{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LYLYYEPJNOQS6ZC5XVOCA6A7TV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"004c672eb2cb0ee4b35a8df8abdca41ddbb2d8bb5b9de5d4bd59ed61d5ff4146","cross_cats_sorted":["math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-12T08:26:11Z","title_canon_sha256":"22dcef8213fc24bf3cf189abf65c4c61c4d94649da5dca0a08817a7e0f62a202"},"schema_version":"1.0","source":{"id":"1306.2744","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2744","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2744v2","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2744","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"pith_short_12","alias_value":"LYLYYEPJNOQS","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LYLYYEPJNOQS6ZC5","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LYLYYEPJ","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:ea872cbfb0690c0059cd3874603fde64489c58ac61a6897c83937a13f466e1c5","target":"graph","created_at":"2026-05-18T03:01:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We propose a geometric approach to dynamical equations of physics, based on the idea of the Tulczyjew triple. We show the evolution of these concepts, starting with the roots lying in the variational calculus for statics, through Lagrangian and Hamiltonian mechanics, and concluding with Tulczyjew triples for classical field theories, illustrated with a numer of important examples.","authors_text":"Janusz Grabowski, Katarzyna Grabowska","cross_cats":["math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-12T08:26:11Z","title":"Tulczyjew triples: from statics to field theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2744","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:83a38e16dc9752d35e3c56eccd850051d04d94f105f2954809a110210379c525","target":"record","created_at":"2026-05-18T03:01:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"004c672eb2cb0ee4b35a8df8abdca41ddbb2d8bb5b9de5d4bd59ed61d5ff4146","cross_cats_sorted":["math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-12T08:26:11Z","title_canon_sha256":"22dcef8213fc24bf3cf189abf65c4c61c4d94649da5dca0a08817a7e0f62a202"},"schema_version":"1.0","source":{"id":"1306.2744","kind":"arxiv","version":2}},"canonical_sha256":"5e178c11e96ba12f645dbd5c20781f9d6834a355f24462c3206798fec1510ca1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e178c11e96ba12f645dbd5c20781f9d6834a355f24462c3206798fec1510ca1","first_computed_at":"2026-05-18T03:01:46.436142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:46.436142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gmxn8W9JAwtfhQSKj4IIIh0ZggN9yi3Me7mN0qeOZb4bH/ODl7jamaBMyhx7OAOkhjJ+Y0uwBCGu0Zn3mG4uCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:46.436720Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.2744","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83a38e16dc9752d35e3c56eccd850051d04d94f105f2954809a110210379c525","sha256:ea872cbfb0690c0059cd3874603fde64489c58ac61a6897c83937a13f466e1c5"],"state_sha256":"3f7ca172423f1e475975f6501abdbcacf128a8b7b49a8c7839eb25ee7c05cea7"}