Structural Genesis of Dynamical Architecture: Deriving the Necessary Form of Physical Law from Conditions on Sustainable Complexity

This paper derives the structural architecture of physical law from minimal conditions on sustainable complexity. Beginning from a single primitive — the existence of distinguishable states (differentiation) — and requiring that distinctions be actualized irreversibly, we derive a chain of structural necessities: metric structure, differentiable state space, second-order dynamics, finite causal propagation speed, covariance with structural invariants, dynamic (state-dependent) metric, and a fundamental action bound. Each feature is forced by the inadequacy of the preceding stage. No physical content is assumed; the derivation uses only structural properties of complex systems (persistence, additivity, compensation, resilience). The resulting architecture is identified as the structural skeleton of Newtonian mechanics, special relativity, general relativity, and quantum mechanics — with the form derived and the content (constants, dimensionality, specific forces) remaining empirical. Key results include: (1) a full proof that second-order dynamics is the unique minimal form compatible with the persistence conditions on a Riemannian state space; (2) a non-overlap theorem showing that the dynamic-metric regime (GR) and the action-bounded regime (QM) are structurally incompatible at the same scale, explaining the quantum gravity unification problem as a theorem rather than an open problem; (3) systematic evidence from virtual world engineering (LOD, chunk loading, spatial partitioning, network tick compensation) showing that engineers independently converge on the same architecture when building complex interactive environments; (4) a detailed analysis of large language models as a structural test case, demonstrating that every derived feature — metric, second-order dynamics, finite causal horizon, dynamic metric, action bound, irreversibility, and even structural analogues of general relativity — manifests in transformer architecture despite the system having no physical space, time, or mass; (5) the concept of time density (Td = effective complexity / physical time) as a unifying measure connecting irreversibility, metric, and the action bound. The paper formulates the Principle of Structural Relativity: any system satisfying the conditions of sustainable complexity must exhibit the same architectural pattern, regardless of substrate. Predictions are stated for cognitive, social, and artificial systems, each with explicit falsification conditions (21 falsifiability points total). A quadrilemma is posed for the virtual-world convergence: structural necessity, simulation hypothesis, coincidence, or shared engineering constraints — with the latter shown to reduce to a weaker formulation of structural necessity. The formal apparatus is designed for transparency and criticizability rather than closure. The paper explicitly distinguishes between necessity claims (irreversibility, metric, finite speed, action bound) and minimal-sufficiency claims (smooth structure, second-order dynamics), and addresses the circularity objection, the analogy-vs-identity distinction, and the role of mathematical proof in architectonic arguments. Part of a broader program of structural systems theory (75+ publications, 1999–2026). Five prior results are directly presupposed; all others are derived within the paper. Keywords: complex systems, structural derivation, persistence, differentiation, dynamical architecture, viability, scale-dependent constraints, structural relativity, philosophy of physics, quantum gravity incompatibility, virtual worlds, large language models, time density, sustainable complexity, metric structure, covariance, action bound, irreversibility Related identifiers: doi:10.5281/zenodo.18268520 (Differentiation as ontological condition) doi:10.5281/zenodo.18341030 (Optimal coherence) doi:10.5281/zenodo.18343870 (Emergence of Newtonian dynamics) doi:10.5281/zenodo.18099738 (Law of scale-specific principles) License: Creative Commons Attribution 4.0 International