Theory
Mathematical foundations of Asgard.
Categorical Semantics
Category theory foundations: traced monoidal categories and circuit composition.
Compilation Process
How equations are translated to computational circuits through isolation and unification.
Coefficient Semantics
The exact coefficient (polynomial) semantics — what each circuit operation does to coefficient arrays. Approximation enters only through truncation.
Stochastic Calculus
Mathematical foundations of stochastic calculus: Itô and Stratonovich integrals, conversion formulas, and the Itô Lemma.
Trace Elimination
Closed-form solutions as trace elimination: the duality between dynamical systems and programs, and why the general problem is conjectured undecidable.