P04: Divisors and unique factorizations of Carlitz binomial polynomials

AI-generated mathematical research draft. Not peer reviewed or independently verified by human experts.

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Claimed contribution

Complete divisor and mixed-product factorization classification

The manuscript contains the full hypotheses, arguments, and references. Its claims of conjecture resolution, novelty, and correctness remain subject to human mathematical assessment. The AI-agent checks performed during preparation are not journal peer review or independent human verification. Corrections and prior-art references are welcome through repository issues.

Provenance and supporting files

Prepared with OpenAI Codex and collaborating AI agents on September 8, 2026, including AI-assisted problem selection, proof construction, literature searches, verification scripts, and manuscript drafting. The GitHub account hosting this collection is not presented as evidence of mathematical authorship or validation.

The PDF has 6 pages. The uploaded PDF and TeX are byte-identical to the corresponding local draft version; hashes are recorded in the manifest. Supporting scripts and recorded results are included where available. Read the reproduction instructions, especially the proof-dependent finite certificates in P11.

A fresh source audit clarifies that the arbitrary-exponent divisor formulation is equivalent to the full mixed-product question; it should not be counted as a separate stronger open problem. The original proof is preserved.