{"paper":{"title":"Unified presentation of four fundamental inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.pop-ph","authors_text":"Fran\\c{c}ois Graner, Joseph Lajzerowicz, Roland Lehoucq","submitted_at":"2017-12-10T07:25:09Z","abstract_excerpt":"We suggest an unified presentation to teach fundamental constants to graduate students, by introducing four lower limits to observed phenomena. The reduced Planck constant $\\hbar$ is the lowest classically definable action. The inverse of invariant speed, $s$, is the lowest observable slowness. The Planck time, $t_{\\rm P}$, is the lowest observable time scale. The Boltzmann constant, $k$, determines the lowest coherent degree of freedom; we recall a Einstein criterion on the fluctuations of small thermal systems and show that it has far-reaching implications, such as demonstrating the relation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10464","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}