Reproducibility Package for Prime-Offset Certificates for Compositeness: Factor-Sensitive Bounds, Product-Set Collisions, and Finite Audit
Description
This dataset is the reproducibility package accompanying the manuscript “Prime-Offset Certificates for Compositeness: Factor-Sensitive Bounds, Product-Set Collisions, and Finite Audit.” It reproduces the finite computer-assisted census of every composite integer N with 4 ≤ N ≤ 1,000,000, comprising 921,501 composite inputs, together with an independently rechecked large-scale stress example. The package contains two independent exact-integer C++17 implementations: a factor-bucket audit and a direct-gcd audit. Both implementations produce byte-identical per-composite depth ledgers, no unresolved cases, maximum certificate depth 11, and the same eight depth-11 maximisers. The package also contains derived frequency and record tables, a deterministic 10,000-row auxiliary sample, verification scripts, the stress-example verifier, machine-readable metadata, build and execution instructions, and SHA-256 checksums. The finite computations are logically independent of the asymptotic theorems in the accompanying manuscript. Package version 1.1, 2 October 2026.
Files
Steps to reproduce
Extract the package and open a terminal in the package directory. The software requires a C++17 compiler and Python 3; no non-standard libraries are required. First verify file integrity with: sha256sum -c SHA256SUMS.txt python3 verify_package.py Compile the three C++ programs with: g++ -std=c++17 -O3 -DNDEBUG -Wall -Wextra audit_depth_factor.cpp -o audit_depth_factor g++ -std=c++17 -O3 -DNDEBUG -Wall -Wextra audit_depth_direct.cpp -o audit_depth_direct g++ -std=c++17 -O3 -DNDEBUG -Wall -Wextra verify_stress_example.cpp -o verify_stress_example Create a rerun directory and execute the two independent full-census implementations: mkdir rerun ./audit_depth_factor rerun/depth_ledger_factor.csv rerun/factor_summary.txt 1000000 20 ./audit_depth_direct rerun/depth_ledger_direct.csv rerun/direct_summary.txt 1000000 20 Compare the independent outputs with: cmp rerun/depth_ledger_factor.csv rerun/depth_ledger_direct.csv cmp rerun/depth_ledger_factor.csv depth_ledger_factor.csv sha256sum rerun/depth_ledger_factor.csv The ledger SHA-256 should be: 0c42cb24233cde9baa1a378bf305ff898c52bf3e893db423b131bab3b4be7fd5 To reproduce the separate large stress example, run: ./verify_stress_example rerun/stress_example_summary.txt cmp rerun/stress_example_summary.txt stress_example_summary.txt The expected full census contains 921,501 composite integers, no unresolved cases, maximum certificate depth 11, and eight depth-11 maximisers.