the right end, append 100 100); PL blocks replay calls; the far left turns the head (over1/over2). Direct sim: no halt to 1e9 (sheet: 1e13); left-end tapes are clean D-digit lists.",
  "Port of ccz181078's certified executor (CBSim): reproduces TM13's halt (tick 64,832) and TM7's (65,400), matches direct sim for 4,000 ticks (21.1M steps). Our start: no halt in 16,551,000 ticks; 602's start: none in 10,000,000; 299's: none in 7,627,000. After ~4e5 ticks the run turns regular: a stack of PL(n)^k_n, n = 0,1,2,..., counts ~1e31 falling ~5x per two levels, small remainders."
 ],
 "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, 10,000 steps",
   "why": "Orientation: the head sweeps the whole tape; the right edge moves out a little per sweep.",
   "primary": true,
   "start": "blank",
   "rows": "every step 0..9,999, squeezed into 500 px by the site's bilinear filter (about one sample per 20 steps)",
   "window": "cells -200..199, 1 px = 1 cell",
   "legend": "white = 1, black = 0 or unvisited, red/green = head (last move right/left)",
   "style": "bbchallenge-default"
  },
  {
   "mode": "every:1000000",
   "png": "img/every1e6_1e9.png",
   "html": null,
   "steps": 1000000000,
   "caption": "One row per million steps up to 10^9",
   "title": "Every 10^6 steps up to 10^9",
   "why": "Rows are snapshots 10^6 steps apart. Compare the fixed left edge with the right edge.",
   "primary": true,
   "start": "blank",
   "rows": "every 1,000,000 steps, 0..1,000,000,000 (1,001 rows)",
   "window": "cells -518..36471, 1 px = 16 cells (every 16th cell sampled; the head is kept)",
   "legend": "white = 1, black = 0 or unvisited, red/green = head (last move right/left)",
   "style": "bbchallenge-default"
  },
  {
   "mode": "every:1",
   "png": "img/two_calls_explore.png",
   "html": null,
   "steps": 180,
   "caption": "Two 111 groups on the left: two sweeps, then the far-left turn",
   "title": "Close-up: two calls from a constructed tape",
   "why": "Start: two 111 groups left of the head. Follow each sweep to the right end and back.",
   "primary": true,
   "start": "constructed: 0^inf 1 111 111 0101 <C 1 111 00 11111 00 1 00 0^inf",
   "rows": "every step, 0..180 (181 rows, 10 px per step)",
   "window": "cells -13..20, 1 px = 0.1 cells (10 px per cell)",
   "legend": "white = 1, slate = 0, head coloured by state: A red, B orange, C blue, D green, E magenta, F cyan",
   "style": "bbchallenge-explore"
  },
  {
   "mode": "explore",
   "png": "img/explore_site.png",
   "html": "img/viewer.html",
   "steps": 49,
   "caption": "Startup from blank in Explore colours (first 50 steps)",
   "title": "Explore view: the first 50 steps",
   "why": "State colours: the first far-left turns (over1/over2) and the first appended digits.",
   "primary": false,
   "start": "blank",
   "rows": "every step 0..49 (the site's 800x500 Explore view, 10 px per step)",
   "window": "cells -40..39, 1 px = 0.1 cells (10 px per cell)",
   "legend": "white = 1, slate = 0, head coloured by state: A red, B orange, C blue, D green, E magenta, F cyan",
   "style": "bbchallenge-explore"
  }
 ],
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 },
 "rules": [
  {
   "name": "moveR",
   "from": "l B> 0100 1^(2n+1) 00 r",
   "to": "l 1(01)^(n+1) B> 0100 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "moveL",
   "from": "l 1(01)^(n+1) <C 1 r",
   "to": "l <C 1 1^(2n+1) 00 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "emptyR",
   "from": "l B> 0100 0^inf",
   "to": "l <C 1 100 100 0^inf",
   "steps": null,
   "cases": "right context is 0^inf",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "blank",
   "from": "l B> 0100 000 r",
   "to": "l <C 1 100 100 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "restartL",
   "from": "l 111 (01)^(b+1) <C 1 r",
   "to": "l (01)^(b+1) B> 0100 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "moveJ",
   "from": "l 1(01)^(n+1) <D 100 r",
   "to": "l <C 1 1^(2n+3) 00 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "restartJ",
   "from": "l 111 (01)^b <D 100 r",
   "to": "l (01)^(b+1) B> 0100 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "finishPL",
   "from": "l 101 10 (01)^(b+1) <C 1 r",
   "to": "l <D 100 1^(2b+3) 00 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "collide",
   "from": "l B> 0100 10 100 100 r",
   "to": "l <D 100 11111 00 10 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "pairR",
   "from": "l B> 0100 10 (1^(2n+5) 00)^2 r",
   "to": "l 101 101 1^(2n) (01)^(n+4) B> 0100 10 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "even",
   "from": "l B> 0100 1^(2n+2) 00 r",
   "to": "l <C 1 1^(2n+3) 00 10 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "over2",
   "from": "0^inf 11 (01)^(b+1) <C 1 r",
   "to": "0^inf 1^(2b+2) 0101 B> 0100 1 r",
   "steps": null,
   "cases": "left context is 0^inf; b >= 0",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "over1",
   "from": "0^inf 1 (01)^(b+1) <C 1 1^(2n+1) 00 r",
   "to": "0^inf 1^(2b) (01)^(n+2) B> 0100 10 r",
   "steps": null,
   "cases": "left context is 0^inf (far left end); b, n >= 0",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "collision",
   "from": "l 101100 <C 1 r",
   "to": "l <D 100 1111 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "turnB",
   "from": "l 11 <C 1 1^(2n+1) 00 r",
   "to": "l (01)^(n+1) B> 0100 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "defect0",
   "from": "l B> 0100 10 100 1 1^(2m) 0 r",
   "to": "l <D 100 1111 1^(2m+1) 00 1 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "defect1",
   "from": "l B> 0100 10 11100 1 1^(2m) 0 r",
   "to": "l <C 1 100 100 1^(2m+3) 00 1 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "defect2",
   "from": "l B> 0100 10 1^(2n+5) 00 1 1^(2m) 0 r",
   "to": "l 101 101 1^(2n) (01)^(m+2) B> 0100 1 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "defectBlank0",
   "from": "l B> 0100 10 100 00 r",
   "to": "l 101 1001 B> 0100 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "defectBlankS",
   "from": "l B> 0100 10 1^(2n+3) 00 00 r",
   "to": "l 101 101 1 1^(2n) 01 B> 0100 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "paired",
   "from": "l B> 0100 (10)^(2k) 1^(2n+1) 00 r",
   "to": "l 101 (1011)^k (01)^n B> 0100 r",
   "steps": null,
   "cases": "k >= 1, n >= 0",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "calls",
   "from": "l (111)^h (01)^(b+1) <C 1 D(v1)..D(vk) 0^inf",
   "to": "l (01)^(b+1) <C 1 D(v1)..D(vk) (100)^(2h) 0^inf",
   "steps": null,
   "cases": "h >= 1, b >= 0, any digit list; right context 0^inf",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "scanR",
   "from": "l B> 01 (11)^k r",
   "to": "l (01)^k B> 01 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "scanB",
   "from": "l (10)^k <C r",
   "to": "l <C (11)^k r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "scanC",
   "from": "l (01)^k <D r",
   "to": "l <D (11)^k r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "scanPair",
   "from": "l B> 01 (0101)^k r",
   "to": "l (1011)^k B> 01 r",
   "steps": null,
   "cases": "all parameters >= 0, any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "halt_window",
   "from": "l 11100 <C r  halts (C reads 0",
   "to": "1LD, ..., F reads 1 = ---)",
   "steps": null,
   "cases": "any l, r",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "executor = machine",
   "from": "blank, our A (= TM13 from D)",
   "to": "each of the first 4,000 executor configurations, in order",
   "steps": "21,071,295 direct steps",
   "cases": "Python port of CBSim; exact tape match at every tick",
   "validated": {
    "instances": 4000,
    "passed": 4000
   },
   "source": "manual"
  }
 ],
 "template": {
  "file": "ChaoticBell1Halt.v",
  "module": "TM13",
  "machine": "1RB1RA_1LC0RE_1LD1LB_1RA0LE_1RA0LF_0LB---",
  "diff": "same table renamed (ours A,B,C,D,E,F = TM13 D,A,B,C,E,F; no mirror); only the start differs (ours = TM13 from D)",
  "applies": "partly",
  "note": "All TM13 lemmas (scan*, right, left, blank, even, restart, overflow1/2, collision, leftJ, turnB, turnJ, finishP, defect*, paired, halt_window, core) are about the table only and hold here after renaming B->A, C->B, D->C. A HALT .v = the CB1/CBMacros/CBSim modules with the state letters renamed, our TM string, check_spec with fuel above the halting tick. That needs a halt, which the port did not find."
 },
 "strategy": "HALT route by the certified executor: no halt in 16.5M ticks (165x). If funded: an exact per-level map for the late PL stack, iterated to the bottom (~80 levels, ~2e8 ticks); cryptid stop on residue branching.",
 "risks": [
  "ccz181078 very likely ran the same executor on the whole class and kept only TM7/TM13; our 100x+ runs agree that these starts do not halt early.",
  "The late phase looks like division by 5 with small remainders: a cryptid sign; a fitted law may branch on residues.",
  "The Python port only predicts; a kill would still need the Coq check_spec run (one coqc) after a halt."
 ],
 "checkpoint_questions": [
  {
   "text": "Close-up: does each `111` group on the left send exactly one sweep to the right end and back, the right end gaining `100 100` (two zero digits) per sweep?",
   "figs": [
    2
   ],
   "kind": "check"
  },
  {
   "text": "Every 10^6 steps: is this one bell whose right edge creeps out while the left edge stays almost fixed (no translated part, no cycle)?",
   "figs": [
    1
   ],
   "kind": "check"
  },
  {
   "text": "No halt in 16.5M executor ticks from our start (TM13 itself halts at 64,832). Park the CB1 cluster (412, 602, 299), or fund one 2 h stage for an exact level accelerator of the late PL stack (cryptid stop if the per-level map branches on remainders mod 5)?",
   "figs": [],
   "kind": "decision"
  }
 ],
 "discord_check": null,
 "stats": {
  "simulated_steps": 2000000000,
  "cells": 47146,
  "nonzeros": 22051,
  "growth": "direct: span ~ sqrt(steps) (37,750 at 1.03e9; 47,146 at 1.6e9). Executor: 10^31 cells at 4.2e5 ticks, then ~10^33 to 1.65e7 ticks; the PL stack is eaten ~1 level per 3e6 ticks"
 },
 "status": "STUCK",
 "status_reason": "Rules exact (26/26 validated). Halting go/no-go: NO-GO, the certified-executor port finds no halt in 16,551,000 ticks from our start (602's start: 1e7; 299's: 7,627,000). Nonhalting not attempted (plan); the late phase is a regular PL stack with a /5-with-remainder look."
}