{
 "tm": "1RB1RF_1LC0RD_---0LD_1LE0LD_1RA0RF_0RE0LB",
 "rank": null,
 "class_sheet": "Bell eats counter",
 "class_guess": "Bell eats counter, partial eat with residue: kill #30's table, started in #30's B",
 "confidence": "high",
 "summary": "Kill #30's table renamed (no mirror), started in #30's B: same rules; Inv reached after 691 epochs",
 "mechanism": [
  "sigma = A->E, B->A, C->B, D->C, E->D, F->F maps #30's table onto this one (12/12 cells), so #30's hub (110)^a 0 (011)^b B> X, local pass, eats and nested D6 sub-epochs apply; blank reaches K(1,3,1) at step 55.",
  "#30's Rocq model from K(1,3,1): 691 epochs to N = 17,712, where #30's Inv holds (k = 11); model = TM on all 518 left records to 1e11; #30's Lemma D checks pass to N = 400,035.",
  "Sibling #7 (740 line 381: same table mirrored, started in #30's E): the model matches it from step 1,059 (K(1,17,1)), and Inv holds after 687 epochs."
 ],
 "diagrams": [
  {
   "mode": "default",
   "png": "img/default_site.png",
   "html": null,
   "steps": 10000,
   "caption": "bbchallenge default view, first 10,000 steps",
   "title": "bbchallenge default view, 10,000 steps",
   "why": "The site's view. Compare with kill #30's card: diagonal stripes inside the bell, busy right edge.",
   "primary": true,
   "start": "blank",
   "rows": "every step: steps 0..9,999 squeezed into 500 px rows as on bbchallenge.org (each px row blends steps 20y+9 and 20y+10, so 1 px row = 20 steps)",
   "window": "cells -200..199, 1 px = 1 cell",
   "legend": "white = 1, black = 0 or never visited, red/green = head after a right/left move (pale = blended by the squeeze)",
   "style": "bbchallenge-default"
  },
  {
   "mode": "state:B:R",
   "png": "img/stateBR_right_3e5.png",
   "html": null,
   "steps": 300000,
   "caption": "One row per B-right entry: epochs as diagonals, counter at right",
   "title": "Epochs: marker diagonals and the counter",
   "why": "Rows are hub visits (B moving right). Follow one down-right diagonal; compare with Fig 2 of #30's card (C there).",
   "primary": true,
   "start": "blank",
   "rows": "one row per entry into state B moving right, steps 0..300,000 (1,446 rows); not evenly spaced in time",
   "window": "cells -439..0, 1 px = 1 cell, counted from the right edge (each row's rightmost visited cell is pinned to the last column)",
   "legend": "white = 1, black = 0 or never visited, red = head (just moved right)",
   "style": "bbchallenge-default"
  },
  {
   "mode": "explore",
   "png": "img/explore_init_60.png",
   "html": null,
   "steps": 60,
   "caption": "First 60 steps: blank tape to the first hub",
   "title": "From blank to the first hub, 60 steps",
   "why": "One row per step. Find the leftmost green-then-magenta cells, then follow the head right to row 55.",
   "primary": true,
   "start": "blank",
   "rows": "every step, steps 0..59 (row r = the configuration after r steps), 10 px per row",
   "window": "cells -10..19, 1 px = 1/10 cell (10 px per cell)",
   "legend": "slate = 0, white = 1, head cell coloured by state: A red, B orange, C blue, D green, E magenta, F cyan",
   "style": "bbchallenge-explore"
  },
  {
   "mode": "records",
   "png": "img/records_1e8.png",
   "html": null,
   "steps": 100000000,
   "caption": "Left/right records to 1e8: right edge 3,252, left only 146",
   "title": "Left and right records to 100M steps",
   "why": "One row per new edge cell. Left edge: 2 cells per epoch; the right edge carries the counter.",
   "primary": false,
   "start": "blank",
   "rows": "the start, then one per new leftmost or rightmost cell (3,399 rows, steps 0..100,000,000); not evenly spaced in time",
   "window": "cells -146..3,252, 1 px = 1 cell",
   "legend": "white = 1, black = 0 or never visited, red/green = head on a new right/left cell",
   "style": "bbchallenge-default"
  },
  {
   "mode": "blaze",
   "png": "img/blaze_1e7.png",
   "html": null,
   "steps": 10000000,
   "caption": "Blaze 1e7: one smooth bell",
   "title": "Blaze, 10 million steps",
   "why": "The bell's outline over 1e7 steps; compare its shape with #30's Blaze figure.",
   "primary": false,
   "start": "blank",
   "rows": "time blocks of 16,384 steps, averaged (611 blocks, steps 0..10,000,000), stretched to 500 px: 1 px ~ 20,000 steps",
   "window": "cells -78..1,452, 1 px = ~1.9 cells (Blaze's 1,531 columns stretched to 800 px)",
   "legend": "white = 0, orange = 1, in-between shades = both mixed inside the pixel's block (averaged); no head",
   "style": "bbchallenge-blaze"
  }
 ],
 "history": {
  "skeleton": "0^inf <E 101 001^k T 0^inf",
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 },
 "rules": [
  {
   "name": "S conjugacy",
   "from": "#30 cell (q, r) = w m q'",
   "to": "W4-1 cell (sigma q, r) = w m sigma(q')",
   "steps": null,
   "cases": "sigma = A->E, B->A, C->B, D->C, E->D, F->F, no mirror; all 12 cells incl. the halt cell",
   "validated": {
    "instances": 24,
    "passed": 24
   },
   "source": "manual"
  },
  {
   "name": "I start",
   "from": "0^inf A> 0^inf",
   "to": "0^inf 110 0 011^3 B> 1 0^inf",
   "steps": "55",
   "cases": "via the pre-record 0^inf <D 01 001^2 000 1 0^inf at step 41 (left record at 42)",
   "validated": {
    "instances": 2,
    "passed": 2
   },
   "source": "manual"
  },
  {
   "name": "Rst restart",
   "from": "0^inf <D 01 001^k 000 Y 0^inf",
   "to": "0^inf 110 0 011^(k+1) B> Y 0^inf",
   "steps": null,
   "cases": "k <= 60, Y random words of every kind (#30 Rst)",
   "validated": {
    "instances": 400,
    "passed": 400
   },
   "source": "manual"
  },
  {
   "name": "LP local pass",
   "from": "l 011 B> X 0^inf",
   "to": "l <E 100 X' 0^inf (d=0) or l <E 101000 X' 0^inf (d=1)",
   "steps": null,
   "cases": "(X',d) = #30's lpf X, 18 constructors (corrected 2026-10-11, was 19): a-block -> b-block; b-block -> a-block + carry; tails; 11 001^x -> 01 001^(x-1) or 00 (absorbs); 01 -> 11; 00 -> 10; 10 a-block (D5); 10 b-block (D6); constant end words. Any left context l",
   "validated": {
    "instances": 4800,
    "passed": 4800
   },
   "source": "manual"
  },
  {
   "name": "D6 nested bounce",
   "from": "l 011 B> 10 101 001^e 000 R 0^inf",
   "to": "l <E 100 0 01 001^k 000 Y 0^inf",
   "steps": null,
   "cases": "(k,Y) = phif 1 (e+1) R: one bounce runs a whole sub-epoch of R (#30's LP_6); e <= 7, R random G words",
   "validated": {
    "instances": 403,
    "passed": 403
   },
   "source": "manual"
  },
  {
   "name": "Phi epoch",
   "from": "l 110^a 0 011^b B> X 0^inf",
   "to": "l <D 01 001^k 000 Y 0^inf",
   "steps": null,
   "cases": "(k,Y) = #30's phif 1.. a b X: bounces then an eat; a <= 30, b <= 40, X random; includes the b = 1 eats below",
   "validated": {
    "instances": 4800,
    "passed": 4800
   },
   "source": "manual"
  },
  {
   "name": "E1 even eat",
   "from": "110^a 0 011 B> 001^(e+1) 000 R",
   "to": "110^(a+2) 0 011^(e+1) B> R",
   "steps": null,
   "cases": "#30's Phi_E1; any rest R",
   "validated": {
    "instances": 937,
    "passed": 937
   },
   "source": "manual"
  },
  {
   "name": "E2 odd eat",
   "from": "110^a 0 011 B> 101 001^e 000 R",
   "to": "<D 01 001^a 000 11 001^(e+d) 000 R'",
   "steps": null,
   "cases": "(R',d) = lpf R (#30's Phi_E2); the residue 11 001^x 000 W seeds the next epoch",
   "validated": {
    "instances": 992,
    "passed": 992
   },
   "source": "manual"
  },
  {
   "name": "Tail eats",
   "from": "110^a 0 011 B> t 0^inf",
   "to": "<D 01 001^(a+1) 000 1 / <D 01 001^a 000 Y_t",
   "steps": null,
   "cases": "t = '', 1, 010001, 110001 and the constant end words (#30's Phi_E0, Et1-Et3)",
   "validated": {
    "instances": 513,
    "passed": 513
   },
   "source": "manual"
  },
  {
   "name": "O model = TM",
   "from": "K(1,3,1)",
   "to": "every TM left record 0^inf <E 101 001^k T 0^inf, by the model",
   "steps": null,
   "cases": "518 records (3..520) to step 99,729,345,754, N = 12,698; no halt in 1e11 steps",
   "validated": {
    "instances": 518,
    "passed": 518
   },
   "source": "manual"
  },
  {
   "name": "FIN finite part",
   "from": "K(1,3,t1)",
   "to": "K(1,17712,Y691) with Inv 11",
   "steps": "691 model epochs",
   "cases": "Python mirror of #30's orbit/phif (reproduces #30's fin694 exactly); Y691 = p11 10 (gw 11 blocks, tail t0); first epoch with Inv for any k",
   "validated": {
    "instances": 1,
    "passed": 1
   },
   "source": "manual"
  },
  {
   "name": "D Lemma D chain",
   "from": "K(1,N,Y) on the orbit",
   "to": "next epoch: digestion beta <= N - 2 and all #30 D.1-D.7 links",
   "steps": null,
   "cases": "#30's check_proof section D from this start: 11,074 epochs to N = 400,035, ALL PASS (the Rocq inv_step needs none of it)",
   "validated": {
    "instances": 11074,
    "passed": 11074
   },
   "source": "manual"
  }
 ],
 "template": {
  "file": null,
  "module": null,
  "machine": "1RB0RF_1RC1RF_1LD0RE_---0LE_1LA0LE_0RA0LC",
  "diff": "none under sigma = EABCDF (A->E, B->A, C->B, D->C, E->D, F->F): all 12 entries equal after renaming, no mirror; the start state differs (#30's B)",
  "applies": "yes",
  "note": "Template = our kill #30's .v (1,726 lines, check_kill PASS, sha256 93a493f5...0c0). Start-independent: Sections 1-10 and inv_step. New: init c0 -->* K 3 t1 (55 steps), fin691 = orbit 100000 691 3 t1 = Some (17712, Y691), inv691 : Inv 11 17712 Y691. Route: rename A->E, C->B, E->D in the es lemmas (#25/F2 recipe), or keep #30's file as tm30 + Perm/perm_halts (#24 recipe, no flip)."
 },
 "strategy": "Delta of kill #30: keep #30's development, add the new start (55 steps to K 3 t1) and a 691-epoch vm_compute finite part to Inv 11 at N = 17,712, then transport by renaming or Perm + perm_halts. Then check_kill; do #7 (same plus flip_halts) alongside.",
 "risks": [
  "The finite part is 691 vm_compute epochs, the same size as #30's fin694 (about 1 s there); fuel 100000 leaves 66,761 spare.",
  "A start lemma from a non-c0 state (conjugacy route) needs solve_initD, not esx (atlas/rocq-notes.md); the rename route uses plain solve_init.",
  "Discord #bb6 not searched for this string; once #30 is public others can port it here, so submit #30, W4-1 and #7 together."
 ],
 "checkpoint_questions": [
  {
   "text": "Fig 2 here and Fig 2 on #30's card are the same view (hub state B here, C there). Do both show the same down-right epoch diagonals with the counter in the right-edge strip?",
   "figs": [
    1
   ],
   "kind": "check"
  },
  {
   "text": "Fig 3: does the head make one sweep left to a new leftmost cell (green, then magenta) and then one sweep right, ending on row 55 next to a single 1?",
   "figs": [
    2
   ],
   "kind": "check"
  },
  {
   "text": "Formalize W4-1 and #7 as one family with #30 and submit the three together (recommended), or post #30 first and do these two later?",
   "kind": "decision"
  }
 ],
 "discord_check": null,
 "stats": {
  "simulated_steps": 100000000000,
  "cells": 7726,
  "nonzeros": 4057,
  "growth": "cells/nonzeros at 1e9 (#30: 7,720 / 4,642); left edge +2 cells/epoch; 520 left records to 1e11, k = 12,697 at step 99,729,345,754"
 },
 "status": "CHECKPOINT_A",
 "status_reason": "Kill #30's table under sigma; every rule validated on this table, the model matches all TM left records to 1e11, and #30's Inv holds after 691 model epochs, so confidence high."
}