The Temporal Openness Coefficient Θ(t): A Structural Extension of the Unified Dynamic Model of Mind

Abstract Dynamic models of mind specify how organisms navigate instantaneous prediction errors and attractor gradients, yet leave unaddressed how the structural space of possible futures is itself constructed. We introduce the Temporal Openness Coefficient Θ(t), defined as the ratio of perceived future branch-count (B_future) to remembered past branch-count (B_past). This paper (v4.1) formally integrates Θ with five published UDMM working papers: (1) The Bio-Informational Continuum, which demonstrates via Fokker-Planck analysis that total equilibrium is equivalent to biological death — establishing Θ → 0 as the topological analogue of the 'death singularity'; (2) The Contextual Frictional Encoding Principle (CFEP), whose trajectory memory V_model = ∫L(bio,env)dτ and attractor-depth formula Γ ∝ ∫F_ric dτ provide the first rigorous basis for measuring B_past as accumulated friction history rather than episodic recall; (3) the Operational Theory of Linguistic Meaning (OTLM), whose cost function J = E_metabolic/(N × A_ros × Φ) formally links Θ_R (path resolution) to the crystallization of future trajectories from fluid to structural knowledge; (4) The Genesis of Reality and Cognitive Ontogenesis, whose Cone of Possibility Ω is formally identified with B_future, and whose Model Age t_model = ∫BAC·ρ(C_m)·G_A dτ becomes the developmental predictor of Θ_B across the life span. Together these integrations derive Θ's evolution equation dΘ/dt from the UDMM Master Equation, operationalize B_past without self-report, ground Θ_R in a physical cost function, and place Θ within the full UDMM developmental architecture. Five falsifiable predictions are derived, including a temporally precise 48–72 hour precedence test designed to discriminate Θ from concurrent mood variables.