{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R21",
  "content_hash": null,
  "slug": "asq-artifact-single-projection-scan",
  "type": "artifact",
  "title": "First-square scanner for one h6 projection",
  "summary": "This C++20 program scans one primitive h6 projection in end-major order and returns the earliest scalar additive square with an exact interval and equal sums.",
  "relevance": "For Infinite additive-square avoidance over a finite integer alphabet, record asq-artifact-single-projection-scan (“First-square scanner for one h6 projection”) supplies evidence or a replay used to check the packet. The record states: This C++20 program scans one primitive h6 projection in end-major order and returns the earliest scalar additive square with an exact interval and equal sums.",
  "relevance_source": "recorded",
  "body": "The command below tests (361,288) with a one-million-symbol limit. Prefix sums make every block comparison exact. End positions increase first, followed by half-lengths, so the returned end is the first endpoint containing any scalar additive square in the fixed point prefix.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "the projection (p,q)=(361,288) of h6^omega(a) through the first scalar additive square ending at 250952",
    "bounds": {
      "prefix_length": {
        "min": 1,
        "max": 250952
      },
      "p": {
        "min": 361,
        "max": 361
      },
      "q": {
        "min": 288,
        "max": 288
      },
      "half_length": {
        "min": 51122,
        "max": 51122
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "complete",
    "kind": "inline_cpp_h6_single_projection_first_square_scan",
    "command": "clang++ -O3 -std=c++20 -Wall -Wextra -pedantic project_h6_single.cpp -o project_h6_single && ./project_h6_single --prefix 1000000 --p 361 --q 288",
    "entrypoint": "Join source_lines with LF, append a terminal LF, and save as project_h6_single.cpp",
    "runtime": "Apple clang 21.0.0, C++20 standard library, macOS 26.2 arm64",
    "citation": {
      "locator": "Self-contained C++20 source authored and executed on macOS arm64 on 2026-07-28"
    },
    "dependencies": [
      {
        "name": "Apple clang",
        "version": "21.0.0",
        "license": "Apache-2.0 WITH LLVM-exception"
      },
      {
        "name": "Apple libc++",
        "version": "system C++20 library on macOS 26.2 arm64",
        "license": "Apache-2.0 WITH LLVM-exception"
      }
    ],
    "outputs": {
      "additive_square_found": true,
      "end": 250952,
      "start": 148708,
      "half": 51122,
      "left_sum": 25859725,
      "right_sum": 25859725,
      "pairs_tested": 15744152222,
      "exact_stdout_sha256": "0c62de4d0af910ef0a3e4c8b889a4080f80f1c916e36efb541a2b0e9eec93cde",
      "peak_resident_bytes_observed": 11796480
    },
    "runtime_seconds": 13.32,
    "inline_source": [
      "#include <array>",
      "#include <cstdint>",
      "#include <cstdlib>",
      "#include <iostream>",
      "#include <numeric>",
      "#include <string>",
      "#include <vector>",
      "",
      "int main(int argc, char** argv) {",
      "    int prefix_length = 1000000;",
      "    int p = 361;",
      "    int q = 288;",
      "    for (int index = 1; index < argc; ++index) {",
      "        const std::string option = argv[index];",
      "        if (option == \"--prefix\" && index + 1 < argc) {",
      "            prefix_length = std::stoi(argv[++index]);",
      "        } else if (option == \"--p\" && index + 1 < argc) {",
      "            p = std::stoi(argv[++index]);",
      "        } else if (option == \"--q\" && index + 1 < argc) {",
      "            q = std::stoi(argv[++index]);",
      "        } else {",
      "            std::cerr << \"invalid argument\\n\";",
      "            return 2;",
      "        }",
      "    }",
      "    if (prefix_length < 2 || (p == 0 && q == 0) ||",
      "        std::gcd(std::abs(p), std::abs(q)) != 1) {",
      "        return 2;",
      "    }",
      "",
      "    const std::array<std::string, 6> image{",
      "        \"ace\", \"adf\", \"bdf\", \"bdc\", \"afe\", \"bce\"",
      "    };",
      "    const std::array<int, 6> x{0, 1, 2, 0, 2, 1};",
      "    const std::array<int, 6> y{0, 1, 1, 1, 0, 0};",
      "",
      "    std::string word = \"a\";",
      "    while (static_cast<int>(word.size()) < prefix_length) {",
      "        std::string next;",
      "        next.reserve(word.size() * 3);",
      "        for (const char letter : word) next += image[letter - 'a'];",
      "        word = std::move(next);",
      "    }",
      "    word.resize(prefix_length);",
      "",
      "    std::vector<long long> prefix_sums(prefix_length + 1, 0);",
      "    for (int index = 0; index < prefix_length; ++index) {",
      "        const int letter = word[index] - 'a';",
      "        prefix_sums[index + 1] =",
      "            prefix_sums[index] + p * x[letter] + q * y[letter];",
      "    }",
      "",
      "    std::uint64_t pairs_tested = 0;",
      "    for (int end = 2; end <= prefix_length; ++end) {",
      "        for (int half = 1; half <= end / 2; ++half) {",
      "            ++pairs_tested;",
      "            const long long left =",
      "                prefix_sums[end - half] - prefix_sums[end - 2 * half];",
      "            const long long right =",
      "                prefix_sums[end] - prefix_sums[end - half];",
      "            if (left == right) {",
      "                std::cout << \"{\\\"prefix_limit\\\":\" << prefix_length",
      "                          << \",\\\"p\\\":\" << p << \",\\\"q\\\":\" << q",
      "                          << \",\\\"additive_square_found\\\":true\"",
      "                          << \",\\\"end\\\":\" << end",
      "                          << \",\\\"start\\\":\" << end - 2 * half",
      "                          << \",\\\"half\\\":\" << half",
      "                          << \",\\\"left_sum\\\":\" << left",
      "                          << \",\\\"right_sum\\\":\" << right",
      "                          << \",\\\"pairs_tested\\\":\" << pairs_tested << \"}\\n\";",
      "                return 0;",
      "            }",
      "        }",
      "    }",
      "    std::cout << \"{\\\"prefix_limit\\\":\" << prefix_length",
      "              << \",\\\"p\\\":\" << p << \",\\\"q\\\":\" << q",
      "              << \",\\\"additive_square_found\\\":false\"",
      "              << \",\\\"pairs_tested\\\":\" << pairs_tested << \"}\\n\";",
      "}"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Self-contained C++20 source authored and executed on macOS arm64 on 2026-07-28"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R25",
      "title": "The smallest height-361 projection survivor fails at 250952",
      "object_type": "attempt",
      "relation": "uses",
      "direction": "incoming"
    },
    {
      "slug": "additive-square-finite-alphabet",
      "title": "additive square finite alphabet",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}