A minimal oracle-based apparatus separating proof, measurement, epistemic justification, and implementability

This work introduces a fully specified black-box theoretical apparatus designed to expose structural separations between four notions that are often implicitly conflated across disciplines: formal provability, operational measurement, epistemic justification, and finite implementability.

The model is formulated as a deterministic, computable oracle with a minimal internal state and a restricted admissibility regime for queries. Queries are partitioned into four semantic classes—meta-queries, historical verification queries, measurement operations, and epistemic acknowledgement queries—each governed by an explicit response rule. The restrictions are imposed on expressibility rather than computational power.

Within this apparatus, a series of separation theorems demonstrate that no admissible strategy can simultaneously achieve provable determination, measurement stability, epistemic justification, and finite implementability. These results are structural rather than psychological or sociological: the model does not represent belief formation, cognition, social interaction, or experimental noise.

The apparatus is intended as a comparative framework. It supports proof-oriented tasks in mathematics, measurement-oriented analyses in physics, justification criteria in epistemology, and protocol design constraints in engineering, while showing that their respective success criteria diverge under shared interaction constraints.

By isolating the minimal conditions under which these divergences arise, the work provides a reusable counterexample framework for discussions at the intersection of computation, measurement theory, epistemology, and systems engineering.