We formalize a program as a mathematical object whose primary function is to "resist" entropy over time. We model programs categorically, define entropy as a degrading endofunctor, and introduce clarity as a measurable bound on adaptability.

We present definitions, propositions, lemmas, and proof sketches, along with counterexamples, applications, and thought experiments. The aim is a minimal, logically consistent framework suitable for both theoretical reasoning and pragmatic software engineering.

devs

Abstract. 

We formalize a program as a mathematical object whose primary function is to "resist" entropy over time. We model programs categorically, define entropy as a degrading endofunctor, and introduce clarity as a measurable bound on adaptability. 

We present definitions, propositions, lemmas, and proof sketches, along with counterexamples, applications, and thought experiments. The aim is a minimal, logically consistent framework suitable for both theoretical reasoning and pragmatic software engineering.