Structural Differentiation Time (SDT) v1.2: A Decisive Observational Test of Emergent Time

This work presents Structural Differentiation Time (SDT) v1. 2, a minimal and falsifiable framework in which time is not treated as a background parameter, but as an emergent observable generated through irreversible structural differentiation. Building on SDT v1. 0 (definition) and SDT v1. 1 (dynamics), this version introduces explicit observational signatures and a decisive test capable of distinguishing structurally generated time from externally imposed temporal frameworks. The framework is based on the minimal structural mapping: τ (D) = 1 − exp (−λD) and its dynamical evolution: dτ/dt = (dτ/dD) (dD/dt) A key contribution of this work is the decomposition of observed temporal deviation: Δτₒbs = Δτᵣel + Δτₛtruct This implies that systems under identical relativistic conditions may exhibit distinguishable temporal behavior if their internal structural differentiation differs. Core claim: Identical relativistic background does not guarantee identical temporal evolution. This leads to a decisive observational test: - General Relativity predicts no temporal separation under identical conditions- SDT predicts structure-dependent temporal splitting If validated, this result establishes time as a physically testable consequence of structural dynamics. The framework further suggests deep structural connections across physical domains: - SDT–SDQ: quantum decoherence may follow structural temporal rate- SDT–SDC: cosmological time may be structure-dependent All figures are fully reproducible using the provided Python implementation, ensuring transparency and reproducibility. This work advances SDT from a conceptual and dynamical framework to a directly testable physical theory.