{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R9",
  "content_hash": null,
  "slug": "ac0123-attempt-updown-million",
  "type": "attempt",
  "title": "The source-informed finite construction reaches one million",
  "summary": "The deterministic alternating-priority search reached its 1,000,000-letter target within a 10-billion-candidate cap and retained a fully checked word digest.",
  "relevance": "For Additive-cube avoidance on the alphabet zero through three, record ac0123-attempt-updown-million (“The source-informed finite construction reaches one million”) documents a concrete method, search boundary, or failed route. The record states: The deterministic alternating-priority search reached its 1,000,000-letter target within a 10-billion-candidate cap and retained a fully checked word digest.",
  "relevance_source": "recorded",
  "body": "The attempt reconstructed the thesis's finite Up-and-Down idea using exact prefix sums. It used ascending priority \\(0,1,2,3\\), descending priority \\(3,2,1,0\\), a failure threshold of 1,209, a retreat of 100 letters, and checkpoints every 10,000 letters. The stopping rule was target length 1,000,000 or 10,000,000,000 tested candidate letters.\n\nThe run reached its target after 2,480,028 tests, 1,271,032 rejected candidates, 208,996 recorded backtracks, and 1,097 direction changes. Construction plus the internal quadratic scan took 180.38 wall seconds. A separate checker took 102.68 wall seconds and accepted the same word. A 250,000-letter calibration run used 617,607 tests and produced digest `c9e5f13458e3bec984fc37f91541edc8a9b0fff78e47d9949626aa0f15a95520`.\n\nThe million-letter execution is a separate deterministic construction. It agrees with the 250,000-letter execution for the first 249,900 symbols, then changes because the longer run retreats 100 symbols at the 250,000 checkpoint.",
  "status": "completed",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "one deterministic Up-and-Down search trajectory over {0,1,2,3} through its one-million-letter target",
    "bounds": {
      "target_word_length": {
        "min": 1000000,
        "max": 1000000
      },
      "tested_letters": {
        "min": 2480028,
        "max": 2480028
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "locator": "Execution of ac0123-artifact-updown-constructor and ac0123-artifact-independent-full-scan on 2026-07-28"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Execution of ac0123-artifact-updown-constructor and ac0123-artifact-independent-full-scan on 2026-07-28"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R12",
      "title": "A finite additive-cube-free word of length 70,880,000 is known",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R5",
      "title": "Deterministic Up-and-Down finite-word constructor",
      "object_type": "artifact",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "R3",
      "title": "Independent exact full-word checker",
      "object_type": "artifact",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "R10",
      "title": "The reconstructed method produces a checked million-letter word",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "additive-cube-four-term-progression-alphabet",
      "title": "additive cube four term progression alphabet",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}