Slime2Slimer: From Philosophy, Logic, and Mathematics to a Commutativity-First Computing Paradigm

This paper introduces Slime2Slimer, a conceptual and formal bridge from philosophical foundations of meaning to a commutativity-first computational architecture. 

We argue that the dominant AI-centric paradigm wastes resources by applying inference to deterministic structure, and propose a layered collapse: philosophy (meaning), logic (inference and equivalence), and mathematics (commutativity and algebraic invariants).

Key contributions:
- Formalization of "order as a tax" and commutativity-first scheduling
- Theorem with proof: sufficient criterion via read/write sets for commutative operations
- Empirical validation: 80-94% cache hit rates on realistic workloads, 99.995% on arithmetic domains, 17.2x compression ratio
- SlimeOS architecture: normalization layer, commutativity analysis, and LLM as "last resort"
- Integration with Related Work (Michael et al. 1996, Rugina & Rinard 2008, Vasiladiotis et al. 2021)

The paper serves as a "map" connecting philosophy, logic, mathematics, compilers, operating systems, and hardware through the unifying principle: "Do not infer the routine. Just look it up."

Part of the Slime Theory series (SlimeCompiler, SlimeLLM, SlimeTree, SlimeNENC, SS Theory).