From Relations to Realized Form: Constraint, History, and Pattern Selection Across Matter, Fields, and Living Architecture
Year: 2026
Type: preprint
Abstract: Physical systems do not have access to every imaginable configuration. Constituents, local laws, relations, environmental conditions, causal structure, and history jointly restrict the set of states that remain physically accessible. Within that restricted region, dynamics and stability criteria select configurations that can persist. The resulting structure may then be characterized geometrically, spectrally, chemically, or morphologically. In some systems a persistent structure further modifies the constraints encountered by subsequent processes, opening a recursive pathway from realized form to new possibility. This paper develops a shared selection architecture for that process. Constituents and local laws are held fixed while relations, constraints, causal accessibility, physical conditions, and history are allowed to vary. The architecture is written as a sequence of intermediate sets: an unconstrained configuration space is reduced by constraints and history to an accessible region; attractors and metastable states within that region determine what can persist; the realized structure is read after the fact. The same formal skeleton is applied to matter, continuous fields, and living architectures. Path dependence is treated as an essential ingredient: identical present ingredients need not yield identical outcomes when histories differ. Version III further investigates the DT historical branching architecture. A realized persistent organization may undergo a Creative Deviation D that reconfigures the Transformation Architecture T of admissible transformations, thereby changing the subsequently accessible state space and the structures that can be selected. Four competing models—M0, M_D, M_T, and M_DT—are compared so that neither D nor T is protected from elimination. Geometry remains a downstream extracted signature rather than an assumed organizing pattern.
Authors: Alhawarat, Ali, Yoshida, Kenji, Tully, C.J, Greaves, Nick, Schimmelpfennig, Yochanan
Language: English
Topic: Complex Systems and Dynamics
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204184062
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