The Right Answer Is Not Enough: RPRM Process Mechanics: What Scientific Descriptions Must Preserve

Abstract

Scientific descriptions become useful through the work they let us do next: predict a response, combine observations, or reuse a result. A correct answer to one question can nevertheless discard a distinction that the next question requires. This paper develops RPRM Process Mechanics as a human-guided method for finding and testing those distinctions. It connects the choice of a representation to three obligations: preserving continuation, composing evidence about compatible sources, and reusing conclusions under the conditions that support them. Measurement interpretation connects the calculation back to the scientific quantity being requested. The mathematical core specializes established factorization results, gives conditions for resolving a question from joint records, and distinguishes logical resolution from probabilistic improvement. Development cases show how these distinctions change the appropriate next step. In known-equation circuits, present state can suffice, timed observations can improve estimation or recover hidden current, and an unprovided future input can remain unresolved. Exact interval summaries compose across 76 law-partition comparisons, while a structurally accepted false summary exposes the limits of a correct Boolean answer. A biological-figure reconstruction retains useful partial results while identifying missing calibration and sampling relations. These are worked diagnoses, not a demonstrated comparative advantage. Existing proposals for protein-folding dynamics and BRCA1 cellular function show how the same reasoning could guide harder applications: test which distinctions a reduced description must retain for the desired behavior or measurement. Those molecular comparisons remain unexecuted. The aim is a usable connection between mathematical sufficiency and the scientific choice of what to retain, what to measure, and what to do next. This separate working paper accompanies The RPRM Manifesto (DOI: 10.5281/zenodo.22650748). The companion archive includes editable manuscript and build files, public evidence, and reproducible verification code. Original prose, diagrams, and data are CC0 1.0; original software is 0BSD. Third-party material retains its identified terms; see the accompanying licensing and notices.