Causal Sets as a Conditional Coarse-Graining of Modal Triplet Theory: Kinematic Construction, Sampling Choices, and Scale-Typing Boundary

A causal set can be obtained from an effective Modal Triplet Theory spacetime once a sampling rule is supplied, but the sampling rule is additional data. For a globally hyperbolic four-dimensional spacetime, any locally finite set of sampled events inherits a partial order from the spacetime causal relation. A Poisson process with intensity proportional to the spacetime volume measure is almost surely locally finite on every relatively compact region; in Minkowski spacetime its law is Lorentz invariant because the intensity measure is invariant. These are exact kinematic statements. They do not identify the causal set as fundamental, derive the sprinkling intensity, or convert an internal q79 spectral gap into a four-dimensional event density. Such a conversion requires a base-resolution theorem with metric normalization and an explicit internal-to-spacetime map. Causal sets therefore remain a valid conditional coarse-graining or observational encoding of an MTT spacetime, not a currently selected consequence of the internal finite geometry.