Supplementary Material for the paper: "Certificate Forests, Finite-Support Obstructions, and Satisfiability Encodings for Odd Perfect Numbers"

This repository contains the supplementary source code and dataset for the research article titled "Certificate Forests, Finite-Support Obstructions, and Satisfiability Encodings for Odd Perfect Numbers".

Overview:

The provided files constitute a deterministic, exact-arithmetic algorithmic verifier. They are used to prove the unconditional finite-support obstruction for the odd perfect number problem over the explicit 171-prime universe ($P_{\dagger}$). By implementing an interval-pruned deficit-vector algorithm, the verifier systematically refutes a formal even-part assignment space of over $4.42 \times 10^{20}$ elements by visiting only 310,806 exact recursive nodes.

Contents of the Repository:

The repository consists of the following 5 files:

support_verifier_pruned.py: The deterministic Python source code. It generates the prime universe, constructs all admissible exponent sets via Zsigmondy's theorem, builds the deficit vectors, and applies the interval-pruned traversal.

support_vector_data.json: The canonical serialized vector data used by the verifier to represent the target components and prime-power deficits.

support_verifier_pruned_output.json: The exact execution output summary, recording the node counts, primitive exponent tests, and the confirmation of zero satisfying assignments.

support_certificate_digest.json: The certificate digest recording the complete admissible-exponent lists $A_{P_{\dagger}}(p)$, the ordered even-option primes, the corresponding option counts, the ordered Euler components, and the SHA-256 hashes of the canonical vector data.

README_support_verifier.txt: Instructions for researchers and reviewers on how to run the source code to independently reproduce the exact node counts and verification results.

Reproducibility:

The computation is entirely deterministic and uses no random choices. Canonical SHA-256 hashes for all files are explicitly recorded in the main manuscript to guarantee absolute transparency and data integrity.