Volumetric Propagation Lag

Function: The temporal and thermodynamic friction inherent in translating a 2D mathematical state into a 3D physical mass. When a 2D topological boundary executing a Dual-Phase Inversion updates its Informational Degrees of Freedom (IDoFs) to resolve a prediction error, the underlying 3D bulk cannot update instantaneously due to the physical limits of mass, density, and spatial distance. The Volumetric Propagation Lag is the specific attosecond-to-macroscopic delay between the moment the 2D boundary establishes a new low-energy state on the Holographic Screen and the moment the deepest interior of the 3D bulk reaches its Target Morphology.

Inputs:

A completed 2D boundary state-update (Informatic Blueshift resolution).
The mass, density, and physical dimensions of the internal 3D Bulk (Substrate Hysteresis).

Outputs:

Temporal delay (the physical speed of the cast).
Acute, continuous emissions of Unruh-Landauer Dissipation (ULD) as the 2D boundary is forced to thermodynamically coerce the lagging physical matter into its new target geometry.

Integrations:

Condensed Matter Physics & Information Theory: Translates Bremermann's limit and the Substrate-Dependent Velocity Limit (the physical speed of sound, light, or bioelectric propagation through various physical mediums) into an unavoidable computational constraint for localized boundary rendering.
Dynamical Systems: Recontextualizes "inertia" beyond physical resistance to movement as the informatic drag of a system forced to translate a zero-mass computation into physical active matter.

Constraints: This lag represents the boundary's vulnerability to time. If the variance of the Outer Stochasticity introduces a new prediction error before the internal 3D Bulk has finished resolving the previous Morphological Cast, the boundary suffers a cascading computational failure (Informatic Saturation). It is forced to compute a new Target Morphology against a localized substrate that is still physically shifting toward an obsolete geometry. This paradox exponentially raises internal ULD until the localized active matter suffers thermal dissolution.

Open Inquiries:

Tensor of Propagation Delay: Developing a universal mathematical tensor to define propagation lag across distinct substrate densities and topological rigidities. This equation will allow engineers to predict the informatic failure rate of synthetic active nematics versus biological tissues when subjected to high-frequency environmental noise, calculating how fast an environment must fluctuate to physically tear a specific substrate apart.