{"paper":{"title":"On the adiabatic invariance of the action of a trapped wave","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"The adiabatic invariant of a trapped wave equals the ratio of its total energy to its frequency.","cross_cats":["math.MP","physics.class-ph"],"primary_cat":"math-ph","authors_text":"Ekaterina V. Shishkina, Serge N. Gavrilov","submitted_at":"2026-02-21T12:19:46Z","abstract_excerpt":"Recently, it has been shown (Gavrilov et al., Nonlinear Dyn, 112, 2024) that in a linear solid discrete-continuous system with several slowly time-varying parameters, the amplitude of a strongly localized mode (a trapped wave) can be calculated as a function of current parameter values and does not depend on the history of the parameter change. This result allows us to introduce the adiabatic invariant for such a system according to the general definition as a quantity that remains approximately constant if the parameters vary slowly. In this paper, we show that, defined in this manner, the ad"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"defined in this manner, the adiabatic invariant can be calculated as the ratio of the total energy of the trapped wave to its frequency","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The total energy of the trapped wave is well-defined and unambiguous in the linear discrete-continuous system, despite the paper noting potential ambiguity in its definition; the prior 2024 result on history-independent amplitude is taken as given.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The adiabatic invariant of a trapped wave is its total energy divided by frequency, generalizing the Hamiltonian case to discrete-continuous systems.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The adiabatic invariant of a trapped wave equals the ratio of its total energy to its frequency.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1bcb0d83fa41d0e9345b7b199c01f66a8d64592bbee7e1fc2b7239bf4648dee5"},"source":{"id":"2602.18815","kind":"arxiv","version":4},"verdict":{"id":"e799b76c-b357-4fe4-9c98-bb75bf3ea80d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T20:35:43.238175Z","strongest_claim":"defined in this manner, the adiabatic invariant can be calculated as the ratio of the total energy of the trapped wave to its frequency","one_line_summary":"The adiabatic invariant of a trapped wave is its total energy divided by frequency, generalizing the Hamiltonian case to discrete-continuous systems.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The total energy of the trapped wave is well-defined and unambiguous in the linear discrete-continuous system, despite the paper noting potential ambiguity in its definition; the prior 2024 result on history-independent amplitude is taken as given.","pith_extraction_headline":"The adiabatic invariant of a trapped wave equals the ratio of its total energy to its frequency."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.18815/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":2,"snapshot_sha256":"8e48c70f5c491b38e78f27a333fd090dbd04400681e66679240aed4d42a50336"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}