Constraint-Phase Memory in Solids A Testable Hypothesis for History-Dependent Physical States

This paper proposes Constraint-Phase Memory (CPM) as a falsifiable hypothesis for describing history-dependent physical states in complex materials. While hysteresis, metastability, structural relaxation, internal variables, and material memory are well-established phenomena, CPM asks whether the collective organization of internal constraints can serve as an additional predictive state descriptor. The hypothesis introduces a phenomenological constraint-memory variable, χ_C, representing the collective organization of interacting microscopic or mesoscopic constraints. The extended material state is expressed as S* = (S_conv, χ_C), where S_conv denotes conventional state variables. A mathematical framework is developed for constraint-history dependence, memory relaxation, path-order effects, and residual observable responses. The paper proposes controlled experiments in which materials with different preparation histories are returned to the same conventional thermodynamic and structural state. It predicts that, if a constraint-memory contribution exists, measurable residual differences may remain and may exhibit characteristic relaxation, path-order dependence, and correlations across independent observables. A rigorous falsification strategy is provided. Conventional explanations involving defects, residual stress, composition, phase fraction, grain structure, surface chemistry, and other known mechanisms must be eliminated before a CPM interpretation can be considered. The paper therefore makes no claim of experimentally established new physics. Instead, it presents a specific mathematical hypothesis and an experimental framework for determining whether collective constraint organization provides predictive information beyond conventional descriptions of material history.