Discrete Cartan Geometry from Path-Independent Proper Time Comparisons

We give an operational construction of Cartan geometry from a single primitive clock-comparison step in special relativity. The primitive is a discrete “tick cell”, an isosceles wedge whose two timelike legs have fixed proper-time length and whose spacelike base has fixed invariant length, with opening angle fixed by Minkowski kinematics. When tick cells are tiled on a discrete complex, demanding loop closure becomes a geometric constraint: failure of frame closure defines curvature, and failure of displacement closure defines torsion. No spacetime metric or affine connection is assumed. Instead, a coframe and a Lorentz connection arise as bookkeeping fields for consistent transport, and the usual continuum identities (Bianchi, metric compatibility, and torsion-free conditions in the appropriate sector) appear as limits of the discrete closure relations. We test the construction on symmetric closure patterns and recover the invariant content of the Schwarzschild and Kerr geometries via a native readout map that converts closure ledger data into standard coordinate form. Probe dynamics and extremal worldlines are treated separately in Paper II.