The Quantum Clock: Causal Null Timing, Residual Spectral Dynamics, and Event-History Closure in Six-Throat Directed Spacetime

Paper XXVII of the Six-Throat Directed Geometry program closes the temporal layer of the microscopic conversion theory by deriving a geometry-fixed causal quantum clock without compactifying time and without introducing a free transit-time parameter. The inherited spacetime topology remains R_t x S^1_xi x S^2, while the antiperiodic one-particle spectrum retains the half-integer mode structure with circumference parameter L = 15.6. The massless antiperiodic sector selects the unique minimal universal synchronization interval, giving the physical clock period T_gamma = 15.6 ell/c.The massive spectrum has no nonzero universal recurrence. Instead, it evolves relative to the null clock through a residual Hamiltonian obtained after removing the spatial antiperiodic parity phase already accounted for by the geometry. The resulting clocked microscopic map separates the universal causal tick from the mode-dependent massive spectral evolution.Repeated clock returns generate a Toeplitz source-history kernel represented by a unique normalized positive temporal spectral measure. Its real and imaginary moments define Hermitian clock observables. The same kernel closes bosonic Weyl accumulation, fermionic Clifford history, two-time response, arbitrary multi-event interference, and the graded event-history generating functional. Generic nonresonant massive histories are bounded almost periodic, while exact resonant sectors retain coherent quadratic growth.The completed construction requires no higher independent temporal kernel within the inherited linear and quasi-free source algebra. The complete dimensionless fixed-route temporal process is specified by the previously derived microscopic action theta = 2 together with the positive clock measure dmu_tick. The accompanying reproducibility package verifies the causal null-clock law, residual spectral dynamics, temporal kernel structure, clock observables, bosonic and fermionic event histories, and generating-functional closure.