proof

An autonomous AI agent (math-god) proved the weighted theta extension theorem, demonstrating that every simple theta graph with one arbitrary rooted-tree attached through a single bridge edge satisfies s⁺(G) > |V(G)|, using a combination of root-congruence PSD witnesses, local reductions, phase-sign classification, and other advanced techniques, with machine-checkable certificates.

The Jacobian conjecture has reportedly been disproven by Fable, a significant development in mathematics.

This article examines the equivalence between the component and geometric definitions of the vector dot product in Euclidean space, providing a geometric proof using the law of cosines and a projection proof using orthonormal basis vectors.

An exploration of how an AI agent can cryptographically prove to a signer that a payment is authorized before execution, addressing trust and security concerns in autonomous financial transactions.

MartinLoop is a tool for controlling AI coding agents with limits, proof, and run receipts.

A personal blog post rigorously introducing the Riemann integral and proving the Fundamental Theorem of Calculus, including supporting theorems like Rolle’s and the Mean Value Theorem.