{
 "tm": "1RB1RF_1LC0RB_1RD0LC_1LE1RA_0RC1LB_---1RE",
 "rank": 49,
 "class_sheet": "Unknown",
 "class_guess": "Nested binary counters of toggling defect walls in a period-5 sea, with engine-dissolving epochs (multi-region)",
 "confidence": "low",
 "summary": "Period-5 sea swept by a zig-zag head; defect walls toggle like binary counters; the global epoch law is unknown",
 "mechanism": [
  "Sea and walls: the tape is mostly the period-5 sea 11100. Right sweeps (B) shift every block 2 cells right and left sweeps (C) shift it back, 7 steps per block. The head turns only at 2-state defect walls. A right-wall bit is the insert 000 (= 0), which reflects a right sweep and becomes 100 (= 1); 100 lets the sweep through and is reset on the way back. Left-wall bits (gap-1 vs run-2) do the same to left sweeps. So the central engine drives a binary counter on each side (counter laws hold on 33,140/33,140 and 5,545/5,545 orbit turns).",
  "Above that it is not understood. Counter overflows feed a second engine/counter pair at the right end and a structure at the left edge. Up to 2.73e9 the inner engine keeps dissolving (43 epochs between 1e9 and 2.73e9, 29e6 to 56e6 steps apart): a wall walks left one block per bounce, eating a 4/5-density sea (11110) back into 11100, and then the engine re-forms. After 2.73e9 there are none in the inner region. Each edge visit adds 3 cells (2,021 cells at 1e10), and edge visits keep slowing down.",
  "Halting: every halt is C reading 0 just before 110 (rule H), for example a right sweep meeting B> 1^n 0 1 0, or a D sweep meeting 110. Neither is seen to 1e10. Cryptid check: nothing Collatz-like. Everything observed is binary counting or linear drift, but the unknown epoch/bit-creation law could still hide parity branching."
 ],
 "diagrams": [
  {
   "mode": "records",
   "png": "img/records_1e10.png",
   "html": null,
   "steps": 10000000000,
   "caption": "Edge records to 1e10: both edges grow; interior defects drift",
   "title": "Edge records to 10 billion steps",
   "why": "One row per new edge cell. Compare the two edges' slopes, then follow the wavy grey lines inside.",
   "primary": true,
   "start": "blank",
   "rows": "the start, then one per new leftmost or rightmost cell (2,021 rows, steps 0..9,957,807,009); not evenly spaced in time",
   "window": "cells -729..1291, 1 px = 1 cell",
   "legend": "white = 1, black = 0 or never visited, red/green = head at a new right/left edge",
   "style": "bbchallenge-default"
  },
  {
   "mode": "every:8",
   "png": "img/counters_1e9_every8.png",
   "html": null,
   "steps": 16000,
   "caption": "Close-up at 1e9: engine zig-zag and right-counter bit columns",
   "title": "Close-up after step 1e9: engine and counters",
   "why": "Time runs down. Note which dark column each right excursion from the engine (x ~ 200) stops at.",
   "primary": true,
   "start": "mid-run: step 1,000,000,000, head at cell 502 in state B moving right",
   "rows": "every 8 steps, 2,001 rows (steps 1e9 .. 1e9 + 16,000)",
   "window": "cells 250..1000, 1 px = 1 cell (column x = cell 250 + x); right-counter bits sit at cells 680, 733, 778, 808, 821, 862, 867, 875",
   "legend": "white = 1, black = 0, red/green = head after a right/left move",
   "style": "bbchallenge-default"
  },
  {
   "mode": "custom",
   "png": "img/turnmap_log_1e9.png",
   "html": null,
   "steps": 1000000000,
   "caption": "Turning points of the head over log time, to 1e9",
   "title": "Where the head turns, log time to 1e9",
   "why": "Each line is a wall the head keeps bouncing off. Note where lines are born and which way they drift.",
   "primary": true,
   "start": "blank",
   "rows": "800 log-spaced time bins from step 1e3 (top) to 1e9 (bottom); a turning point is a sweep's extreme cell before the head moves 8+ cells back",
   "window": "cells -549..988, 1 px = 1 cell",
   "legend": "white = no turn; red = right turning point (R -> L); green = left turning point (L -> R); dark = both; darker = more turns in the bin (log scale)",
   "style": "custom"
  },
  {
   "mode": "blaze",
   "png": "img/blaze_1e9.png",
   "html": null,
   "steps": 1000000000,
   "caption": "Blaze 1e9: slow two-sided growth, defect columns inside",
   "title": "Blaze view, 1 billion steps",
   "why": "Time runs down. Edges grow on both sides; the paler vertical bands are defect-rich zones.",
   "primary": false,
   "start": "blank",
   "rows": "Blaze time blocks of 1,048,576 steps (954 rows, each averaged), steps 0..1e9",
   "window": "cells -549..988, 1 px = 1 cell",
   "legend": "white = 0, orange = 1; pale orange = a cell that is 1 for part of its time block",
   "style": "bbchallenge-blaze"
  },
  {
   "mode": "default",
   "png": "img/default_site.png",
   "html": null,
   "steps": 10000,
   "caption": "Site view: early sweeps over the 11100 sea",
   "title": "bbchallenge Default view, first 10,000 steps",
   "why": "For orientation: what bbchallenge.org shows for this machine.",
   "primary": false,
   "start": "blank",
   "rows": "10,000 steps squeezed into 500 px rows (1 px row = 20 steps; the site 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 after a right/left move",
   "style": "bbchallenge-default"
  }
 ],
 "history": {
  "skeleton": "span lo..hi of the visited tape; drift = wall-walk runs so far (8+ left turns in a row, each 5 cells left of the last; one epoch can give 2-3 runs)",
  "vars": [
   "lo",
   "hi",
   "cells",
   "drift"
  ],
  "rows": [
   {
    "step": 1000,
    "values": [
     -12,
     28,
     41,
     0
    ]
   },
   {
    "step": 3000,
    "values": [
     -15,
     37,
     53,
     0
    ]
   },
   {
    "step": 10000,
    "values": [
     -21,
     61,
     83,
     0
    ]
   },
   {
    "step": 30000,
    "values": [
     -30,
     70,
     101,
     0
    ]
   },
   {
    "step": 100000,
    "values": [
     -51,
     118,
     170,
     0
    ]
   },
   {
    "step": 300000,
    "values": [
     -81,
     175,
     257,
     0
    ]
   },
   {
    "step": 1000000,
    "values": [
     -123,
     256,
     380,
     2
    ]
   },
   {
    "step": 3000000,
    "values": [
     -177,
     361,
     539,
     2
    ]
   },
   {
    "step": 10000000,
    "values": [
     -285,
     529,
     815,
     9
    ]
   },
   {
    "step": 30000000,
    "values": [
     -381,
     715,
     1097,
     9
    ]
   },
   {
    "step": 100000000,
    "values": [
     -432,
     796,
     1229,
     9
    ]
   },
   {
    "step": 300000000,
    "values": [
     -465,
     844,
     1310,
     13
    ]
   },
   {
    "step": 1000000000,
    "values": [
     -549,
     988,
     1538,
     30
    ]
   },
   {
    "step": 3000000000,
    "values": [
     -684,
     1216,
     1901,
     136
    ]
   },
   {
    "step": 10000000000,
    "values": [
     -729,
     1291,
     2021,
     141
    ]
   }
  ]
 },
 "rules": [
  {
   "name": "S_R  right sweep over the sea",
   "from": "B> (11100)^n",
   "to": "(00111)^n B>",
   "steps": "7n",
   "cases": "any n >= 1, random 12-cell contexts on both sides",
   "validated": {
    "instances": 200,
    "passed": 200
   },
   "source": "manual"
  },
  {
   "name": "S_L  left sweep over the sea",
   "from": "(00111)^n <C",
   "to": "<C (11100)^n",
   "steps": "7n",
   "cases": "any n >= 1, any context",
   "validated": {
    "instances": 200,
    "passed": 200
   },
   "source": "manual"
  },
  {
   "name": "RB0  right bit 0 reflects, becomes 1",
   "from": "(00111)^n B> 000",
   "to": "<C (11100)^n 100",
   "steps": "7n+1",
   "cases": "n >= 1; the turn and the start of the return sweep",
   "validated": {
    "instances": 200,
    "passed": 200
   },
   "source": "manual"
  },
  {
   "name": "RB1  right bit 1 passes the sweep",
   "from": "B> 100",
   "to": "111 B>",
   "steps": "5",
   "cases": "any context",
   "validated": {
    "instances": 200,
    "passed": 200
   },
   "source": "manual"
  },
  {
   "name": "RB1r  return sweep resets a passed bit",
   "from": "(00111)^n 111 <C",
   "to": "<C (11100)^n 000",
   "steps": "7n+3",
   "cases": "n >= 1; together RB1 then RB1r take bit 1 -> 0",
   "validated": {
    "instances": 200,
    "passed": 200
   },
   "source": "manual"
  },
  {
   "name": "LB0  left bit 0 (gap 1) reflects, becomes run 2",
   "from": "00011 10111 (00111)^n <C",
   "to": "00011 00111 (00111)^n B>",
   "steps": "14n+13",
   "cases": "n >= 1, constructed context. The pass-through case (left bit 1) depends on the phase of the sea on its right and is not yet an exact rule",
   "validated": {
    "instances": 200,
    "passed": 200
   },
   "source": "manual"
  },
  {
   "name": "D_R  D sweep: 3/5 sea -> 4/5 sea",
   "from": "D> (11100)^n",
   "to": "(11101)^n D>",
   "steps": "5n",
   "cases": "any n >= 1. A block 110.. instead of 111.. makes F read 0, which halts",
   "validated": {
    "instances": 200,
    "passed": 200
   },
   "source": "manual"
  },
  {
   "name": "H  the only way to halt",
   "from": "0 <C 110  or  C> 0110",
   "to": "halt",
   "steps": "4",
   "cases": "C0, D1, A1, then F reads 0. F is entered only by A1, A only by D1 and D only by C0, so every halt has this form (200 random contexts per direction)",
   "validated": {
    "instances": 400,
    "passed": 400
   },
   "source": "manual"
  },
  {
   "name": "CR  inner right counter = binary +1",
   "from": "bits b0..b7 = inserts 000 (0) / 100 (1) in the 11100 sea (cells 680..875 at 1e9); a right sweep leaves the engine",
   "to": "turns at the first 0 bit j; bits < j become 0 and bit j becomes 1",
   "steps": null,
   "cases": "real orbit, steps 1e9..1.03e9: every right turn in cells 600..900 after a left turn left of cell 600; 33,139/33,139 next states are exact +1. Depth counts 16,634 / 8,318 / 4,158 / 2,080 / 1,040 / 520 / 260 / 130",
   "validated": {
    "instances": 33140,
    "passed": 33140
   },
   "source": "manual"
  },
  {
   "name": "CL  inner left counter = binary +1",
   "from": "4 low bits in cells 315..435: run-2 defect (1) / gap-1 defect 3 cells right (0)",
   "to": "turns at the first 0 bit; lower bits -> 0, that bit -> 1",
   "steps": null,
   "cases": "real orbit, steps 1e9..1.01e9, every left turn after a right turn right of the zone; 5,371/5,371 exact +1; 346 carries past bit 3",
   "validated": {
    "instances": 5545,
    "passed": 5545
   },
   "source": "manual"
  },
  {
   "name": "EP  engine-dissolving epochs (open)",
   "from": "inner engine + counters",
   "to": "the engine dissolves; a wall walks left 5 cells per bounce, eating the 11110 sea; the engine re-forms further left",
   "steps": null,
   "cases": "Wall-walk detector (8+ left turns in a row, each 5 cells left of the last): 136 runs from 5e5 to 2.73e9. Between 1e9 and 2.73e9 they form 43 epochs, 2.9e7 to 5.6e7 steps apart. 5 runs near the right end (3.7e9..4.6e9), none after that to 1e10. No exact rule yet",
   "validated": {
    "instances": 0,
    "passed": 0
   },
   "source": "manual"
  }
 ],
 "template": {
  "file": "verify/CPS_LRU_v3.v:2133",
  "module": null,
  "machine": "1RB0RF_1LC0RB_1RD0LC_1LE1RA_0RC1LB_---0LE",
  "diff": "A1 1RF->0RF, F1 1RE->0LE",
  "applies": "no",
  "note": "Nearest proved machines by table (2 cells away): a CPS_LRU_v3 certificate (this one; it stops growing at 124 cells by 1e8), CPS_LRU_v4 and RWL_mod_v1. All three are decider certificates, not structural proofs. The targeting row's verify/CounterCmp_v1.v (TM1) compares two unary counters, which is a different mechanism. Kill #12's recursive run-length counter is the closest kill in spirit, but its tape is runs of 1s, not a period-5 sea with toggling walls. No template applies."
 },
 "strategy": "Not ready for a proof. Next: (1) an exact catalogue of every wall shape in both sea phases; (2) an abstract walls-and-counters simulator checked against the TM to 1e10; (3) the epoch and bit-creation law, plus an invariant that rules out C reading 0 before 110 (B> 1^n 0 1 0, D> 110).",
 "risks": [
  "Several levels: two engine/counter pairs, edge structures and engine-dissolving epochs; the regime changed at ~2.7e9, so 1e10 steps may not show every regime.",
  "The defect algebra has real halting routes (B> 1^n 0 1 0, D> 110), so non-halting needs a global invariant on defect shapes, not just the counter laws.",
  "Nobody has simulated it to 1e14 (sheet). qsim does not accelerate it (block size 1, 0 rules by 5.4e6 steps), and direct simulation of the growing gaps between edge visits is slow."
 ],
 "checkpoint_questions": [
  {
   "text": "Close-up after step 1e9: do the right excursions stop at the dark bit columns in a binary-ruler order (1st, 2nd, 1st, 3rd, 1st, 2nd, ...)?",
   "figs": [
    1
   ],
   "kind": "check"
  },
  {
   "text": "Turn map: do the lines read to you as several separate wall systems (an inner one and one per edge) rather than one counter?",
   "figs": [
    2
   ],
   "kind": "check"
  },
  {
   "text": "Priority call: spend one more stage on the epoch/bit-creation law (abstract wall simulator), or park this machine as STUCK at observe?",
   "figs": [],
   "kind": "decision"
  }
 ],
 "discord_check": null,
 "stats": {
  "simulated_steps": 10000000000,
  "cells": 2021,
  "nonzeros": 1224,
  "growth": "+3 cells per edge visit; visits slow down (left edge about every 4e7 steps near 1.5e9, about every 1.5e9 near 8e9); 1,538 cells at 1e9"
 },
 "status": "CHECKPOINT_A",
 "status_reason": "Observe done. Low confidence: the sea sweeps, wall toggles and both inner counter laws are validated, but the global epoch/bit-creation law is not, so proof work waits for Dennis."
}