Information Probe Calculus: Observation, Refinement, Composition, and Stopping Conditions for Numerical Information Objects

Defines a probe as a typed, partial observation operator in six kinds (extractive, derived, comparative, relational, spectral, bidirectional), with composition, cost, certificate, closure and stopping rules. The one lemma — adding a probe only refines the indistinguishability relation (∼_{P∪{P'}} ⊆ ∼_P) — is a one-line fact. 'Calculus' in the title is so far a name only: the differential, integral and curvature sections are one-line placeholders, and the 'probe category' is explicitly not developed here.