This paper presents a structural constraint (no-go) theorem governing the form of arrow-like directedness in physical and informational descriptions. Under minimal and widely accepted assumptions—time-reversal symmetric admissible dynamics and information-losing operational reduction—the work proves that any direction-sensitive diagnostic defined on a reduced description must be boundary-radial: it can depend only on unsigned separation from a conditioning boundary, not on intrinsic temporal orientation. The result is taxonomic and diagnostic, rather than mechanistic. It does not propose a new arrow-of-time model, select a preferred boundary, or introduce asymmetric dynamics. Instead, it classifies all arrow-like diagnostics by the locus of asymmetry, showing that apparent arrows can arise only from one of three sources:(1) intrinsic asymmetry in the admissible dynamics,(2) asymmetry in the operational projection, or(3) explicit boundary-selection principles. A key consequence is a forced-disclosure criterion: any account attributing arrow-like behavior to symmetric dynamics must explicitly identify where oriented asymmetry enters, rather than allowing it to remain implicit in projection structure or boundary conditioning. The paper formalizes an operational boundary-reflection test that distinguishes intrinsic arrows from projection-induced artifacts, and demonstrates its use through a worked diagnostic case study of Boltzmann’s H-theorem, locating the irreversibility it describes in boundary-selection asymmetry rather than in mechanical dynamics. The framework applies uniformly across thermodynamic, quantum-measurement, decoherence, and computational contexts, and is positioned alongside other foundational constraint theorems (e.g., Bell, Kochen–Specker, no-cloning) as a methodological tool for auditing arrow explanations rather than generating new dynamics. This work is intended for researchers in foundations of physics, statistical mechanics, philosophy of physics, and related fields who seek a precise, falsifiable framework for analyzing the origin and status of arrow-like directedness in reduced descriptions.
A. R. Wells (Sun,) studied this question.