Discrete Cartan Geometry from Path-Independent Proper Time Comparisons

We construct Cartan geometric data from a single operational primitive: a discrete "tick cell" encoding one step of a clock comparison in special relativity. The cell is an isosceles wedge with two timelike legs of proper-time length meeting at a mutual event, joined by a spacelike base of invariant length . The opening angle is not free; it is fixed by Minkowski geometry. When such cells are tiled to cover a region, consistency of the tiling (loop closure) forces geometric structure: frame mismatch around loops becomes curvature; displacement mismatch becomes torsion. No spacetime metric or affine connection is postulated as primitive; the local Lorentz structure is input, and coframe, spin connection, and curvature emerge as continuum limits of the discrete closure constraints. Standard identities (Bianchi, metric compatibility, torsion-freeness) follow as consequences of closure rather than independent axioms. To demonstrate that the construction reproduces known physics, we apply it to symmetric configurations: the Schwarzschild and Kerr metrics emerge as the invariant content of the closure ledger, packaged into standard coordinates via explicit readout calibrations (radar-diamond consistency, Minkowski-limit matching). The Ernst potential arises from path-independence of the two-channel ledger.