{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T07:47:17Z","timestamp":1774338437492,"version":"3.50.1"},"reference-count":70,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T00:00:00Z","timestamp":1759795200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Terra Quantum"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2013information duality, inferring today\u2019s 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\u00b10.4 cycles. The finite Hilbert capacity enforces an absolute ceiling: propagating the holographic write rate and accounting for instability channels implies only Nfuture=7.8\u00b11.6 additional cycles before saturation halts further bounces. Integrating Kodama-vector proper time across all completed cycles yields a total cumulative age tQMM=62.0\u00b12.5Gyr, compared to the 13.8\u00b10.2Gyr of the current expansion usually described by \u039bCDM. The framework makes concrete, testable predictions: an enhanced faint-end UV luminosity function at z\u227312 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 \u03b1\u22432\/3 accessible to pulsar-timing arrays. These signatures provide near-term opportunities to confirm, refine, or falsify the cyclical QMM chronology.<\/jats:p>","DOI":"10.3390\/e27101043","type":"journal-article","created":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T12:46:56Z","timestamp":1759841216000},"page":"1043","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Counting Cosmic Cycles: Past Big Crunches, Future Recurrence Limits, and the Age of the Quantum Memory Matrix Universe"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2562-1618","authenticated-orcid":false,"given":"Florian","family":"Neukart","sequence":"first","affiliation":[{"name":"Leiden Institute of Advanced Computer Science, Leiden University, Gorlaeus Gebouw-BE-Vleugel, Einsteinweg 55, 2333 Leiden, The Netherlands"},{"name":"Terra Quantum AG, Kornhausstrasse 25, 9000 St. Gallen, Switzerland"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-0228-1296","authenticated-orcid":false,"given":"Eike","family":"Marx","sequence":"additional","affiliation":[{"name":"Terra Quantum AG, Kornhausstrasse 25, 9000 St. Gallen, Switzerland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0977-3515","authenticated-orcid":false,"given":"Valerii","family":"Vinokur","sequence":"additional","affiliation":[{"name":"Terra Quantum AG, Kornhausstrasse 25, 9000 St. Gallen, Switzerland"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,7]]},"reference":[{"key":"ref_1","first-page":"602","article-title":"The Hypothesis of Cores Retarded During Expansion and the Hot Cosmological Model","volume":"10","author":"Novikov","year":"1967","journal-title":"Sov. 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