Causal Time and the Four-Dimensional Opening of a Complete Event: The Pentachoron Principle

We derive a local four-dimensional structure from a locally finite causal order augmented by explicitly stated local axioms, without assuming an ambient manifold, a prior cell dimension, or a fixed coupling. Events carry bounded fermionic occupation; a composition axiom characterises the exponential clock family, and proper time is the accumulated causal weight of a history. Two complementary routes identify the five-vertex cell. In the internal-viewpoint route, three-dimensional visibility implies N = 5; in a separate parameter-free route, three structurally distinct vertex-local counts coincide only at N = 5, which returns d_vis = 3 under the same self-exclusion rule. Universal coupling and flag completion then identify the minimal complete event as the four-simplex. Conditional on a graph-entropy correspondence, the triangular capacity of that cell fixes one fermionic mode and α* = 1/(4 ln 2). Its ten squared edges reconstruct the Gram metric, split as 6 + 3 + 1, admit an exact local Lorentzian signature domain, and reduce under the (2, 1, 2) causal profile to a weighted K5 Laplacian with closed spectrum. What is proved is kept separate from the single structural frontier of global assembly and from the downstream particle and mass constructions. The executable companion is an integral, claim-directed part of the paper.