JaP: A Proposed Classification for Hypothetical Planck-Scale Entities of Matter

Description Version 0.4 develops the JaP proposal as a framework-relative classification for hypothetical entities of matter whose effective radii are compared with the Planck length. This version introduces a framework-specific resolution parameter, δ_F, for theoretical frameworks in which a directly identifiable nearest candidate below or above the Planck length may not exist. It defines an unresolved interval around the Planck length, establishes conditions for assigning the JaP− and JaP+ boundary designations, and distinguishes attained boundary values from unattained limiting values. Version 0.4 also clarifies how candidate-radius uncertainties affect classification, introduces resolution-sensitivity analysis, and proposes a procedure for investigating whether a universal dimensionless resolution parameter can be physically justified across different theoretical frameworks. The exact JaP designation remains reserved for a candidate whose effective radius equals the Planck length. JaP is presented as a proposed terminology and classification scheme, not as an experimentally established particle or accepted physical classification. This revision extends the earlier versions by refining the mathematical definitions, boundary-existence conditions, uncertainty treatment, and recommended reporting procedure.