{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R127",
  "content_hash": null,
  "slug": "cds-artifact-rgs-packed-replay",
  "type": "artifact",
  "title": "Packed-factor restricted-growth replay",
  "summary": "A complete C++17 program checks every alphabet-renaming class through length 14 and reports total, primitive, and nonprimitive maxima.",
  "relevance": "For The three-halves bound for distinct squares in circular words, record cds-artifact-rgs-packed-replay (“Packed-factor restricted-growth replay”) supplies evidence or a replay used to check the packet. The record states: A complete C++17 program checks every alphabet-renaming class through length 14 and reports total, primitive, and nonprimitive maxima.",
  "relevance_source": "recorded",
  "body": "The program recursively generates restricted-growth strings. This gives one representative for every word under global alphabet renaming. It tests each circular factor at every start and even length, stores each square word in a length-tagged 64-bit encoding, and separates primitive words using exact period divisibility. The largest layer contains Bell(14)=190,899,322 strings. The run uses exact comparisons and no random choices.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "every finite word of lengths 1 through 14, modulo global alphabet renaming",
    "bounds": {
      "word_length": {
        "min": 1,
        "max": 14
      },
      "alphabet_size": {
        "min": 1,
        "max": 14
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "complete",
    "kind": "inline_cpp_exhaustive_enumerator",
    "command": "clang++ -O3 -std=c++17 -Wall -Wextra -pedantic circular_squares_replay.cpp -o circular_squares_replay && /usr/bin/time -l ./circular_squares_replay 14",
    "entrypoint": "Join source_lines with LF characters, append a final LF, and save as circular_squares_replay.cpp",
    "runtime": "Apple clang 21.0.0, C++17 standard library, macOS 26.2 arm64",
    "citation": {
      "locator": "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": "ff8e665c674ad476c5ecdd63e8418f39cff533478523e23cddd633aac8482e4c",
      "normalized_stdout_sha256": "05522d1ef84a3ea39ee9160a4fca1717d1e1a494c2d8b99eaf5f786603f7f717",
      "exact_maxima": [
        0,
        1,
        1,
        2,
        3,
        4,
        4,
        6,
        6,
        9,
        8,
        10,
        11,
        13
      ],
      "primitive_maxima": [
        0,
        0,
        1,
        2,
        3,
        3,
        4,
        6,
        6,
        7,
        8,
        10,
        11,
        11
      ],
      "nonprimitive_maxima": [
        null,
        1,
        1,
        2,
        2,
        4,
        3,
        6,
        4,
        9,
        5,
        9,
        6,
        13
      ],
      "restricted_growth_counts": [
        1,
        2,
        5,
        15,
        52,
        203,
        877,
        4140,
        21147,
        115975,
        678570,
        4213597,
        27644437,
        190899322
      ],
      "peak_resident_bytes_observed": 1441792
    },
    "runtime_seconds": 76,
    "inline_source": [
      "#include <algorithm>",
      "#include <cstdint>",
      "#include <iostream>",
      "#include <set>",
      "#include <sstream>",
      "#include <string>",
      "#include <unordered_set>",
      "#include <vector>",
      "",
      "struct Row {",
      "    unsigned long long generated = 0;",
      "    int maximum = -1;",
      "    unsigned long long maximizers = 0;",
      "    std::vector<int> first;",
      "    int primitive_maximum = -1;",
      "    std::vector<int> primitive_first;",
      "    int nonprimitive_maximum = -1;",
      "    std::vector<int> nonprimitive_first;",
      "};",
      "",
      "static int square_count(const std::vector<int>& word) {",
      "    const int n = static_cast<int>(word.size());",
      "    std::vector<int> doubled(word);",
      "    doubled.insert(doubled.end(), word.begin(), word.end());",
      "    std::unordered_set<std::uint64_t> squares;",
      "    for (int start = 0; start < n; ++start) {",
      "        for (int half = 1; 2 * half <= n; ++half) {",
      "            bool square = true;",
      "            for (int j = 0; j < half; ++j) {",
      "                if (doubled[start + j] != doubled[start + half + j]) {",
      "                    square = false;",
      "                    break;",
      "                }",
      "            }",
      "            if (!square) continue;",
      "            const int length = 2 * half;",
      "            std::uint64_t packed = static_cast<std::uint64_t>(length) << 56;",
      "            for (int j = 0; j < length; ++j) {",
      "                packed |= static_cast<std::uint64_t>(doubled[start + j])",
      "                          << (4 * (length - 1 - j));",
      "            }",
      "            squares.insert(packed);",
      "        }",
      "    }",
      "    return static_cast<int>(squares.size());",
      "}",
      "",
      "static bool is_primitive(const std::vector<int>& 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;",
      "}",
      "",
      "static void visit(std::vector<int>& word, int position, int maximum, Row& row) {",
      "    const int n = static_cast<int>(word.size());",
      "    if (position == n) {",
      "        ++row.generated;",
      "        const int count = square_count(word);",
      "        if (count > row.maximum) {",
      "            row.maximum = count;",
      "            row.maximizers = 1;",
      "            row.first = word;",
      "        } else if (count == row.maximum) {",
      "            ++row.maximizers;",
      "        }",
      "        if (is_primitive(word) && count > row.primitive_maximum) {",
      "            row.primitive_maximum = count;",
      "            row.primitive_first = word;",
      "        }",
      "        if (!is_primitive(word) && count > row.nonprimitive_maximum) {",
      "            row.nonprimitive_maximum = count;",
      "            row.nonprimitive_first = word;",
      "        }",
      "        return;",
      "    }",
      "    for (int letter = 0; letter <= maximum + 1; ++letter) {",
      "        word[position] = letter;",
      "        visit(word, position + 1, std::max(maximum, letter), row);",
      "    }",
      "}",
      "",
      "static std::string render(const std::vector<int>& word) {",
      "    std::ostringstream out;",
      "    for (int letter : word) out << letter;",
      "    return out.str();",
      "}",
      "",
      "int main(int argc, char** argv) {",
      "    if (argc != 2) {",
      "        std::cerr << \"usage: circular_squares_replay MAX_N\\n\";",
      "        return 2;",
      "    }",
      "    const int max_n = std::stoi(argv[1]);",
      "    for (int n = 1; n <= max_n; ++n) {",
      "        Row row;",
      "        std::vector<int> word(n, 0);",
      "        visit(word, 1, 0, row);",
      "        std::cout << \"n=\" << n",
      "                  << \" rgs=\" << row.generated",
      "                  << \" max=\" << row.maximum",
      "                  << \" rgs_maximizers=\" << row.maximizers",
      "                  << \" first=\" << render(row.first)",
      "                  << \" primitive_max=\" << row.primitive_maximum",
      "                  << \" primitive_first=\" << render(row.primitive_first)",
      "                  << \" nonprimitive_max=\" << row.nonprimitive_maximum",
      "                  << \" nonprimitive_first=\" << render(row.nonprimitive_first)",
      "                  << \"\\n\";",
      "    }",
      "}"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Self-contained C++17 source executed on macOS arm64 on 2026-07-28"
  },
  "models": [],
  "relations": [
    {
      "slug": "R133",
      "title": "Exact maxima for every alphabet through length fourteen",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "circular-distinct-squares-three-halves",
      "title": "circular distinct squares three halves",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}