{
 "tm": "1RB---_0LC1RF_1LE0RD_0RB1RC_1RD0LE_0RC1RA",
 "rank": null,
 "class_sheet": "Sync bouncer counter",
 "class_guess": "Sync bouncer counter: kill #4's table renamed EDBCFA (no mirror), started in #4's F",
 "confidence": "high",
 "summary": "Kill #4's table renamed EDBCFA, started in #4's F: same rules and hexagon; new base S(6,14,4) at step 16,590",
 "mechanism": [
  "Same machine as kill #4 up to state names (A->E, B->D, C->B, D->C, E->F, F->A); it starts in #4's F, so its orbit differs.",
  "Same words and rules as #4: binary counter (1010/0010) on the left, A/B blocks 00111/10111 and a front 111 on the right; R1-R5o.",
  "From blank it reaches S(6,14,4) = Q(7,65,1,14,4) at step 16,590, inside #4's hexagon (facet 4Y+2Z >= N tight); #4's cycle lemma does the rest."
 ],
 "diagrams": [
  {
   "mode": "records",
   "png": "img/records_2.7e6.png",
   "html": null,
   "steps": 2700000,
   "caption": "Counter strip, overflow resets, one diagonal front per cycle",
   "title": "Left/right records to 2.7M steps",
   "why": "Same view as the first figure on #4's card. Overflow resets are record rows 78, 122, 306, 390, 1,139.",
   "primary": true,
   "start": "blank",
   "rows": "left/right records: the start, then one row each time the head reaches a new leftmost or rightmost cell (1,406 rows, steps 0..2,700,000; rows are not equal time)",
   "window": "cells -20..1385, 1 px = 0.5 cells (each cell is 2x2 px)",
   "legend": "white = 1, black = 0 or never visited, red/green = head just moved right/left",
   "style": "bbchallenge-default"
  },
  {
   "mode": "every:50",
   "png": "img/every50_cycle7_from_base.png",
   "html": null,
   "steps": 58294,
   "caption": "One cycle from the base S(6,14,4): front, conversion, bounces, overflow",
   "title": "One cycle from the base, every 50 steps",
   "why": "Starts at the base S(6,14,4). Top: front steps; middle: conversion; then bounces until the overflow at the bottom.",
   "primary": true,
   "start": "mid-run: step 16590 (the real tape there is exactly Q(7,65,1,14,4) with head B; rebuilt from that formula and checked identical)",
   "rows": "every 50 steps (1,166 rows: steps 16,590..74,840; S(7,25,29) follows at step 74,884), so one bounce spans many rows",
   "window": "cells -130..177, 1 px = 0.5 cells (each cell is 2x2 px); cell 0 = the head cell at step 16,590, i.e. real cells -16..291",
   "legend": "white = 1, black = 0 or never visited, red/green = head just moved right/left",
   "style": "bbchallenge-default"
  },
  {
   "mode": "every:16",
   "png": "img/every16_init.png",
   "html": null,
   "steps": 16590,
   "caption": "Blank tape to the base: irregular start, then rule-governed",
   "title": "Initial segment, every 16 steps",
   "why": "Steps 0 to 16,576: the run before the base. Rule-governed from step 1,711 (about row 107).",
   "start": "blank",
   "rows": "every 16 steps (1,037 rows: steps 0..16,576; the base follows at step 16,590)",
   "window": "cells -14..112, 1 px = 0.5 cells (each cell is 2x2 px)",
   "legend": "white = 1, black = 0 or never visited, red/green = head just moved right/left",
   "style": "bbchallenge-default"
  },
  {
   "mode": "default",
   "png": "img/default_site.png",
   "html": null,
   "steps": 10000,
   "caption": "bbchallenge default view, first 10k steps",
   "title": "bbchallenge default view, first 10,000 steps",
   "why": "The site's view: a bouncer growing to the right from an almost fixed left end.",
   "start": "blank",
   "rows": "every step 0..10,000, squeezed 20:1 into 500 px as on bbchallenge.org (px row y blends steps 20y+9 and 20y+10)",
   "window": "cells -200..199, 1 px = 1 cell",
   "legend": "white = 1, black = 0 or never visited, red/green = head just moved right/left",
   "style": "bbchallenge-default"
  }
 ],
 "history": {
  "skeleton": "0^inf C_k(n) (00111)^x [111 (00111)^y] (10111)^z 00 B> 0^inf",
  "vars": [
   "phase",
   "k",
   "n",
   "x",
   "y",
   "z"
  ],
  "rows": [
   {
    "step": 1711,
    "values": [
     "Q",
     5,
     20,
     3,
     1,
     0
    ]
   },
   {
    "step": 3047,
    "values": [
     "P",
     5,
     27,
     7,
     "-",
     0
    ]
   },
   {
    "step": 4371,
    "values": [
     "P",
     5,
     31,
     7,
     "-",
     4
    ]
   },
   {
    "step": 4864,
    "values": [
     "Q",
     6,
     33,
     1,
     5,
     5
    ]
   },
   {
    "step": 6186,
    "values": [
     "Q",
     6,
     39,
     5,
     1,
     7
    ]
   },
   {
    "step": 14036,
    "values": [
     "P",
     6,
     60,
     16,
     "-",
     0
    ]
   },
   {
    "step": 15825,
    "values": [
     "P",
     6,
     63,
     16,
     "-",
     3
    ]
   },
   {
    "step": 16590,
    "values": [
     "Q",
     7,
     65,
     1,
     14,
     4
    ]
   },
   {
    "step": 25889,
    "values": [
     "Q",
     7,
     86,
     15,
     0,
     11
    ]
   },
   {
    "step": 34947,
    "values": [
     "P",
     7,
     99,
     27,
     "-",
     0
    ]
   },
   {
    "step": 72951,
    "values": [
     "P",
     7,
     127,
     27,
     "-",
     28
    ]
   },
   {
    "step": 74884,
    "values": [
     "Q",
     8,
     129,
     1,
     25,
     29
    ]
   },
   {
    "step": 109472,
    "values": [
     "Q",
     8,
     165,
     25,
     1,
     41
    ]
   },
   {
    "step": 248150,
    "values": [
     "P",
     8,
     254,
     70,
     "-",
     0
    ]
   },
   {
    "step": 250437,
    "values": [
     "P",
     8,
     255,
     70,
     "-",
     1
    ]
   },
   {
    "step": 252898,
    "values": [
     "Q",
     9,
     257,
     1,
     68,
     2
    ]
   },
   {
    "step": 428172,
    "values": [
     "Q",
     9,
     359,
     69,
     0,
     36
    ]
   },
   {
    "step": 535510,
    "values": [
     "P",
     9,
     397,
     106,
     "-",
     0
    ]
   },
   {
    "step": 1135428,
    "values": [
     "P",
     9,
     511,
     106,
     "-",
     114
    ]
   },
   {
    "step": 1142673,
    "values": [
     "Q",
     10,
     513,
     1,
     104,
     115
    ]
   },
   {
    "step": 1733589,
    "values": [
     "Q",
     10,
     669,
     105,
     0,
     167
    ]
   },
   {
    "step": 2759783,
    "values": [
     "P",
     10,
     838,
     273,
     "-",
     0
    ]
   },
   {
    "step": 4932158,
    "values": [
     "P",
     10,
     1023,
     273,
     "-",
     185
    ]
   },
   {
    "step": 4947035,
    "values": [
     "Q",
     11,
     1025,
     1,
     271,
     186
    ]
   },
   {
    "step": 8405806,
    "values": [
     "Q",
     11,
     1430,
     271,
     1,
     321
    ]
   },
   {
    "step": 17498220,
    "values": [
     "Q",
     12,
     2142,
     63,
     532,
     0
    ]
   },
   {
    "step": 29322686,
    "values": [
     "Q",
     12,
     2940,
     595,
     0,
     266
    ]
   },
   {
    "step": 35576808,
    "values": [
     "P",
     12,
     3208,
     862,
     "-",
     0
    ]
   },
   {
    "step": 72673681,
    "values": [
     "P",
     12,
     4095,
     862,
     "-",
     887
    ]
   },
   {
    "step": 72729902,
    "values": [
     "Q",
     13,
     4097,
     1,
     860,
     888
    ]
   },
   {
    "step": 111659028,
    "values": [
     "Q",
     13,
     5387,
     861,
     0,
     1318
    ]
   },
   {
    "step": 175916622,
    "values": [
     "P",
     13,
     6707,
     2180,
     "-",
     0
    ]
   },
   {
    "step": 314746210,
    "values": [
     "P",
     13,
     8191,
     2180,
     "-",
     1484
    ]
   },
   {
    "step": 314863727,
    "values": [
     "Q",
     14,
     8193,
     1,
     2178,
     1485
    ]
   },
   {
    "step": 537600100,
    "values": [
     "Q",
     14,
     11460,
     2179,
     0,
     2574
    ]
   },
   {
    "step": 823412430,
    "values": [
     "P",
     14,
     14036,
     4754,
     "-",
     0
    ]
   },
   {
    "step": 1268701603,
    "values": [
     "P",
     14,
     16383,
     4754,
     "-",
     2347
    ]
   },
   {
    "step": 1268929120,
    "values": [
     "Q",
     15,
     16385,
     1,
     4752,
     2348
    ]
   }
  ]
 },
 "rules": [
  {
   "name": "R1 P-bounce",
   "from": "0^inf C_k(n) (00111)^X (10111)^z 00 B> 0^inf",
   "to": "0^inf C_k(n+1) (00111)^X (10111)^(z+1) 00 B> 0^inf",
   "steps": "32X+32z+16t(n)+47, t(n) = trailing 1-bits of n",
   "cases": "n+1 <= 2^k-1",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "R2 overflow",
   "from": "0^inf C_k(2^k-1) (00111)^X (10111)^z 00 B> 0^inf",
   "to": "0^inf C_(k+1)(2^k+1) 00111 111 (00111)^(X-2) (10111)^(z+1) 00 B> 0^inf",
   "steps": "32X+32z+16k+61",
   "cases": "X >= 2",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "R3 front step",
   "from": "0^inf C_k(n) (00111)^x 111 (00111)^(y+2) (10111)^z 00 B> 0^inf",
   "to": "0^inf C_k(n+3) (00111)^(x+2) 111 (00111)^y (10111)^(z+1) 00 B> 0^inf",
   "steps": "96x+32y+32z+16(t(n)+t(n+1)+t(n+2))+197",
   "cases": "n+3 <= 2^k-1, x >= 1",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "R4 even conversion",
   "from": "0^inf C_k(n) (00111)^x 111 (10111)^z 00 B> 0^inf",
   "to": "0^inf C_k(n+z+2) (00111)^(x+z+1) 00 B> 0^inf",
   "steps": null,
   "cases": "n+z+2 <= 2^k-1",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "R5 odd conversion",
   "from": "0^inf C_k(n) (00111)^x 111 00111 (10111)^z 00 B> 0^inf",
   "to": "0^inf C_k(n+2z+7) (00111)^(x+z+4) 00 B> 0^inf",
   "steps": null,
   "cases": "n+2z+7 <= 2^k-1",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "R5o odd conversion + overflow",
   "from": "0^inf C_k(n) (00111)^x 111 00111 (10111)^z 00 B> 0^inf",
   "to": "0^inf C_(k+1)(2^k+1+3m) (00111)^(1+2m) 111 (00111)^(x+z+2-2m) 00 B> 0^inf",
   "steps": null,
   "cases": "m = n+2z+7-2^k >= 0, x+z+2-2m >= 1, 3m <= 2^k-2",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "R4o (remark, never used)",
   "from": "0^inf C_k(n) (00111)^x 111 (10111)^z 00 B> 0^inf",
   "to": "0^inf C_(k+1)(2^k+1+3m) (00111)^(1+2m) 111 (00111)^(x+z-1-2m) 00 B> 0^inf",
   "steps": null,
   "cases": "m = n+z+2-2^k >= 0, x+z-1-2m >= 1, 3m <= 2^k-2",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  }
 ],
 "template": {
  "file": null,
  "module": null,
  "machine": "1RB0LA_0RC1RD_0LD1RE_1LA0RB_0RD1RF_1RC---",
  "diff": "none after renaming states by EDBCFA (no mirror); without renaming every cell differs. Start = #4's F",
  "applies": "yes",
  "note": "Template = kill #4's passing .v (machines/1RB0LA_0RC1RD_0LD1RE_1LA0RB_0RD1RF_1RC---, sha256 51e3dea1...). Delta: TM string, `{{A}}`->`{{E}}`, `{{C}}`->`{{B}}`, `{{E}}`->`{{F}}`, a 16,590-step `esx` init to `CfgF 5 0 14 4`; `cycle_step`/`Inv` verbatim. rocq/plan_check.v compiles (6.7 s, closed)."
 },
 "strategy": "Delta of kill #4 (proof.md section 5): #4's .v with state names renamed by EDBCFA and a new init (one 16,590-step esx to CfgF 5 0 14 4).\ncycle_step, Inv and all macro lemmas verbatim. rocq/plan_check.v already compiles; next: clean kill file + check_kill.",
 "risks": [
  "None found in the argument: the base sits on the hexagon facet 4Y+2Z >= N (tight, 64 = 64), which Inv allows (<=); #4's base is tight on the same facet.",
  "On mxdys's UBRRBA_TODO and dyuan01's longitudinal lists (fair game per Dennis); re-read those threads before posting."
 ],
 "checkpoint_questions": [
  {
   "text": "Fig 1 beside the first figure on #4's card: the same picture, i.e. a counter strip on the left, a reset at each overflow, then one diagonal front?",
   "figs": [
    0
   ],
   "kind": "check"
  },
  {
   "text": "Fig 2: in the top rows, does the front step right through the A blocks before the conversion and the bounces that follow?",
   "figs": [
    1
   ],
   "kind": "check"
  },
  {
   "text": "Formalize by script from #4's .v (rename + 16,590-step init, as rocq/plan_check.v already does), then run check_kill?",
   "kind": "decision"
  }
 ],
 "discord_check": null,
 "stats": {
  "simulated_steps": 3000000000,
  "cells": 47451,
  "nonzeros": 18841,
  "growth": "span ~ t^0.5 (cycle k: ~2^k blocks in ~4^k steps); left edge -2 cells per cycle; 29,054 cells at 1e9 vs #4's 23,607"
 },
 "status": "CHECKPOINT_A",
 "status_reason": "Relation to kill #4 established by simulation (unique renaming EDBCFA, lockstep, rules on the twin's table, base in the hexagon, orbit 9/9 cycle states to 5.04e9); delta proof.md validated (live status in status.json: CHECKPOINT_B).",
 "sweep_id": "F3"
}