Five selected research manuscripts
Revised 8 September 2026. These are five consolidated algebra and number-theory manuscripts, selected for general structural results and reusable consequences. Four substantially strengthen the earlier drafts; P06 retains its conjecture resolutions and asymptotic, with corrected source pinpoints. The original thirteen drafts remain in original collection.
Status: full mathematical manuscripts with internal AI proof and source audits. No human expert review, journal acceptance, guaranteed priority, or predicted citation impact is claimed. Each assessment states the nearest prior results, source-access limits, and the case for specialist significance. Compilation and conversion checks are separate from mathematical review.
| ID | Full Markdown paper | Main contribution | |
|---|---|---|---|
| P01 | Integral Lefschetz decompositions of fully whiskered simplicial complexes | Integral operator splitting; all-characteristic ranks and Jordan data; exact WLP/SLP classification; broader Gorenstein applications | |
| P02 | Exact Dold repair for matrix powers and integral recurrences | Complete spectral criterion, exact local prime exponents, uniform recurrence factor and one attaining initialization | |
| P06 | Prime support and growth of Stirling repair factors | Miska–Ward Conjectures 1, 2, 3, 4(d); sharp families and square-root logarithmic growth beyond the radical | |
| P09 | Unique addition in centerless metabelian Lie algebras of finite length | Bracket alone determines addition for finite-length centerless metabelian Lie algebras over commutative rings | |
| P13 | Additive periods of power maps lie in the prime radical | Universal period–radical inclusion; nilperiod rings are 2-primal; finite classification and exact twisted-ring counts |
Every folder contains manuscript.tex, manuscript.pdf, the complete manuscript.md, ASSESSMENT.md, and hash-bound conversion records. The Markdown includes the full proofs, equations, theorem numbering, and linked bibliography; it is not an abstract or summary. It targets GitHub's math syntax. Local MathJax syntax checking does not by itself certify GitHub's live visual rendering.
Evidence and boundaries
| ID | Independent proof evidence | Current source comparison |
|---|---|---|
| P01 | Extension and final transfer | Source audit |
| P02 | Extension, final transfer | Source audit |
| P06 | Fresh reconstruction, final transfer | Source comparison within the fresh audit |
| P09 | Extension, final transfer | Source audit |
| P13 | Extension, final transfer | Source audit |
“Independent” here means a separate AI agent reconstructed the argument; it does not mean an external human referee. Internal reviewers found no remaining mathematical gap in these final statements. Exact finite checks support the hand proofs and are not premises of their infinite conclusions. A bounded literature search cannot exclude every prior or unpublished result.
The selection does not count each corollary as another paper. P01 combines the conjecture and all operator consequences. P02 combines the matrix theorem, recurrence theorem, Lucas factor and universal exponent. P06 is distinct because its central results concern cancellations and asymptotics of one scalar combinatorial sequence, which the uniform matrix classification does not determine. P09 combines the finite-length theorem and its examples. P13 combines the radical theorem with its applications.
The concrete reasons for selecting these five, and the explicit remaining research frontiers, are in DOWNSTREAM.md. Build and validation instructions are in REPRODUCIBILITY.md. The final manifest records exact artifact hashes and checks.
These are substantive specialist research candidates. The length or technical complexity of a proof does not certify historical difficulty, and no document here claims five field-changing breakthroughs or guarantees future citations.
Version-specific citation links and BibTeX identify the exact revised manuscript snapshot.