{
 "tm": "1RB1RA_1LC1RE_---0LD_1LE1LD_0RA0LF_1LF0LB",
 "rank": 26,
 "class_sheet": "Bouncer + Chaotic Edge",
 "class_guess": "Bouncer + Chaotic Edge; exact mirror twin of #5 (same edge, same open erosion bound)",
 "confidence": "med",
 "summary": "Mirror image of #5 with renamed states: same chaotic edge eating the block, so the same open erosion problem",
 "mechanism": [
  "#26 = #5 mirrored (L<->R), states renamed A..F -> D,E,A,B,C,F, but started in #5's state C.",
  "From bounce 2 on, the tape is #5's tape mirrored with one fewer 1 at the wall (all 102,240 bounces to 1e10 steps).",
  "So #5's verdict carries over: no-00 invariant, halts only if the edge eats the block; no erosion bound is known."
 ],
 "diagrams": [
  {
   "mode": "default",
   "png": "img/default_site.png",
   "html": "img/viewer.html",
   "steps": 10000,
   "caption": "bbchallenge default view: the first 10,000 steps, as on the site",
   "title": "bbchallenge default view, first 10,000 steps",
   "why": "The site's view. White block on the left, textured edge on its right; compare with #5's picture mirrored.",
   "primary": true,
   "start": "blank",
   "rows": "every step 0..10000 squeezed into 500 px rows as on the site (each px row 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 moving R/L",
   "style": "bbchallenge-default"
  },
  {
   "mode": "custom: records, two machines",
   "png": "img/twin_vs_5_mirrored.png",
   "html": null,
   "steps": 99584,
   "caption": "Left #26, right #5 mirrored: identical except one wall cell",
   "title": "#26 beside its twin #5, mirrored",
   "why": "One row per bounce. Compare the two panels cell by cell; red marks every cell where they differ.",
   "primary": true,
   "start": "blank",
   "rows": "one row per bounce, bounces 1..200: left panel = each new left record of #26, right panel = each new right record of #5",
   "window": "cells -201..192, 1 px = 1 cell (#26 cells; right panel: #5 cell x drawn at column -x-1, i.e. mirrored and shifted 1 cell)",
   "legend": "white = 1, black = 0, red = cell where the two tapes differ, grey = gap between the panels; no head drawn",
   "style": "custom"
  },
  {
   "mode": "every:400000",
   "png": "img/edge_every4e5_1e9.png",
   "html": null,
   "steps": 1000000000,
   "caption": "Chaotic edge (fine texture) creeps into the white block of 1s",
   "title": "The edge eating into the block, to 1e9",
   "why": "One row per 400,000 steps. Follow the textured fringe's left boundary against the white block as time goes down.",
   "primary": true,
   "start": "blank",
   "rows": "every 400000 steps: 2,501 rows for steps 0..1e9",
   "window": "cells -2250..349, 1 px = 1 cell (the right 2,600 cells of the 32,607-cell tape; the block runs on left to cell -32,262)",
   "legend": "white = 1, black = 0 or never visited, red/green dot = head (last move R/L)",
   "style": "bbchallenge-default"
  },
  {
   "mode": "every:1",
   "png": "img/closeup_bounces54-57.png",
   "html": null,
   "steps": 699,
   "caption": "Three trips: walk the block, dive into the edge, walk back",
   "title": "Close-up: bounces 54 to 57, every step",
   "why": "Every step, Explore colours. Red diagonals: A walking right; green: D walking left; zigzags: the 7 rules.",
   "primary": false,
   "start": "mid-run: step 12180 (bounce 54, simulated from the blank tape)",
   "rows": "every step: steps 12180..12879 = bounces 54 to 57 (1 step = 4 px tall)",
   "window": "cells -56..73, 1 px = 0.25 cells (each cell 4 px wide; the whole visited tape)",
   "legend": "white = 1, slate = 0, head cell coloured by state: red = A, orange = B, blue = C, green = D, magenta = E, cyan = F",
   "style": "bbchallenge-explore"
  }
 ],
 "history": {
  "skeleton": "0^inf <E 1^n w 0^inf",
  "vars": [
   "bounce",
   "|w| (edge width)",
   "n (block)",
   "lo",
   "dive depth of next trip",
   "first 16 cells of w"
  ],
  "rows": [
   {
    "step": 4,
    "values": [
     2,
     2,
     1,
     -2,
     7,
     "0100000000000000"
    ]
   },
   {
    "step": 31,
    "values": [
     3,
     8,
     1,
     -3,
     12,
     "0100110100000000"
    ]
   },
   {
    "step": 223,
    "values": [
     5,
     19,
     1,
     -5,
     11,
     "0100111010010101"
    ]
   },
   {
    "step": 514,
    "values": [
     8,
     23,
     2,
     -8,
     28,
     "0101010111101111"
    ]
   },
   {
    "step": 732,
    "values": [
     10,
     30,
     2,
     -10,
     32,
     "0100110111011011"
    ]
   },
   {
    "step": 1108,
    "values": [
     12,
     37,
     4,
     -12,
     10,
     "0101010100110111"
    ]
   },
   {
    "step": 2011,
    "values": [
     15,
     52,
     2,
     -15,
     11,
     "0100111010010101"
    ]
   },
   {
    "step": 2241,
    "values": [
     17,
     54,
     2,
     -17,
     19,
     "0101010111101110"
    ]
   },
   {
    "step": 2488,
    "values": [
     20,
     51,
     8,
     -20,
     10,
     "0101010100110111"
    ]
   },
   {
    "step": 3165,
    "values": [
     25,
     56,
     18,
     -25,
     21,
     "0101010111101111"
    ]
   },
   {
    "step": 3754,
    "values": [
     30,
     52,
     27,
     -30,
     48,
     "0101010111101110"
    ]
   },
   {
    "step": 4859,
    "values": [
     35,
     53,
     36,
     -35,
     16,
     "0100101101010110"
    ]
   },
   {
    "step": 6412,
    "values": [
     40,
     63,
     33,
     -40,
     11,
     "0100111010010101"
    ]
   },
   {
    "step": 9141,
    "values": [
     45,
     71,
     38,
     -45,
     58,
     "0101010111010101"
    ]
   },
   {
    "step": 10720,
    "values": [
     50,
     79,
     39,
     -50,
     11,
     "0100111010010110"
    ]
   },
   {
    "step": 13262,
    "values": [
     60,
     88,
     44,
     -60,
     38,
     "0101010111101110"
    ]
   },
   {
    "step": 27326,
    "values": [
     80,
     156,
     52,
     -80,
     10,
     "0101010100110111"
    ]
   },
   {
    "step": 35934,
    "values": [
     100,
     160,
     76,
     -100,
     150,
     "0101010111101111"
    ]
   },
   {
    "step": 63286,
    "values": [
     150,
     161,
     140,
     -150,
     10,
     "0101010100110111"
    ]
   },
   {
    "step": 99184,
    "values": [
     200,
     195,
     196,
     -200,
     10,
     "0101010100110111"
    ]
   },
   {
    "step": 182400,
    "values": [
     300,
     268,
     255,
     -300,
     19,
     "0101010111101110"
    ]
   },
   {
    "step": 390928,
    "values": [
     500,
     325,
     418,
     -500,
     11,
     "0100111010010110"
    ]
   },
   {
    "step": 695342,
    "values": [
     700,
     350,
     637,
     -700,
     19,
     "0101010111101110"
    ]
   },
   {
    "step": 1277888,
    "values": [
     1000,
     364,
     923,
     -1000,
     24,
     "0101010110010101"
    ]
   },
   {
    "step": 2648416,
    "values": [
     1500,
     371,
     1416,
     -1500,
     379,
     "0100110111011011"
    ]
   },
   {
    "step": 4513188,
    "values": [
     2000,
     371,
     1924,
     -2000,
     27,
     "0101010110010101"
    ]
   },
   {
    "step": 9727650,
    "values": [
     3000,
     389,
     2906,
     -3000,
     148,
     "0101010111101111"
    ]
   },
   {
    "step": 16922028,
    "values": [
     4000,
     429,
     3874,
     -4000,
     10,
     "0101010100110111"
    ]
   },
   {
    "step": 25973774,
    "values": [
     5000,
     596,
     4747,
     -5000,
     27,
     "0101010111010101"
    ]
   },
   {
    "step": 49346400,
    "values": [
     7000,
     739,
     6604,
     -7000,
     43,
     "0101010111101110"
    ]
   },
   {
    "step": 98637738,
    "values": [
     10000,
     929,
     9414,
     -10000,
     126,
     "0101010111101110"
    ]
   },
   {
    "step": 185605711,
    "values": [
     13759,
     876,
     13226,
     -13759,
     111,
     "0101010111010101"
    ]
   },
   {
    "step": 220407016,
    "values": [
     15000,
     987,
     14356,
     -15000,
     10,
     "0101010100110111"
    ]
   },
   {
    "step": 389010184,
    "values": [
     20000,
     1467,
     18876,
     -20000,
     17,
     "0100110111011010"
    ]
   },
   {
    "step": 604389822,
    "values": [
     25000,
     1770,
     23573,
     -25000,
     74,
     "0101010111010011"
    ]
   },
   {
    "step": 866078562,
    "values": [
     30000,
     2009,
     28334,
     -30000,
     11,
     "0100111010010101"
    ]
   },
   {
    "step": 999879502,
    "values": [
     32262,
     2206,
     30399,
     -32262,
     26,
     "0101010111101111"
    ]
   }
  ]
 },
 "rules": [
  {
   "name": "walk right",
   "from": "x A> 1^k y",
   "to": "x 1^k A> y",
   "steps": "k",
   "cases": null,
   "validated": {
    "instances": 60,
    "passed": 60
   },
   "source": "manual"
  },
  {
   "name": "walk left",
   "from": "x 1^k <D y",
   "to": "x <D 1^k y",
   "steps": "k",
   "cases": null,
   "validated": {
    "instances": 60,
    "passed": 60
   },
   "source": "manual"
  },
  {
   "name": "bounce",
   "from": "0^inf 1^n <D y",
   "to": "0^inf 1^(n+1) A> y",
   "steps": "2n+3",
   "cases": null,
   "validated": {
    "instances": 60,
    "passed": 60
   },
   "source": "manual"
  },
  {
   "name": "T turn",
   "from": "x A> 0 0 y",
   "to": "x <D 0 1 y",
   "steps": "3",
   "cases": "A reads 0: right context 00 / 010 / 011 (complete)",
   "validated": {
    "instances": 60,
    "passed": 60
   },
   "source": "manual"
  },
  {
   "name": "Ca carry",
   "from": "x A> 0 1 0 y",
   "to": "x 1 1 0 A> y",
   "steps": "3",
   "cases": "A reads 0, context 010",
   "validated": {
    "instances": 60,
    "passed": 60
   },
   "source": "manual"
  },
  {
   "name": "Fo fold",
   "from": "x A> 0 1 1 y",
   "to": "x 1 0 A> 0 y",
   "steps": "6",
   "cases": "A reads 0, context 011",
   "validated": {
    "instances": 60,
    "passed": 60
   },
   "source": "manual"
  },
  {
   "name": "E1 re-dive",
   "from": "x 1 1 1 0 <D y",
   "to": "x 1 0 A> 0 1 y",
   "steps": "5",
   "cases": "D reads 0: left context 1110 / 11010 / 10110 / 101010 (complete under no-00)",
   "validated": {
    "instances": 60,
    "passed": 60
   },
   "source": "manual"
  },
  {
   "name": "E2 re-dive",
   "from": "x 1 1 0 1 0 <D y",
   "to": "x 1 0 1 A> 0 1 y",
   "steps": "7",
   "cases": "D reads 0, context 11010",
   "validated": {
    "instances": 60,
    "passed": 60
   },
   "source": "manual"
  },
  {
   "name": "P1 pass",
   "from": "x 1 0 1 1 0 <D y",
   "to": "x <D 0 1 0 0 1 y",
   "steps": "5",
   "cases": "D reads 0, context 10110",
   "validated": {
    "instances": 60,
    "passed": 60
   },
   "source": "manual"
  },
  {
   "name": "P2 pass",
   "from": "x 1 0 1 0 1 0 <D y",
   "to": "x <D 0 1 0 1 0 1 y",
   "steps": "6",
   "cases": "D reads 0, context 101010",
   "validated": {
    "instances": 60,
    "passed": 60
   },
   "source": "manual"
  },
  {
   "name": "halting door",
   "from": "x 0 0 1 0^j 1 0 <D y",
   "to": "halt",
   "steps": "j+5",
   "cases": "the only route to C0 (D0, E1, F0^j, F1, B0, C0); needs 00 left of the head",
   "validated": {
    "instances": 60,
    "passed": 60
   },
   "source": "manual"
  },
  {
   "name": "twin map (bounce k >= 2)",
   "from": "#26: 0^inf <E 1^n w 0^inf at step t",
   "to": "#5: 0^inf rev(w) 1^(n+1) B> 0^inf at step t+2k",
   "steps": null,
   "cases": "bounce k = k-th new left record of #26 / right record of #5",
   "validated": {
    "instances": 102240,
    "passed": 102240
   },
   "source": "manual"
  }
 ],
 "template": {
  "file": "verify/Bouncer_v3.v",
  "module": "TM1",
  "machine": "1LB1RA_0RA0RC_---1RD_1RE1RB_1LF0LE_0RD0LE",
  "diff": null,
  "applies": "no",
  "note": "Bouncer_v3 TM1 needs an eventually periodic side: RC i pumps exponents 363+128i and 1+3i, and one BigStep = 128 bounces checked by native computation. #26's edge is aperiodic with positive entropy, so no RC i exists. InfiniteRect_v1 (periodic boundary tokens) and LongNv1 (explicit exponent patterns) assume the same kind of regularity."
 },
 "strategy": "Park with #5 as one cryptid candidate: any erosion bound for #5 transfers verbatim through the mirror map, giving both kills. Cryptid protocol still owes a Rocq rule reduction (bounce + 7 rules + no-00 invariant); one file can do both twins.",
 "risks": [
  "No deterministic erosion bound is known for the shared edge (#5 research: potentials miss by 5-12x).",
  "#26's block is one cell shorter than #5's, so its halting threshold is one cell closer; irrelevant after bounce 40 (block >= 33).",
  "The twin map is checked to 1e10 steps; its all-time proof is the mirror identity of the tables plus the wall-model argument."
 ],
 "checkpoint_questions": [
  {
   "text": "Twin figure: are the two panels the same picture, with red only on the diagonal at the block's wall end (one extra 1 in #5)?",
   "figs": [
    1
   ],
   "kind": "check"
  },
  {
   "text": "Edge view to 1e9: does the textured fringe creep slowly into the white block while the block still grows, as in #5's Fig 1 mirrored?",
   "figs": [
    2
   ],
   "kind": "check"
  },
  {
   "text": "Park #26 with #5 as a cryptid candidate (your 2026-10-10 #5 call), or should we fund the shared Rocq rule reduction now?",
   "figs": [],
   "kind": "decision"
  }
 ],
 "discord_check": null,
 "stats": {
  "simulated_steps": 10000000000,
  "cells": 32607,
  "nonzeros": 31699,
  "growth": "t^0.5 (bouncer: 32,262 bounces by 1e9; 102,241 by 1e10)"
 },
 "status": "CRYPTID_CANDIDATE",
 "status_reason": "Exact mirror twin of #5 (cryptid candidate, 2026-10-10): same edge dynamics, same open erosion bound. Stopped before proof work."
}