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, deterministic non-invertibility, sequential dependency, and irreversible commitment together with non-deterministic outcome selection. The contribution of the framework is not the discovery of a new dynamical law—but rather 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 independently removable. 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.
Claudio Irrgang (2026) studied this question.