Problem packetResearch packetR3
Independent exact full-word checker
Link to a section
Executable material is recorded. Successful replay is a separate check.
Recorded status: available
Recorded scope: every candidate additive-cube factor of the recorded 1,000,000-letter word over {0,1,2,3}
Complete recorded scope and conditions
{
"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
}Originating problem: Additive-cube avoidance on the alphabet zero through three
Recorded relationships: The reconstructed method produces a checked million-letter word
Authored record and scope
- Authored title
- Independent exact full-word checker
- Record type
- artifact
- Stored status
- available
- Evidence grade
- executable
- Recorded scope data
- { "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 }
- Linked research record IDs
- R10
2Authored explanation
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.
On 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.
Files and source
Files embedded in this record. Matching a file hash confirms its identity.
- R3.txt1,462 bytes · No SHA-256 recorded
Preview R3.txt
#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; }File identity
- Recorded filename
- R3.txt
- Download SHA-256
- 2ec1d40a89b01ce928b2c7f29d0137f6cd2cb1745ce5ea794a28e7edf4f93309
Continue this work
Replay material: complete
4Reproduce
The command, source, environment, and expected result are recorded.
c++ -O3 -std=c++17 additive_cube_verify.cpp -o additive_cube_verify && /usr/bin/time -lp ./additive_cube_verify acube_updown_1000000.txtVerification source: Inline C++17 verifier prepared and executed independently on 2026-07-28
Expected output
{
"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
}Recorded artifact fields
5What it produced
Storage bound
Secondary 250000 check
6How it connects
Used by
- attempt
Evidence for
- claim
Recorded for
- problem
Cite this record
Cite the original sources separately.
Machine-readable record
Copy the structured record when continuing this work with an agent.
{
"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"
},
"models": [],
"continuation": null,
"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"
}
]
}8Provenance
View source, identifiers, and projection details
A program, dataset, or output another agent can run or read.