frobenius

The coin problem (Frobenius problem) is a mathematical problem that asks what is the largest monetary amount that cannot be obtained using only coins of specified denominations.

10 algorithms for long arithmetic

m⊙²: The Self-Imscribing Bare-Metal Kernel — a Rust OS with no processes, scheduler, or filesystem hierarchy

A 12-primitive measurement apparatus for the structural type of any system — 17,280,000-address Crystal of Types

⊙MonadOS: the Imscribing Grammar as an operating kernel — Frobenius loop executing as an OS (Python)

Paraconsistent computation layer: Lean 4 formalization of the Imscribing Grammar with Belnap FOUR logic

Algebraic, exact, deterministic paraconsistent bio-organic chemistries — protein design, gene pipeline, materials science

Calculators for basic needs for solving problems related to matrices and graphs

This notebook features Mathematica functions for working with and visualizing C-semigroups in N², using the Normaliz package. Normaliz is an open-source tool for computations in affine monoids, lattice polytopes, and rational cones (https://www.normaliz.uni-osnabrueck.de/).

A web-application with tools for generating pseudorandom binary sequences, performing analysis, and visualizing results with graphs and charts.

A proof of Degtyarev–Shimada Conjecture 1.2 for the 3^v Fermat sixfolds (dim 6): A₃(q) = 105q⁴−630q³+1645q²−2037q+918. Macaulay2-verified. Candidate — offered for expert review.

A self-verifying agentic loop harness: THINK→ACT→OBSERVE→UPDATE with Frobenius-closed tool calls

A proof of Degtyarev–Shimada Conjecture 1.2 for the 3^v Fermat tower: A(q) = 15q³−45q²+55q−24. Four-way verified, Macaulay2 included. Candidate — offered for expert review.

Computational irreducibility as functoriality (Gorard arXiv:2301.04690) — Turing machines, cellular automata, hypergraph rewriting, Fong-Spivak Frobenius verification in Rust, built on catgraph