Conditional Cosmological Recurrence in Finite Hilbert Spaces and Holographic Bounds Within Causal Patches

A conditional framework of Conditional Cosmological Recurrence (CCR) is introduced, as follows: if a causal patch admits a finite operational Hilbert space dimension D (as motivated by holographic and entropy bounds), then unitary quantum dynamics guarantee almost-periodic evolution, leading to recurrences. The central contribution is the explicit formulation of a micro-to-macro bridge, as follows: (i) finite regions discretize field modes; (ii) gravitational bounds cap entropy and energy; and (iii) the number of accessible states is finite, yielding CCR. The analysis differentiates global microstate recurrences (with double-exponential timescales in $S_{max}$) from operationally relevant coarse-grained returns (exponential in subsystem entropy), with conservative timescale estimates. For predictivity in eternally inflating settings, a causal-diamond measure with xerographic typicality and a single no-Boltzmann-brain constraint is employed, thereby avoiding volume-weighting pathologies. The scope is explicitly conditional: if future quantum gravity demonstrates $D=\infty$ for causal patches, CCR is falsified.