{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T17:05:50Z","timestamp":1779210350962,"version":"3.51.4"},"reference-count":38,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T00:00:00Z","timestamp":1778457600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We propose a microphysical completion for the scalar sector of dilatonic gravity by identifying the dilaton with the coarse-grained stiffness mode of a constrained complex tension field defined on a discrete relational network. Under a controlled ordered-regime coarse-graining, the real projection of the tension scales as \u03a6(\u0398)=\u03a60cos\u0398, so the Planck mass varies with the phase angle \u0398 and the Einstein-frame canonical scalar becomes \u03c6\u221dln[\u03a6(\u0398)\/\u03a60]. This logarithmic structure emerges naturally from the Weyl map and provides the correct canonical variable for vacuum models inspired by the Logarithmic Schr\u00f6dinger Equation (LogSE). We outline how this scalar\u2013tensor interface can satisfy Solar-System constraints through environmental locking and discuss avenues for laboratory and astrophysical tests based on stiffness\u2013coherence coupling. This paper does not introduce a new scalar\u2013tensor EFT class as such; rather, it provides a controlled microphysical origin for a specific scalar stiffness law, \u03a6(\u0398)\u221dcos\u0398, and for the resulting logarithmic Einstein-frame canonical structure.<\/jats:p>","DOI":"10.3390\/e28050544","type":"journal-article","created":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T16:07:26Z","timestamp":1779206846000},"page":"544","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Complex Tension Origin for Dilaton Gravity: Jordan Stiffness and Logarithmic Einstein Dynamics"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5939-3708","authenticated-orcid":false,"given":"Micha\u00ebl","family":"Vaillant","sequence":"first","affiliation":[{"name":"Meta-Connexions, 234 Route de Seysses, 31100 Toulouse, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0228-1673","authenticated-orcid":false,"given":"Tony C.","family":"Scott","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Physikalische Chemie, RWTH Aachen University, 52056 Aachen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1103\/PhysRev.124.925","article-title":"Mach\u2019s Principle and a Relativistic Theory of Gravitation","volume":"124","author":"Brans","year":"1961","journal-title":"Phys. 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