The Coherence Envelope: Defining the Minimum Structural Unit of Action in Quantum Substrate Dynamics

The coherence support scale, Lcoh, defines the foundational unit of structure in Quantum Substrate Dynamics (QSD), governing when and how energy, mass, and radiation emerge from a Lorentz-invariant substrate. We define the Lcoh³ envelope as the minimum volumetric region required to support a stable, phase-locked mass-phase structure. This coherence boundary sets the conditions for quantized action, scalar recovery, and inertial behavior. Planck’s constant h-bar arises structurally from transverse coherence throughput, scalar collapse velocity, and the support area via the relation: h-bar = (cₜ⁴ / cₛ) * (Lcoh² / G) This reframes quantization as a geometric offload condition. Inertia is shown to reflect the cost of reconfiguring all locked envelopes during acceleration, while inertial lag emerges from scalar pacing constraints. Spectral emissions from mass-phase collapse are serialized by scalar pacing and reflect internal waveform geometry. Stability further requires internal symmetry, providing a structural origin for symmetry in quantum field theory. In this framework, Lcoh defines the substrate’s minimal condition for coherent emergence. Time, mass, inertia, and radiation are not postulates—but outcomes of substrate structure and recovery dynamics.