{
 "tm": "1RB1RF_1LC0RF_1LE0LD_1RC0LB_---1RA_1LB1RA",
 "rank": 36,
 "class_sheet": "Bouncer + Chaotic Edge",
 "class_guess": "Bouncer + Chaotic Edge; twin of #13 at the cycle level (same bulk, junction and tail orbit D_n)",
 "confidence": "med",
 "summary": "#13's twin: same period-10 bouncer, same 7 junction words, same chaotic tail D_n cycle for cycle. Tail = whole problem.",
 "mechanism": [
  "Bulk (1101101101)^a on a left wall moves 1 cell left per bounce (62a steps); the junction cycles through #13's 7 words; 1 bounce in 7 touches the tail D.",
  "D_n equals #13's D_n in all 1,952 shared cycles, and the probe map P is #13's (217/217 tested, 0 disagree). #35 = this table renamed; #34 = #13 mirrored.",
  "Halt only via B reading 0 with 00 on its left. Never seen: the edge map is clean to 1.5e7 cycles (about 4.9e16 steps). The tail has no proof."
 ],
 "diagrams": [
  {
   "mode": "records:L",
   "png": "img/records_L_1.2e6.png",
   "html": "img/viewer.html",
   "steps": 1140693,
   "caption": "One row per bounce from blank: bulk, seam, ragged tail",
   "title": "One row per bounce, first 1.1M steps",
   "why": "Rows are bounces. Left: striped bulk; middle: diagonal seam; right: ragged part. Compare their widths, top vs bottom.",
   "primary": true,
   "start": "blank",
   "rows": "left records: the start, then one row per new leftmost cell = one row per bounce (400 rows, steps 0..1,140,693; rows are not equal time)",
   "window": "cells -399..597, 1 px = 1 cell (cell 0 = the start cell)",
   "legend": "white = 1, black = 0 or never visited, red/green = head just moved right/left",
   "style": "bbchallenge-default"
  },
  {
   "mode": "custom: tail D_n per cycle, this machine | #13 | XOR",
   "png": "img/twin_tail_vs_13.png",
   "html": null,
   "steps": 47105452,
   "caption": "Tail D_n per cycle: this machine, #13, and their XOR",
   "title": "Our tail vs #13's tail, per cycle",
   "why": "One row per 7-bounce cycle. Compare left and middle panels row by row; the right panel shows differences in red.",
   "primary": true,
   "start": "mid-run: step 679,041 (row 0 = cycle start C_0(58, D_0) of the run from blank; #13's row 0 is its C_0(59, D_0) at step 784,041)",
   "rows": "one row per 7-bounce cycle n = 0..399, taken at each cycle start (this machine: steps 679,041..47,105,452)",
   "window": "cells 0..423, 1 px = 1 cell, of D in each of 3 panels (cell 0 = first cell right of the 54-cell junction X0); panels: this machine | #13 | XOR",
   "legend": "white = 1, black = 0, dark grey = past the end of D, blue-grey bar = panel separator; XOR panel: black = same cell, red = cells differ",
   "style": "custom"
  },
  {
   "mode": "records:L frame=right width=1200",
   "png": "img/records_L_1e8_right1200.png",
   "html": "img/viewer.html",
   "steps": 100000000,
   "caption": "Right edge pinned, last 1,200 cells: the ragged band",
   "title": "Right end only, 100 million steps",
   "why": "Rows are shifted so the right edge stays put. Compare the ragged band's width at top and bottom.",
   "primary": true,
   "start": "blank",
   "rows": "left records: the start, then one row per new leftmost cell = one row per bounce (4,580 rows, steps 0..100,000,000; rows are not equal time)",
   "window": "cells -1199..0, 1 px = 1 cell, counted from the right edge (each row is shifted so its rightmost visited cell is at 0; the bulk continues off-picture to the left)",
   "legend": "white = 1, black = 0 or never visited, red/green = head just moved right/left",
   "style": "bbchallenge-default"
  },
  {
   "mode": "blaze",
   "png": "img/blaze_1e7.png",
   "html": "img/viewer.html",
   "steps": 10000000,
   "caption": "Blaze view, 10 million steps",
   "title": "Blaze view, 10 million steps",
   "why": "Whole run to 1e7 steps. Compare the smooth left edge with the ragged right edge.",
   "primary": false,
   "start": "blank",
   "rows": "Blaze time blocks of 16,384 steps (averaged), 611 blocks stretched to 500 px, so 1 px row ~ 20,000 steps (steps 0..10,000,000)",
   "window": "cells -1346..1137, 1 px = 3.1 cells",
   "legend": "white = 0, orange = 1, paler orange = mixed (each pixel averages its cells over its time block); no head drawn",
   "style": "bbchallenge-blaze"
  },
  {
   "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, first 10,000 steps",
   "why": "For orientation: the start of the run as bbchallenge.org shows it.",
   "primary": false,
   "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 <D 0 (1101101101)^a X0 D 0^inf   (X0 = 110111100110011101100100100111101100100110110111010011, #13's X0)",
  "vars": [
   "a",
   "|D|",
   "D (first 24 cells)"
  ],
  "rows": [
   {
    "step": 679041,
    "values": [
     58,
     261,
     "011001001101101100100110"
    ]
   },
   {
    "step": 710472,
    "values": [
     59,
     258,
     "011001001001100100100110"
    ]
   },
   {
    "step": 739157,
    "values": [
     60,
     255,
     "011101101100100110011011"
    ]
   },
   {
    "step": 771604,
    "values": [
     61,
     252,
     "001001001100100110110010"
    ]
   },
   {
    "step": 801867,
    "values": [
     62,
     249,
     "011001001100100100110111"
    ]
   },
   {
    "step": 833752,
    "values": [
     63,
     246,
     "011101101100100111011011"
    ]
   },
   {
    "step": 864985,
    "values": [
     64,
     243,
     "001001001100100110110010"
    ]
   },
   {
    "step": 992699,
    "values": [
     68,
     231,
     "011001001101101110100110"
    ]
   },
   {
    "step": 1349053,
    "values": [
     78,
     201,
     "011001001101101110100110"
    ]
   },
   {
    "step": 2711163,
    "values": [
     108,
     321,
     "001001001100100110110010"
    ]
   },
   {
    "step": 5831403,
    "values": [
     158,
     321,
     "011101101100100111011011"
    ]
   },
   {
    "step": 15317035,
    "values": [
     258,
     291,
     "011101101100100110011011"
    ]
   },
   {
    "step": 29137475,
    "values": [
     358,
     351,
     "011001001001100100100110"
    ]
   },
   {
    "step": 69822111,
    "values": [
     558,
     351,
     "001001001100100110110010"
    ]
   },
   {
    "step": 127853013,
    "values": [
     758,
     321,
     "011001001101101110100110"
    ]
   },
   {
    "step": 247450499,
    "values": [
     1058,
     411,
     "001001001100100110110010"
    ]
   },
   {
    "step": 406142429,
    "values": [
     1358,
     291,
     "011101101100100110011011"
    ]
   },
   {
    "step": 603885785,
    "values": [
     1658,
     321,
     "001001001100100110110010"
    ]
   },
   {
    "step": 884868232,
    "values": [
     2009,
     348,
     "011001001100100100110111"
    ]
   },
   {
    "step": 999698415,
    "values": [
     2136,
     327,
     "011101101100100111011011"
    ]
   }
  ]
 },
 "rules": [
  {
   "name": "WALL",
   "from": "0^inf <D 0 110110 r",
   "to": "0^inf 11101111 B> r",
   "steps": "12",
   "cases": null,
   "validated": {
    "instances": 30,
    "passed": 30
   },
   "source": "manual"
  },
  {
   "name": "RS right sweep",
   "from": "B> (1101110110)^n",
   "to": "(0110101111)^n B>",
   "steps": "12n",
   "cases": null,
   "validated": {
    "instances": 30,
    "passed": 30
   },
   "source": "manual"
  },
  {
   "name": "LS left sweep",
   "from": "(0111101101)^n <D",
   "to": "<D (0110110111)^n",
   "steps": "50n",
   "cases": null,
   "validated": {
    "instances": 30,
    "passed": 30
   },
   "source": "manual"
  },
  {
   "name": "B_k bounce, k=1..5",
   "from": "0^inf <D 0 (1101101101)^a X_k D 0^inf",
   "to": "0^inf <D 0 (1101101101)^(a+[k=5]) X_(k+1) D 0^inf",
   "steps": "62a+b_k, b = 13, 433, 55, 49, 73",
   "cases": "any D (random and orbit); X_k = #13's junction words",
   "validated": {
    "instances": 200,
    "passed": 200
   },
   "source": "manual"
  },
  {
   "name": "B_6 cycle close",
   "from": "0^inf <D 0 (1101101101)^a X6 D 0^inf",
   "to": "0^inf <D 0 (1101101101)^a X0 D 0^inf",
   "steps": "62a+13",
   "cases": "any D",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "probe B_0",
   "from": "0^inf <D 0 (1101101101)^a X0 D 0^inf",
   "to": "0^inf <D 0 (1101101101)^a X1 P(D) 0^inf",
   "steps": "62a+c(D)",
   "cases": "P = #13's probe map: orbit D 120/120 same; random D 97 same + 103 break in both, 0 disagree",
   "validated": {
    "instances": 120,
    "passed": 120
   },
   "source": "manual"
  },
  {
   "name": "cycle",
   "from": "0^inf <D 0 (1101101101)^a X0 D_n 0^inf",
   "to": "0^inf <D 0 (1101101101)^(a+1) X0 D_(n+1) 0^inf",
   "steps": "434a+698+c(D_n)",
   "cases": "D_n = #13's D_n; also 2,079/2,079 real cycles to 1e9",
   "validated": {
    "instances": 60,
    "passed": 60
   },
   "source": "manual"
  },
  {
   "name": "halt",
   "from": "00 B> 0",
   "to": "halt",
   "steps": "3",
   "cases": "also 000 <B; the only way to halt (B0, C0, E0)",
   "validated": {
    "instances": 40,
    "passed": 40
   },
   "source": "manual"
  },
  {
   "name": "init",
   "from": "0^inf A> 0^inf",
   "to": "0^inf <D 0 (1101101101)^57 X1 D_0 0^inf",
   "steps": "657139",
   "cases": "first cycle start C_0(58, D_0) at step 679,041",
   "validated": {
    "instances": 1,
    "passed": 1
   },
   "source": "manual"
  }
 ],
 "template": {
  "file": "verify/Bouncer_v3.v",
  "module": "TM1",
  "machine": "1LB1RA_0RA0RC_---1RD_1RE1RB_1LF0LE_0RD0LE",
  "diff": null,
  "applies": "partly",
  "note": "sideRLs: a fixed crossing protocol into a one-sided right part fits (ours: 14 fixed round trips 2 cells left of the X0|D cut), but TM1's RC i is an explicit word; our D is chaotic and needs a closed language (#13's lemma E'). The A-C neighbours in RWL_mod_v2.v / CPS_LRU_v1.v are decider certificates: same parameters give false here."
 },
 "strategy": "Everything except the edge is routine (Bouncer_v3/sideRLs shape; init by direct execution, 657,139 steps). A kill needs #13's edge lemma (E'): a closed language for D under P. It is shared by #13, #34, #35 and #36, so one lemma would mean 4 kills. Until then, park with #13.",
 "risks": [
  "Edge lemma open: #13 refuted SFT_k invariants for k <= 36 and plain n-gram CPS (n <= 26); no regular invariant is known.",
  "mxdys listed the family on UBRRBA_TODO (a halting tool): a late break or halt is possible; edge map clean to 1.5e7 cycles (about 4.9e16 steps).",
  "Even with (E'), this machine needs its own .v: same architecture, but the wall, the sweeps (62a) and the step constants differ from #13."
 ],
 "checkpoint_questions": [
  {
   "text": "Fig 1: is the bulk on the left a clean striped bouncer with one seam, so only the ragged right part is new?",
   "figs": [
    0
   ],
   "kind": "check"
  },
  {
   "text": "Fig 2: do the left and middle panels match row by row, with the right (XOR) panel all black?",
   "figs": [
    1
   ],
   "kind": "check"
  },
  {
   "text": "Should we park this with #13 (one shared edge lemma for #13/#34/#35/#36), or fund a family stage on that lemma?",
   "kind": "decision"
  }
 ],
 "discord_check": null,
 "stats": {
  "simulated_steps": 1000000000,
  "cells": 21745,
  "nonzeros": 15171,
  "growth": "both edges ~ sqrt(t): lo = -0.47 sqrt(t), hi = +0.22 sqrt(t) at 1e9"
 },
 "status": "CHECKPOINT_A",
 "status_reason": "Mechanism exact and validated, and identical to parked #13 at the cycle level; no non-halting argument for the chaotic tail D (shared edge lemma E'). Confidence med: proof work waits on Dennis (decision.json)."
}