In this project, we attempt to reformulate various notions from classical commutative algebra (such as flatness, regularity, smoothness, etc.) in an entirely categorical manner, so as to be able to later write down their analogues in derived algebraic geometry without having to develop extra theory. We will also be presenting certain application…
Sato-Tate Groups and Distributions of y^{\ell} = x(x^{\ell}-1)
Definition of Serre's twisting sheaf (work in progress)
Formalization experiments around structural behavior near critical points of arithmetic functions.
A visual guide to étale cohomology at four progressive levels, from high school to graduate school. The mathematics edition of the "Buildings in the Desert" series.
End-to-end SageMath verification of Pisot Dimensional Theory's foundational numerical claims. Runs in under a minute.
Abelian unramified geometric class field theory
Verification code for "Arithmetic Geometry at the Pisot Boundary" — five arithmetic theorems and the Dimensional Norm-Hodge Theorem for the PDT polynomials
The Arithmetic Gauge: Cross-Ratios and Projective Invariants
The strong coupling constant α_s(M_Z) = Ω₄/23 = 0.117921 from the real period of elliptic curve 1132b1 divided by the discriminant prime of x³−x−1. Zero free parameters. 0.02% match to PDG.
AI-assisted, unverified verification dossier for a degree-50 RM(7) pullback in generalized Fermat research; reproducible code and open questions.
Étale cohomology of schemes and rigid-analytic varieties; L-functions; anabelian geometry
A Thermodynamic Heuristic Framework for the Birch and Swinnerton-Dyer Conjecture
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