Structure as Survival: Geometric Constraint and the Emergence of Definiteness Author: Ognjen Puljak

This paper proposes that structure emergence—whether quantum measurement outcomes or galactic morphology—follows a universal pattern: geometric constraints filter possibility space, and surviving configurations become definite through irreversible anchoring. The framework introduces dimensionless stabilization parameters (W for quantum systems, Γ for galaxies) constructed as ratios of competing timescales weighted by geometric coupling. Both parameters exhibit O(1) thresholds by dimensional necessity, not fine-tuning, with sigmoid transitions between distinct structural states. For quantum measurement, W = Iτ/τ₀ captures accumulated which-path information relative to coherence time, recovering the Englert complementarity relation V² + D² ≤ 1 as a limiting case. For galactic structure, Γ = A²D combines angular momentum alignment (A) with the ratio of dynamical to cooling time (D), predicting three morphological states: hot halos (D < 1), photometric discs (D > 1, Γ < 1), and kinematically anchored discs (Γ > 1). The alignment exponent k = 2 is derived from the quadratic dependence of centrifugal support on the cosine of misalignment angle. The framework makes testable predictions: high-redshift galaxies (z > 4) should show systematic divergence between photometric disc fractions and kinematic disc fractions, as the entropy floor suppresses coherent angular momentum organization. Recent JWST observations of kinematically hot "disc-like" systems at z ~ 4–6 provide preliminary support. The parallel between quantum and galactic stabilization is structural, not analogical: both involve constraint-driven phase space contraction, threshold-crossing dynamics, and irreversible commitment via entropy export. Structure, in this view, is not created but survives. Keywords: structure formation, quantum measurement, galaxy morphology, phase space, decoherence, angular momentum, stabilization threshold