{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MYZTUJK4SFGJIUS6KZ6KXU4RO6","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":"514d8ee45ccac8e6bd4e261bab64a94f9617a8c24a088ace3df8792860c20b92","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-09-19T11:20:46Z","title_canon_sha256":"5b2ba3cd3f76e8c77c13dbb627645cc1cc5cd8f37523cc030bb74cc00515201e"},"schema_version":"1.0","source":{"id":"1409.5604","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5604","created_at":"2026-05-18T02:42:26Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5604v1","created_at":"2026-05-18T02:42:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5604","created_at":"2026-05-18T02:42:26Z"},{"alias_kind":"pith_short_12","alias_value":"MYZTUJK4SFGJ","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MYZTUJK4SFGJIUS6","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MYZTUJK4","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:266920a98e503b3fb62533319f524694979790a9b069fd23cab31f33e598aa3b","target":"graph","created_at":"2026-05-18T02:42:26Z","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":"This book is devoted to review two of the most relevant approaches to the study of classical field theories of first order, say k-symplectic and k-cosymplectic. In the last part, we relate the k-symplectic and k-cosymplectic manifolds with the multisymplectic theory.","authors_text":"M. De Le\\'On, M. Salgado, S. Vilari\\~no","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-09-19T11:20:46Z","title":"Methods of Differential Geometry in Classical Field Theories: k-symplectic and k-cosymplectic approaches"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5604","kind":"arxiv","version":1},"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:ff55e6f3bc043bbaed044a2c207eeb3ddc99c545ea6722a0d80807d4d81494a6","target":"record","created_at":"2026-05-18T02:42:26Z","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":"514d8ee45ccac8e6bd4e261bab64a94f9617a8c24a088ace3df8792860c20b92","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-09-19T11:20:46Z","title_canon_sha256":"5b2ba3cd3f76e8c77c13dbb627645cc1cc5cd8f37523cc030bb74cc00515201e"},"schema_version":"1.0","source":{"id":"1409.5604","kind":"arxiv","version":1}},"canonical_sha256":"66333a255c914c94525e567cabd391778efab34d514368d2008a405ec76d1ddf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66333a255c914c94525e567cabd391778efab34d514368d2008a405ec76d1ddf","first_computed_at":"2026-05-18T02:42:26.855667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:26.855667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rJGVCci02XVensX2Ox50dUvXlWgYHQkjHrOdACJquwLucsmf7lPCGQGmR6iVWmKYmUbdIIyEJGGvQ/5rD2MXAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:26.856508Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5604","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff55e6f3bc043bbaed044a2c207eeb3ddc99c545ea6722a0d80807d4d81494a6","sha256:266920a98e503b3fb62533319f524694979790a9b069fd23cab31f33e598aa3b"],"state_sha256":"26e9625ed0737a64d809115d684bae8be7c61951f9376f4b0e5860fa813ddde9"}