What Does an Integer-Factorization Experiment Prove? Exact Bounded-Search Records, Independent Checking, and Fault Attribution

A factorization report may assert a valid divisor, a complete bounded search, faithful intermediate arithmetic, public-input provenance, or computational superiority; these assertions require different evidence. We examine exact, non-succinct Fermat-search records and canonical Euclidean greatest-common-divisor transcripts through a two-kernel verification interface with strict decoding and explicit resource-policy outcomes. The original fixed-budget experiment used six synthetic semiprimes and 60 controlled mutations; two separately coded Fermat checkers and a conventional recomputation baseline agreed on every outcome. An expanded evaluation includes 227 cross-language Fermat comparisons, 749 matched Euclidean decisions, and an 812-case corpus yielding 260 accepted, 544 rejected, and eight resource-limited inputs, with complete agreement against conventional recomputation. The reported first failed invariant belonged to the independently recomputed violated-invariant set for all 544 rejected records, although 260 multi-mutant cases admit no unique causal interpretation. Eighteen benchmark configurations yielded 1,386 timing observations and 72 memory observations without establishing an end-to-end speed advantage. A pinned separate checkout reproduced 22 evidence-file hashes and three deterministic datasets. The results establish bounded record consistency under stated assumptions and reproducibility of selected tests, not historical execution provenance, a new factoring method, or superiority over conventional checking.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-02
DOI
https://doi.org/10.5281/zenodo.23888904
Primary Topic
Cryptography and Residue Arithmetic
Type
preprint
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preprint

What Does an Integer-Factorization Experiment Prove? Exact Bounded-Search Records, Independent Checking, and Fault Attribution

Md. Amir Khusru Akhtar
4 links
Zenodo (CERN European Organization for Nuclear Research)
Cryptography and Residue Arithmetic
preprint

What Does an Integer-Factorization Experiment Prove? Exact Bounded-Search Records, Independent Checking, and Fault Attribution

Md. Amir Khusru Akhtar
preprint en

Abstract

A factorization report may assert a valid divisor, a complete bounded search, faithful intermediate arithmetic, public-input provenance, or computational superiority; these assertions require different evidence. We examine exact, non-succinct Fermat-search records and canonical Euclidean greatest-common-divisor transcripts through a two-kernel verification interface with strict decoding and explicit resource-policy outcomes. The original fixed-budget experiment used six synthetic semiprimes and 60 controlled mutations; two separately coded Fermat checkers and a conventional recomputation baseline agreed on every outcome. An expanded evaluation includes 227 cross-language Fermat comparisons, 749 matched Euclidean decisions, and an 812-case corpus yielding 260 accepted, 544 rejected, and eight resource-limited inputs, with complete agreement against conventional recomputation. The reported first failed invariant belonged to the independently recomputed violated-invariant set for all 544 rejected records, although 260 multi-mutant cases admit no unique causal interpretation. Eighteen benchmark configurations yielded 1,386 timing observations and 72 memory observations without establishing an end-to-end speed advantage. A pinned separate checkout reproduced 22 evidence-file hashes and three deterministic datasets. The results establish bounded record consistency under stated assumptions and reproducibility of selected tests, not historical execution provenance, a new factoring method, or superiority over conventional checking.

Zenodo (CERN European Organization for Nuclear Research)
Cryptography and Residue Arithmetic
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