{"paper":{"title":"Mesh Field Theory: Port-Hamiltonian Formulation of Mesh-Based Physics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Mesh-based physics admits a local factorization into port-Hamiltonian form where mesh topology alone fixes the conservative interconnection.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Satoshi Noguchi, Yoshinobu Kawahara","submitted_at":"2026-05-01T04:35:21Z","abstract_excerpt":"We present Mesh Field Theory (MeshFT) and its neural realization, MeshFT-Net: a structure-preserving framework for mesh-based continuum physics that cleanly separates the physics' topological structure from its metric structure. Imposing minimal physical principles (locality, permutation equivariance, orientation covariance, and energy balance/dissipation inequality), we prove a reduction theorem for mesh-based physics. Under these conditions, the physical dynamics admit a local factorization into a port-Hamiltonian form: the conservative interconnection is fixed uniquely by mesh topology, whe"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove a reduction theorem for mesh-based physics. Under these conditions, the physical dynamics admit a local factorization into a port-Hamiltonian form: the conservative interconnection is fixed uniquely by mesh topology, whereas metric effects enter only through constitutive relations and dissipation.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The minimal physical principles (locality, permutation equivariance, orientation covariance, and energy balance/dissipation inequality) are sufficient to guarantee that the conservative interconnection is fixed uniquely by mesh topology alone.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Mesh Field Theory reduces mesh-based physics to port-Hamiltonian form with topology fixing interconnections and metrics entering only via constitutive relations, enabling MeshFT-Net to achieve near-zero energy drift, correct dispersion, momentum conservation, and strong out-of-distribution fidelity.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Mesh-based physics admits a local factorization into port-Hamiltonian form where mesh topology alone fixes the conservative interconnection.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"56be85443085e370bbc56c5b1b07afab248d313ce29930c72e0aaa97d6eb24fd"},"source":{"id":"2605.00394","kind":"arxiv","version":2},"verdict":{"id":"7a9faa91-4f1d-406d-ba17-e70b006e8443","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T20:18:45.935366Z","strongest_claim":"We prove a reduction theorem for mesh-based physics. Under these conditions, the physical dynamics admit a local factorization into a port-Hamiltonian form: the conservative interconnection is fixed uniquely by mesh topology, whereas metric effects enter only through constitutive relations and dissipation.","one_line_summary":"Mesh Field Theory reduces mesh-based physics to port-Hamiltonian form with topology fixing interconnections and metrics entering only via constitutive relations, enabling MeshFT-Net to achieve near-zero energy drift, correct dispersion, momentum conservation, and strong out-of-distribution fidelity.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The minimal physical principles (locality, permutation equivariance, orientation covariance, and energy balance/dissipation inequality) are sufficient to guarantee that the conservative interconnection is fixed uniquely by mesh topology alone.","pith_extraction_headline":"Mesh-based physics admits a local factorization into port-Hamiltonian form where mesh topology alone fixes the conservative interconnection."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.00394/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T19:43:22.586894Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:12:24.864590Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"c480c8f3a005d68610482da87fafc8e098cd85cc92f95b37d06e151165b4c0c1"},"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"}