Resolution-Limited Admissibility: A Pre-Foundational Note on Finite-Scale Physical Modeling
Description
This preprint is motivated by a simple physical constraint: below a fundamental length scale (canonically the Planck length), the continuum idealization used by many differential-equation models has no clear operational meaning. Accordingly, physically testable statements should be formulated at a finite resolution and over a finite time horizon, using only quantities that can be registered, stored, and compared at that scale.
The note proposes a minimal, theory-agnostic principle called resolution-limited admissibility (RLA). RLA separates (1) mathematical questions posed in idealized limits (such as “arbitrarily small scales” or “infinite time”) from (2) physically meaningful questions about predictability and stability at fixed finite resolution and finite time. The framework is presented in a record-first way: finite operational records and cross-scale coarsening maps are treated as primitive, while continuum fields are optional analytic representations.
The discussion is positioned relative to coarse-graining practice and Large Eddy Simulation (LES), where filtered equations at a fixed resolution are evolved together with a subgrid closure, and stability and energy behavior are key design criteria. The note also points to related analytical formulations that express energy balance using coarse-graining.
Intended use: This note is meant to serve as a pre-axiom layer for subsequent work on finite-resolution physical commitments (including a later framework release), providing a stable citation for the operational assumptions used there.
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Additional details
References
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