Irreversible Compression Commitment: A Typed Axiomatic Framework for Evolution, Extraction, and Commitment

This paper introduces Irreversible Compression Commitment (ICC), a typed axiomatic framework for sequential irreversible commitment processes. Each commitment step is decomposed into a three-stage pipeline with explicit domain and codomain types: deterministic flow on density matrices, deterministic many-to-one extraction of outcome probabilities, and non-deterministic sampling to a single committed outcome. Three axioms constrain the pipeline (finite distinguishability, boundary compression, and commitment decomposition), with compression stated at the finite boundary level of distinguishable inputs and outputs rather than on the continuous density-matrix interior. Under these axioms, the main theorem is structural. It establishes strict boundary compression, non-recoverability of prior inputs from committed outcomes, and non-deterministic irreversibility; a corollary captures the discreteness, irreversibility, and sequentiality of the chain index. The primary nontrivial content of the framework, however, is not this single-step theorem but the chain accumulation theorem and the typed collision-geometry proposition: the exponential growth of compatible histories under iterated compression, and the typed constraint on where collisions occur. The contribution is not the discovery of a new dynamical law, but the formal isolation of a compact typed package sufficient for these consequences and the explicit tracking of which axioms support which results. Three targeted weakenings produce three distinct loss patterns, demonstrating that the structural ingredients are independent. The framework does not resolve the physical mechanism of single-outcome selection, and it does not establish that any physical system instantiates ICC. Rather, it provides an abstract target for comparing candidate realizations, weakened variants, and neighboring formal frameworks.