{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R124",
  "content_hash": null,
  "slug": "cds-artifact-binary-direct-replay",
  "type": "artifact",
  "title": "Direct-string independent binary replay",
  "summary": "A second binary implementation uses substring comparison and reproduces all five maxima series through length 26.",
  "relevance": "For The three-halves bound for distinct squares in circular words, record cds-artifact-binary-direct-replay (“Direct-string independent binary replay”) supplies evidence or a replay used to check the packet. The record states: A second binary implementation uses substring comparison and reproduces all five maxima series through length 26.",
  "relevance_source": "recorded",
  "body": "This program represents each word as a string, checks square halves with string comparison, and deduplicates factors by direct substring comparison. Exact string periods separate primitive and nonprimitive words. It independently reproduces the total, short, long, primitive, and nonprimitive maxima. Its raw 26-line output equals the normalized rows of the packed replay.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "every binary word of lengths 1 through 26, with complements identified",
    "bounds": {
      "word_length": {
        "min": 1,
        "max": 26
      },
      "alphabet_size": {
        "min": 2,
        "max": 2
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "complete",
    "kind": "inline_cpp_independent_binary_enumerator",
    "command": "clang++ -O3 -std=c++17 -Wall -Wextra -pedantic circular_squares_binary_direct.cpp -o circular_squares_binary_direct && /usr/bin/time -l ./circular_squares_binary_direct 26",
    "entrypoint": "Join source_lines with LF characters, append a final LF, and save as circular_squares_binary_direct.cpp",
    "runtime": "Apple clang 21.0.0, C++17 standard library, macOS 26.2 arm64",
    "citation": {
      "locator": "Independent self-contained C++17 source executed on macOS arm64 on 2026-07-28"
    },
    "dependencies": [
      {
        "name": "Apple clang and libc++",
        "version": "21.0.0",
        "license": "Apache-2.0 WITH LLVM-exception"
      }
    ],
    "outputs": {
      "raw_stdout_sha256": "1d5976f1b85dfa11ce67701e6dfe7cf5dadbe470719821d2bb7de00019f3cf18",
      "normalized_rows_sha256": "1d5976f1b85dfa11ce67701e6dfe7cf5dadbe470719821d2bb7de00019f3cf18",
      "exact_binary_maxima": [
        0,
        1,
        1,
        2,
        3,
        4,
        4,
        6,
        6,
        9,
        8,
        10,
        11,
        13,
        13,
        16,
        15,
        18,
        17,
        19,
        21,
        22,
        22,
        25,
        24,
        28
      ],
      "exact_binary_primitive_maxima": [
        0,
        0,
        1,
        2,
        3,
        3,
        4,
        6,
        6,
        7,
        8,
        10,
        11,
        11,
        13,
        15,
        15,
        17,
        17,
        19,
        21,
        20,
        22,
        24,
        24,
        26
      ],
      "exact_binary_nonprimitive_maxima": [
        null,
        1,
        1,
        2,
        2,
        4,
        3,
        6,
        4,
        9,
        5,
        9,
        6,
        13,
        9,
        16,
        8,
        18,
        9,
        19,
        13,
        22,
        11,
        25,
        14,
        28
      ],
      "exact_binary_short_maxima": [
        0,
        0,
        0,
        2,
        2,
        2,
        2,
        4,
        4,
        5,
        5,
        9,
        8,
        10,
        9,
        12,
        12,
        13,
        13,
        16,
        16,
        17,
        18,
        19,
        20,
        20
      ],
      "exact_binary_long_maxima": [
        0,
        1,
        1,
        2,
        2,
        3,
        3,
        4,
        4,
        6,
        7,
        6,
        7,
        9,
        11,
        10,
        11,
        14,
        13,
        13,
        17,
        16,
        17,
        20,
        19,
        20
      ],
      "peak_resident_bytes_observed": 1376256
    },
    "runtime_seconds": 178.83,
    "inline_source": [
      "#include <cstdint>",
      "#include <iostream>",
      "#include <string>",
      "#include <utility>",
      "#include <vector>",
      "",
      "struct Counts { int total = 0, short_count = 0, long_count = 0; };",
      "",
      "static std::string make_word(std::uint32_t code, int n) {",
      "    std::string word(n, '0');",
      "    for (int i = 0; i < n; ++i) word[i] = char('0' + ((code >> i) & 1U));",
      "    return word;",
      "}",
      "",
      "static Counts inspect(const std::string& word) {",
      "    const int n = static_cast<int>(word.size());",
      "    const std::string doubled = word + word;",
      "    std::vector<std::pair<int, int>> factors;",
      "    Counts counts;",
      "    for (int start = 0; start < n; ++start) {",
      "        for (int length = 2; length <= n; length += 2) {",
      "            const int half = length / 2;",
      "            if (doubled.compare(start, half, doubled, start + half, half) != 0) {",
      "                continue;",
      "            }",
      "            bool duplicate = false;",
      "            for (auto [old_start, old_length] : factors) {",
      "                if (length == old_length &&",
      "                    doubled.compare(start, length, doubled, old_start, length) == 0) {",
      "                    duplicate = true;",
      "                    break;",
      "                }",
      "            }",
      "            if (duplicate) continue;",
      "            factors.emplace_back(start, length);",
      "            ++counts.total;",
      "            if (2 * length <= n) ++counts.short_count;",
      "            else ++counts.long_count;",
      "        }",
      "    }",
      "    return counts;",
      "}",
      "",
      "static bool primitive(const std::string& word) {",
      "    const int n = static_cast<int>(word.size());",
      "    for (int period = 1; period < n; ++period) {",
      "        if (n % period != 0) continue;",
      "        bool repeats = true;",
      "        for (int i = period; i < n; ++i) {",
      "            if (word[i] != word[i % period]) {",
      "                repeats = false;",
      "                break;",
      "            }",
      "        }",
      "        if (repeats) return false;",
      "    }",
      "    return true;",
      "}",
      "",
      "int main(int argc, char** argv) {",
      "    if (argc != 2) return 2;",
      "    const int max_n = std::stoi(argv[1]);",
      "    for (int n = 1; n <= max_n; ++n) {",
      "        const std::uint32_t count = 1U << (n - 1);",
      "        Counts maxima{-1, -1, -1};",
      "        int primitive_maximum = -1, nonprimitive_maximum = -1;",
      "        std::string total_word, short_word, long_word;",
      "        std::string primitive_word, nonprimitive_word;",
      "        for (std::uint32_t tail = 0; tail < count; ++tail) {",
      "            const std::string word = make_word(tail << 1, n);",
      "            const Counts value = inspect(word);",
      "            const bool is_primitive = primitive(word);",
      "            if (value.total > maxima.total) {",
      "                maxima.total = value.total;",
      "                total_word = word;",
      "            }",
      "            if (value.short_count > maxima.short_count) {",
      "                maxima.short_count = value.short_count;",
      "                short_word = word;",
      "            }",
      "            if (value.long_count > maxima.long_count) {",
      "                maxima.long_count = value.long_count;",
      "                long_word = word;",
      "            }",
      "            if (is_primitive && value.total > primitive_maximum) {",
      "                primitive_maximum = value.total;",
      "                primitive_word = word;",
      "            }",
      "            if (!is_primitive && value.total > nonprimitive_maximum) {",
      "                nonprimitive_maximum = value.total;",
      "                nonprimitive_word = word;",
      "            }",
      "        }",
      "        std::cout << \"length=\" << n",
      "                  << \" checked=\" << count",
      "                  << \" total=\" << maxima.total << \" total_word=\" << total_word",
      "                  << \" short=\" << maxima.short_count << \" short_word=\" << short_word",
      "                  << \" long=\" << maxima.long_count << \" long_word=\" << long_word",
      "                  << \" primitive=\" << primitive_maximum",
      "                  << \" primitive_word=\" << primitive_word",
      "                  << \" nonprimitive=\" << nonprimitive_maximum",
      "                  << \" nonprimitive_word=\" << nonprimitive_word",
      "                  << \"\\n\";",
      "    }",
      "}"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Independent self-contained C++17 source executed on macOS arm64 on 2026-07-28"
  },
  "models": [],
  "relations": [
    {
      "slug": "R132",
      "title": "Exact binary maxima through length twenty-six",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "R130",
      "title": "The short-square half-length charge fails at twelve",
      "object_type": "attempt",
      "relation": "tests",
      "direction": "outgoing"
    },
    {
      "slug": "circular-distinct-squares-three-halves",
      "title": "circular distinct squares three halves",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}