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 cycles. The finite Hilbert capacity…

5. Forecasting Future Cycles 5.1. Write Rate and Dust-like Back-Reaction The calibrated imprint write-rate of Section 3.2 isBecause the entropy per comoving cell remains small, the imprint field contributes to the Friedmann system with at leading order. Hence , mimicking a dust-like component whose normalization grows monotonically with . During expansion epochs, the ratio remains subdominant for (as satisfied above), and becomes dynamically important only near the bounce when . The scaling index thus controls how rapidly the imprint field back-reacts to slow expansion and trigger contraction. Away from the narrow bounce interval, the effective equation of state (Appendix B), so the only secular driver toward the next contraction is the cumulative increase in encoded in ; this is why the write-rate directly forecasts the inter-bounce interval. 5.2. Maximum Remaining Cycles from Entropy Saturation The covariant Bousso–Bekenstein entropy bound caps the Hilbert capacity of the Universe: where with present curvature radius . This givesSubtracting the current imprint load [Equation (10)] and dividing by the fixed increment per cycle, , yields the absolute ceiling Thus, no more t…

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