{"paper":{"title":"Design Principle for Mode-Consistent Galerkin Closure under a Physical Energy Metric for Hyperbolic Systems","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Hirofumi Tomita","submitted_at":"2026-07-07T03:12:16Z","abstract_excerpt":"This paper derives a design principle for Galerkin approximations of energy-conserving hyperbolic systems, following Arakawa's philosophy of structure preservation. The aim is to reproduce, within a resolved finite-mode space, the modal-energy-exchange structure of the continuous system, so that total energy conservation follows as a consequence. We introduce a state-dependent metric H(U) representing the physical energy density and derive the corresponding energy-compatibility identity. In the exact-integration infinite-mode reference model, H-orthogonalization makes the volume operator antis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05781","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/2607.05781/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"}