{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6VYF6JFY4SATOKWZSL3SUX43HP","short_pith_number":"pith:6VYF6JFY","schema_version":"1.0","canonical_sha256":"f5705f24b8e481372ad992f72a5f9b3bc25956d1dfa07f0e6d23fca5c346bfc3","source":{"kind":"arxiv","id":"1706.06156","version":2},"attestation_state":"computed","paper":{"title":"Weak Form of Stokes-Dirac Structures and Geometric Discretization of Port-Hamiltonian Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.NA"],"primary_cat":"math.DS","authors_text":"Bernhard Maschke, Laurent Lef\\`evre, Paul Kotyczka","submitted_at":"2017-06-19T20:08:25Z","abstract_excerpt":"We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac structure by a finite-dimensional Dirac structure is realized using a mixed Galerkin approach and power-preserving linear maps, which define minimal discrete "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1706.06156","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-19T20:08:25Z","cross_cats_sorted":["cs.SY","math.NA"],"title_canon_sha256":"6350631646bbd300584219fb6523af0759127365d5786868c44465c6a1df0a6a","abstract_canon_sha256":"5581999265a8990ab09286ea8f4a8902742a4cad0538713dcb6787f07382e125"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:16.160876Z","signature_b64":"U2NvGodvGpk3RvJVAwFMjXz6ITGgi2/I7BKd/ZRDRggAR3mgeHWAdg2am/ssUM0QNsK/K0GBki2Fk8EmqE8cBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5705f24b8e481372ad992f72a5f9b3bc25956d1dfa07f0e6d23fca5c346bfc3","last_reissued_at":"2026-05-18T00:22:16.160261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:16.160261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak Form of Stokes-Dirac Structures and Geometric Discretization of Port-Hamiltonian Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.NA"],"primary_cat":"math.DS","authors_text":"Bernhard Maschke, Laurent Lef\\`evre, Paul Kotyczka","submitted_at":"2017-06-19T20:08:25Z","abstract_excerpt":"We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac structure by a finite-dimensional Dirac structure is realized using a mixed Galerkin approach and power-preserving linear maps, which define minimal discrete "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06156","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1706.06156","created_at":"2026-05-18T00:22:16.160341+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.06156v2","created_at":"2026-05-18T00:22:16.160341+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06156","created_at":"2026-05-18T00:22:16.160341+00:00"},{"alias_kind":"pith_short_12","alias_value":"6VYF6JFY4SAT","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6VYF6JFY4SATOKWZ","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6VYF6JFY","created_at":"2026-05-18T12:31:03.183658+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6VYF6JFY4SATOKWZSL3SUX43HP","json":"https://pith.science/pith/6VYF6JFY4SATOKWZSL3SUX43HP.json","graph_json":"https://pith.science/api/pith-number/6VYF6JFY4SATOKWZSL3SUX43HP/graph.json","events_json":"https://pith.science/api/pith-number/6VYF6JFY4SATOKWZSL3SUX43HP/events.json","paper":"https://pith.science/paper/6VYF6JFY"},"agent_actions":{"view_html":"https://pith.science/pith/6VYF6JFY4SATOKWZSL3SUX43HP","download_json":"https://pith.science/pith/6VYF6JFY4SATOKWZSL3SUX43HP.json","view_paper":"https://pith.science/paper/6VYF6JFY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.06156&json=true","fetch_graph":"https://pith.science/api/pith-number/6VYF6JFY4SATOKWZSL3SUX43HP/graph.json","fetch_events":"https://pith.science/api/pith-number/6VYF6JFY4SATOKWZSL3SUX43HP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6VYF6JFY4SATOKWZSL3SUX43HP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6VYF6JFY4SATOKWZSL3SUX43HP/action/storage_attestation","attest_author":"https://pith.science/pith/6VYF6JFY4SATOKWZSL3SUX43HP/action/author_attestation","sign_citation":"https://pith.science/pith/6VYF6JFY4SATOKWZSL3SUX43HP/action/citation_signature","submit_replication":"https://pith.science/pith/6VYF6JFY4SATOKWZSL3SUX43HP/action/replication_record"}},"created_at":"2026-05-18T00:22:16.160341+00:00","updated_at":"2026-05-18T00:22:16.160341+00:00"}