{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R26",
  "content_hash": null,
  "slug": "asq-attempt-rational-projection-screen",
  "type": "attempt",
  "title": "Screen rational projections of the Z^2 construction",
  "summary": "An exact screen of every primitive direction of coefficient height at most 1000 found 656,301 directions whose projected h6 word survives through 378,367 symbols; the smallest surviving direction is (383,37).",
  "relevance": "For Infinite additive-square avoidance over a finite integer alphabet, record asq-attempt-rational-projection-screen (“Screen rational projections of the Z^2 construction”) documents a concrete method, search boundary, or failed route. The record states: An exact screen of every primitive direction of coefficient height at most 1000 found 656,301 directions whose projected h6 word survives through 378,367 symbols; the smallest surviving direction is (383,37).",
  "relevance_source": "recorded",
  "body": "For each primitive pair (p,q), identify (p,q) with (-p,-q) by choosing p>0 or p=0,q>0, and project a vector (x,y) to px+qy. There are 1,216,768 normalized directions with 0<=p<=1000 and |q|<=1000. At prefix 200,000, the screen had marked 363,649 directions and left 853,119 survivors; the smallest survivor (361,288) later failed at end 250,952. At 300,000 symbols, the smallest survivor (376,-217) later failed at end 357,217. At 357,217 symbols, the smallest survivor (376,27) later failed at end 378,367. The final run checked 35,790,396,672 adjacent block pairs, marked 560,467 directions, and left 656,301 finite-prefix candidates. Its smallest survivor is (383,37).",
  "status": "completed",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "all primitive normalized integer projections of height at most 1000 on the first 378367 symbols of h6^omega(a)",
    "bounds": {
      "prefix_length": {
        "min": 378367,
        "max": 378367
      },
      "coefficient_height": {
        "min": 1,
        "max": 1000
      },
      "projection_count": {
        "min": 1216768,
        "max": 1216768
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "locator": "Exact C++20 difference-vector screen of the Rao-Rosenfeld h6 fixed point, executed on macOS arm64 on 2026-07-28"
    },
    "runtime_seconds": 475.94,
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Exact C++20 difference-vector screen of the Rao-Rosenfeld h6 fixed point, executed on macOS arm64 on 2026-07-28"
  },
  "models": [],
  "relations": [
    {
      "slug": "R31",
      "title": "A six-letter morphic construction works over Z^2",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R20",
      "title": "Exact h6 rational-projection screen",
      "object_type": "artifact",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "R25",
      "title": "The smallest height-361 projection survivor fails at 250952",
      "object_type": "attempt",
      "relation": "tests",
      "direction": "incoming"
    },
    {
      "slug": "R23",
      "title": "The direct h6 template criterion fails by dimension",
      "object_type": "attempt",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "additive-square-finite-alphabet",
      "title": "additive square finite alphabet",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}