Geometric Transition Dynamics: Minimal Four-Volume Cells, a Strict Solution of TrinityE, and Testable Predictions for Emergent Quantum Observation

Preprint. This paper introduces Geometric Transition Dynamics (GTD), a constructive framework in which quantum open dynamics and observation emergence are generated from covariant transition geometry rather than assumed as primitives. The fundamental update parameter is not a preferred time coordinate but the four-volume element dΩ = √−g d⁴x, and dynamics proceeds on minimal four-volume cells Ω₀. The operational evolution law, the Geometric Transition Equation (GTE), is defined as a local convex mixture of unitary conjugations driven by mixed-loop events on an internal K₅ transition graph, which guarantees a completely positive and trace-preserving (CPTP) evolution. In a weak-kick Markov limit, the GTE reduces to the standard GKSL/Lindblad structure. A key design principle is that a “time-leg” description is not assumed: it emerges only after a declared reported-layer factorization dΩ = dτ dV₃, treated as an interface convention. Consistency between reported time/volume rescalings and phase residuals is enforced by the spacetime-safety linkage ln(1+α) = ε/π, together with a rank-one measure representation that maintains strict non-degeneracy of the reported volume element without introducing new degrees of freedom. Within GTD, the observation structure ρψ = {S₀, πψ, Qψ} is defined operationally as low-order moments of loop-induced kicks, while mass-sector weights are selected as a fixed point of loop-polynomial reinforcement under forced exponential suppression by information cost. The resulting closed system realizes TrinityE as a strict simultaneous fixed point and yields testable predictions, including a constrained complementarity-decay rate Γ = 2S₀ and characteristic anisotropic (bi-exponential) visibility envelopes. Related (DOI only)10.5281/zenodo.18158333 | 10.5281/zenodo.18158453 | 10.5281/zenodo.18169038 | 10.5281/zenodo.18169180 | 10.5281/zenodo.18160918 | 10.5281/zenodo.18160477 | 10.5281/zenodo.18158537 | 10.5281/zenodo.18159246