# Noncoverage for Distinct Odd Moduli with at Most Three Prime Divisors

Michael Schroeder, Independent Researcher. Version 1.0.
Manuscript: 9 September 2026; revised 15 September 2026.
ORCID: https://orcid.org/0009-0004-3249-0195
DOI: https://doi.org/10.5281/zenodo.22760638

- [Paper](three_prime_factors_per_modulus.pdf)
- [Complete paper and proof package](three_prime_factors_complete.zip)
- [Supporting materials](companion.html)
- [LaTeX source](main.tex)
- [BibTeX citation](CITATION.bib)
- [License](LICENSE.md)

The PDF and complete ZIP match the Zenodo edition exactly. The complete ZIP
contains the manuscript, original proof sources, exact arithmetic checkers,
certificates, pinned dependency manifest and historical verification records.
Theorem 1.1 is formalized end to end in Lean; the separate Theorem 1.2
largest-prime cutoff extension is not formalized. Third-party dependencies
and compiled caches are not bundled. The publication update preserves the
mathematical proof and audited sources and does not claim a fresh kernel replay.

The paper and prose use CC BY 4.0; original verification code and exact
inputs use MIT. See LICENSE.md for component boundaries and third-party notices.