{
  "tm": "1RB0LD_1RC0RD_1LA0RC_1RE1LB_1LF0LA_---0LE",
  "holdout_line": 282,
  "updated_utc": "2026-10-14T17:31:56.841758+00:00",
  "stage": "funded_mechanism_study_complete",
  "proof_status": "unproved",
  "halting_status": "unknown",
  "observed_nonhalting_through": 1000000000,
  "engine": "existing tools/sim/tmsim C core",
  "end": {
    "step": 1000000000,
    "state": "A",
    "dir": "L",
    "pos": -28752,
    "lo": -29278,
    "hi": 228,
    "nonzeros": 17521,
    "halted": false
  },
  "mechanism_confidence": "low",
  "possible_chaotic_edge": true,
  "confirmed_cryptid": false,
  "no_arithmetic_return_map_extracted": true,
  "observed_behavior": "The visited span expands mainly left. The right record moves from 154 at one million steps to 228 at one billion. Long left/right sweeps rewrite a word with many short blocks; a bounded list of counter exponents has not been identified.",
  "ranking_within_pair": 1,
  "ranking_reason": "More promising of these two for a bounded word-transducer investigation: the sampled 12-bit-factor count stabilizes at 102, and three fixed local windows cover 1,024 of the first 1,282 left-record gaps. The long return gaps and the changing whole word are still unexplained.",
  "qsim": {
    "ev": "end",
    "reason": "max_loops",
    "loops": 30000,
    "step": 324434,
    "steps_exact": true,
    "nonzeros": 397,
    "rules": 10,
    "rules_by_level": {
      "1": 10
    },
    "collatz_rules": 0,
    "failed_proofs": 0,
    "macro_moves": 23010,
    "chain_moves": 6980,
    "rule_moves": 10,
    "block_size": 3,
    "seconds": 0.784
  },
  "independent_1e6_crosscheck": {
    "matches_C_snapshot": true,
    "transition_counts": {
      "A0": 100155,
      "B0": 100155,
      "C0": 100155,
      "A1": 63598,
      "D1": 116521,
      "C1": 119551,
      "B1": 116521,
      "D0": 63597,
      "E0": 78075,
      "F1": 78075,
      "E1": 63597
    },
    "F_neighborhoods_distinct": 71,
    "F_neighborhoods_top20": [
      [
        "1011101110110",
        5803
      ],
      [
        "1111011100110",
        4917
      ],
      [
        "1111011101011",
        4837
      ],
      [
        "1111101110110",
        4622
      ],
      [
        "1111111101101",
        4375
      ],
      [
        "1011011100010",
        3272
      ],
      [
        "1101111101011",
        3272
      ],
      [
        "0110111101101",
        3265
      ],
      [
        "1111101110101",
        3240
      ],
      [
        "0111111101101",
        3134
      ],
      [
        "1101101110010",
        3032
      ],
      [
        "1011111100100",
        2996
      ],
      [
        "1111101110010",
        2750
      ],
      [
        "1110111101101",
        2728
      ],
      [
        "1111111100101",
        2700
      ],
      [
        "0111111101100",
        2669
      ],
      [
        "1110101110010",
        2510
      ],
      [
        "0110111100101",
        2346
      ],
      [
        "1110111100100",
        2346
      ],
      [
        "0111101101100",
        2338
      ]
    ],
    "first_F_entries": [
      {
        "step": 18,
        "pos": 4,
        "word": "0111101100000",
        "head_offset": 6,
        "read": 1
      },
      {
        "step": 20,
        "pos": 2,
        "word": "0001111101000",
        "head_offset": 6,
        "read": 1
      },
      {
        "step": 31,
        "pos": 1,
        "word": "0001101110100",
        "head_offset": 6,
        "read": 1
      },
      {
        "step": 33,
        "pos": -1,
        "word": "0000011101101",
        "head_offset": 6,
        "read": 1
      },
      {
        "step": 67,
        "pos": 7,
        "word": "1011101100000",
        "head_offset": 6,
        "read": 1
      },
      {
        "step": 69,
        "pos": 5,
        "word": "0110111101000",
        "head_offset": 6,
        "read": 1
      },
      {
        "step": 74,
        "pos": 2,
        "word": "1110111100101",
        "head_offset": 6,
        "read": 1
      },
      {
        "step": 79,
        "pos": -1,
        "word": "0001111100100",
        "head_offset": 6,
        "read": 1
      },
      {
        "step": 90,
        "pos": -2,
        "word": "0001101110010",
        "head_offset": 6,
        "read": 1
      },
      {
        "step": 92,
        "pos": -4,
        "word": "0000011101100",
        "head_offset": 6,
        "read": 1
      },
      {
        "step": 123,
        "pos": 1,
        "word": "1011011100010",
        "head_offset": 6,
        "read": 1
      },
      {
        "step": 146,
        "pos": 4,
        "word": "1110101110100",
        "head_offset": 6,
        "read": 1
      }
    ],
    "head_offset": 6
  },
  "samples": [
    {
      "step": 1000000,
      "state": "D",
      "dir": "L",
      "pos": -42,
      "lo": -893,
      "hi": 154,
      "span": 1048,
      "ones": 795,
      "one_run_histogram": {
        "1": 35,
        "2": 102,
        "3": 1,
        "4": 34,
        "8": 51,
        "9": 1
      },
      "distinct_12mers": 90,
      "dp_k12_chars": 617
    },
    {
      "step": 10000000,
      "state": "A",
      "dir": "L",
      "pos": -1864,
      "lo": -2918,
      "hi": 192,
      "span": 3111,
      "ones": 2052,
      "one_run_histogram": {
        "1": 230,
        "2": 572,
        "3": 2,
        "4": 44,
        "8": 62
      },
      "distinct_12mers": 101,
      "dp_k12_chars": 1912
    },
    {
      "step": 100000000,
      "state": "A",
      "dir": "L",
      "pos": -4898,
      "lo": -9313,
      "hi": 217,
      "span": 9531,
      "ones": 6614,
      "one_run_histogram": {
        "1": 543,
        "2": 1582,
        "3": 1,
        "4": 176,
        "8": 275
      },
      "distinct_12mers": 102,
      "dp_k12_chars": 5749
    },
    {
      "step": 1000000000,
      "state": "A",
      "dir": "L",
      "pos": -28752,
      "lo": -29278,
      "hi": 228,
      "span": 29507,
      "ones": 17521,
      "one_run_histogram": {
        "1": 3000,
        "2": 7089,
        "3": 1,
        "4": 21,
        "8": 32
      },
      "distinct_12mers": 102,
      "dp_k12_chars": 17304
    }
  ],
  "local_window_runs": [
    {
      "state_before": "A",
      "state_after": "B",
      "head_before": 0,
      "head_after": -1,
      "window_start": 0,
      "word_before": "000",
      "word_after": "101",
      "steps": 5,
      "observed_record_gaps": 513,
      "reads_stay_inside_window": true
    },
    {
      "state_before": "B",
      "state_after": "A",
      "head_before": 0,
      "head_after": -1,
      "window_start": 0,
      "word_before": "01000",
      "word_after": "00101",
      "steps": 11,
      "observed_record_gaps": 256,
      "reads_stay_inside_window": true
    },
    {
      "state_before": "B",
      "state_after": "A",
      "head_before": 0,
      "head_after": -1,
      "window_start": 0,
      "word_before": "0101101100100",
      "word_after": "0010110110101",
      "steps": 81,
      "observed_record_gaps": 255,
      "reads_stay_inside_window": true
    }
  ],
  "diagram": {
    "path": "img/space-time-labeled.svg",
    "sampling": "every 1000 steps through 2,000,000",
    "cols": [
      -1283,
      165
    ]
  },
  "preflight": "astra/bouncer-triage/preflight.json (root supplied; current open PRs, saved sheet/Discord, exact conjugacies checked)",
  "next": "Deferred by user decision; retain the completed study and evidence.",
  "rank": 282,
  "class_sheet": "Bouncer + Chaotic Edge",
  "class_guess": "Bouncer with unresolved word dynamics",
  "confidence": "low",
  "summary": "Two exact return families are established; a closed language protecting the irregular edge remains unknown.",
  "mechanism": [
    "Two context-independent families return to the left edge in 20n+41 steps (n≥1) or 12n+69 steps (n≥0); their finite components give explicit concatenation arguments.",
    "An exact B/E word-rewrite model reproduces all 1,283 saved left records through two million steps. The simple families cover 1,027 of 1,282 gaps.",
    "Fitted word languages fail at the far endpoint, even with length modulo6. The unproved safety condition is exclusion of E reading0 with another0 immediately left."
  ],
  "diagrams": [
    {
      "mode": "every:1000",
      "png": "img/every-1000-through-2e6.png",
      "html": null,
      "steps": 2000000,
      "caption": "Sampled sweeps and the expanding visited span",
      "title": "First two million steps",
      "why": "Time increases downward. Compare the expanding left boundary with the opposite boundary.",
      "primary": true,
      "start": "blank",
      "rows": "every 1000 steps, from 0 through 2000000; each sampled row is 2 pixels high",
      "window": "cells -1283..165, 1 px = 0.5 cells; two raster pixels per cell",
      "legend": "white = 1, slate = 0 or unvisited, red = A, orange = B, blue = C, green = D, magenta = E, cyan = F",
      "style": "bbchallenge-explore"
    }
  ],
  "history": null,
  "rules": [
    {
      "name": "5-step finite window",
      "from": "state A, head 0; cells 0..2: 000",
      "to": "state B, head -1; same cells: 101",
      "steps": "5",
      "cases": "One exact finite input; all reads stay inside the specified window. No global closure claim.",
      "validated": {
        "instances": 1,
        "passed": 1
      },
      "source": "manual"
    },
    {
      "name": "11-step finite window",
      "from": "state B, head 0; cells 0..4: 01000",
      "to": "state A, head -1; same cells: 00101",
      "steps": "11",
      "cases": "One exact finite input; all reads stay inside the specified window. No global closure claim.",
      "validated": {
        "instances": 1,
        "passed": 1
      },
      "source": "manual"
    },
    {
      "name": "81-step finite window",
      "from": "state B, head 0; cells 0..12: 0101101100100",
      "to": "state A, head -1; same cells: 0010110110101",
      "steps": "81",
      "cases": "One exact finite input; all reads stay inside the specified window. No global closure claim.",
      "validated": {
        "instances": 1,
        "passed": 1
      },
      "source": "manual"
    },
    {
      "name": "Parameterized R1",
      "from": "B at cell0; window: 010 (110)^n 0100",
      "to": "A at cell−1; same window: 00 (101)^(n+1) 01",
      "steps": "20n+41",
      "cases": "n≥1. Exact finite components compose; all reads stay in the input window. n=0 excluded. No whole-orbit closure claim.",
      "validated": {
        "instances": 131,
        "passed": 131
      },
      "source": "manual"
    },
    {
      "name": "Parameterized R2",
      "from": "B at cell0; window: 010 (110)^n 101100100",
      "to": "B at cell−1; same window: 100 (010)^(n+1) 110101",
      "steps": "12n+69",
      "cases": "n≥0. Exact finite components compose; all reads stay in the input window. No whole-orbit closure claim.",
      "validated": {
        "instances": 132,
        "passed": 132
      },
      "source": "manual"
    }
  ],
  "template": {
    "file": null,
    "module": null,
    "machine": null,
    "diff": null,
    "applies": "unknown",
    "note": "No complete configuration family or reusable proof template has been identified."
  },
  "strategy": "A future research stage should derive a word grammar with endpoint phases and prove closure/safety. No formal proof stage has started.",
  "risks": [
    "Neither the finite blank run nor the exact partial return rules proves nonhalting.",
    "The complete word-rewrite relation has an E00 failure branch; its global exclusion is unproved.",
    "Observed factor/endpoint languages are not closed, and a length residue alone does not repair them."
  ],
  "discord_check": null,
  "stats": {
    "simulated_steps": 1000000000,
    "cells": 29507,
    "nonzeros": 17521,
    "growth": "Visited span grows mainly left in the sampled blank-tape run."
  },
  "status": "SKIPPED",
  "status_reason": "User chose to defer further research on line 282. The completed local study is retained; the nonlocal word-language invariant remains unresolved.",
  "checkpoint_questions": [
    {
      "text": "Prioritize a bounded word-transducer/return-map investigation, or leave this candidate at observation?",
      "figs": [
        0
      ],
      "kind": "decision",
      "answer": "study",
      "note": "Follow your recommendations for the 5",
      "date": "2026-10-14"
    }
  ],
  "study_report": "study.md",
  "study_result": "study-20261014/result.json"
}