Abstract
We present a quantitative theory of contraction and expansion cycles within the Quantum Memory Matrix (QMM) cosmology. In this framework, spacetime consists of finite-capacity Hilbert cells that store quantum information. Each non-singular bounce adds a fixed increment of imprint entropy, defined as the cumulative quantum information written irreversibly into the matrix and distinct from coarse-grained thermodynamic entropy, thereby providing an intrinsic, monotonic cycle counter. By calibrating the geometry-information duality, inferring today's cumulative imprint from CMB, BAO, chronometer, and large-scale-structure constraints, and integrating the modified Friedmann equations with imprint back-reaction, we find that the Universe has already completed Npast=3.6±0.4 cycles. The finite Hilbert capacity enforces an absolute ceiling: propagating the holographic write rate and accounting for instability channels implies only Nfuture=7.8±1.6 additional cycles before saturation halts further bounces. Integrating Kodama-vector proper time across all completed cycles yields a total cumulative age tQMM=62.0±2.5Gyr, compared to the 13.8±0.2Gyr of the current expansion usually described by ΛCDM. The framework makes concrete, testable predictions: an enhanced faint-end UV luminosity function at z≳12 observable with JWST, a stochastic gravitational-wave background with f2/3 scaling in the LISA band from primordial black-hole mergers, and a nanohertz background with slope α≃2/3 accessible to pulsar-timing arrays. These signatures provide near-term opportunities to confirm, refine, or falsify the cyclical QMM chronology.