{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R3",
  "content_hash": null,
  "slug": "ac0123-artifact-independent-full-scan",
  "type": "artifact",
  "title": "Independent exact full-word checker",
  "summary": "A separate 42-line C++17 program loops by block length and start position and checks all 166,666,500,000 candidate factors of the million-letter word.",
  "relevance": "For Additive-cube avoidance on the alphabet zero through three, record ac0123-artifact-independent-full-scan (“Independent exact full-word checker”) supplies evidence or a replay used to check the packet. The record states: A separate 42-line C++17 program loops by block length and start position and checks all 166,666,500,000 candidate factors of the million-letter word.",
  "relevance_source": "recorded",
  "body": "This checker shares the prefix-sum formula with the mathematical definition and shares no construction or backtracking code. Its outer loop is block length and its inner loop is start position, unlike the constructor's internal end-position loop. It reads a word file, rejects symbols outside \\(0,1,2,3\\), and returns the first additive cube or the count of all checked pairs.\n\nOn the million-letter output it completed all 166,666,500,000 admissible \\((\\text{block length},\\text{start})\\) pairs and returned valid=true. The same source checked the separately generated 250,000-letter output over 10,416,625,000 pairs.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "every candidate additive-cube factor of the recorded 1,000,000-letter word over {0,1,2,3}",
    "bounds": {
      "word_length": {
        "min": 1000000,
        "max": 1000000
      },
      "block_length": {
        "min": 1,
        "max": 333333
      },
      "candidate_pairs": {
        "min": 166666500000,
        "max": 166666500000
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "complete",
    "kind": "inline_cpp17_deterministic_full_scan_verifier",
    "command": "c++ -O3 -std=c++17 additive_cube_verify.cpp -o additive_cube_verify && /usr/bin/time -lp ./additive_cube_verify acube_updown_1000000.txt",
    "entrypoint": "Join source_lines with LF characters and append one terminal LF as additive_cube_verify.cpp; source_sha256 includes that terminal LF",
    "runtime": "Apple clang version 21.0.0, target arm64-apple-darwin25.2.0, ISO C++17, standard library only",
    "citation": {
      "locator": "Inline C++17 verifier prepared and executed independently on 2026-07-28"
    },
    "dependencies": [
      {
        "name": "Apple clang",
        "version": "21.0.0",
        "license": "Apache-2.0 WITH LLVM-exception"
      },
      {
        "name": "Apple libc++",
        "version": "system toolchain for arm64-apple-darwin25.2.0",
        "license": "Apache-2.0 WITH LLVM-exception"
      }
    ],
    "outputs": {
      "expected_stdout": "length=1000000 checked_pairs=166666500000 valid=true\n",
      "expected_stdout_sha256": "e4f1df602141d68e70cf5fffe508b79e91086787fa8877dbd17f21bd19ca7289",
      "source_sha256": "6ceb58fdc7d47d8c810272707bdaf70c22974eaa89b3834d9813f295232bedc1",
      "word_file_sha256_including_final_lf": "15d439b42fefa8501203775cf0b4457f7eaf19bae14ae5797b5d405e03ed1846",
      "maximum_resident_bytes": 11976704
    },
    "runtime_seconds": 102.68,
    "inline_source": [
      "#include <cstdint>",
      "#include <fstream>",
      "#include <iostream>",
      "#include <string>",
      "#include <vector>",
      "",
      "int main(int argc, char **argv) {",
      "    if (argc != 2) {",
      "        std::cerr << \"usage: additive_cube_verify_root WORD_FILE\\n\";",
      "        return 2;",
      "    }",
      "    std::ifstream input(argv[1]);",
      "    std::string word;",
      "    input >> word;",
      "    std::vector<std::uint64_t> prefix(word.size() + 1, 0);",
      "    for (std::size_t i = 0; i < word.size(); ++i) {",
      "        if (word[i] < '0' || word[i] > '3') {",
      "            std::cerr << \"invalid letter at \" << i << '\\n';",
      "            return 1;",
      "        }",
      "        prefix[i + 1] = prefix[i] + static_cast<unsigned>(word[i] - '0');",
      "    }",
      "    std::uint64_t checked = 0;",
      "    for (std::size_t block = 1; 3 * block <= word.size(); ++block) {",
      "        for (std::size_t start = 0; start + 3 * block <= word.size(); ++start) {",
      "            ++checked;",
      "            const auto first = prefix[start + block] - prefix[start];",
      "            const auto second = prefix[start + 2 * block] - prefix[start + block];",
      "            if (first != second) {",
      "                continue;",
      "            }",
      "            const auto third = prefix[start + 3 * block] - prefix[start + 2 * block];",
      "            if (second == third) {",
      "                std::cerr << \"cube start=\" << start << \" block=\" << block << '\\n';",
      "                return 1;",
      "            }",
      "        }",
      "    }",
      "    std::cout << \"length=\" << word.size() << \" checked_pairs=\" << checked",
      "              << \" valid=true\\n\";",
      "    return 0;",
      "}"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Inline C++17 verifier prepared and executed independently on 2026-07-28"
  },
  "relations": [
    {
      "slug": "R9",
      "title": "The source-informed finite construction reaches one million",
      "object_type": "attempt",
      "relation": "uses",
      "direction": "incoming"
    },
    {
      "slug": "R10",
      "title": "The reconstructed method produces a checked million-letter word",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "additive-cube-four-term-progression-alphabet",
      "title": "additive cube four term progression alphabet",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}