{"paper":{"title":"Absence of hidden analytic conserved quantities in harmonically confined rods","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.CD"],"primary_cat":"cond-mat.stat-mech","authors_text":"Abhishek Dhar, Sahil Kumar Singh, Sanjay Moudgalya","submitted_at":"2026-07-21T09:04:28Z","abstract_excerpt":"Systems of hard rods of equal length in a one-dimensional harmonic trap have been observed to exhibit peculiar non-ergodic behavior that might suggest the existence of a novel hidden conserved quantity beyond the two well known ones, i.e., the total energy and the center-of-mass energy. In this work, we investigate this possibility by systematically constraining the forms of the conserved quantities, and we rigorously rule out the existence of any extra hidden conserved quantity that is analytic in the positions and momenta of the rods involved. We do so by showing two key results: conservatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18872","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.18872/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}