{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:T24QG7GWREL3RZINVPGFLXIVBA","short_pith_number":"pith:T24QG7GW","canonical_record":{"source":{"id":"2506.11873","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math-ph","submitted_at":"2025-06-13T15:26:02Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a1fc8e088afec8da69d312e6e1ac1ec03f8e68c0fe4a07f0e3591f9dc4b89301","abstract_canon_sha256":"6b657ffe2b55e18a49c79472c02b1e5a0178b82b6eee52f8e5e3130319faa07b"},"schema_version":"1.0"},"canonical_sha256":"9eb9037cd68917b8e50dabcc55dd1508036b62ec0aa8214ef4cd5ec1bd6226ac","source":{"kind":"arxiv","id":"2506.11873","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.11873","created_at":"2026-07-05T11:21:12Z"},{"alias_kind":"arxiv_version","alias_value":"2506.11873v1","created_at":"2026-07-05T11:21:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11873","created_at":"2026-07-05T11:21:12Z"},{"alias_kind":"pith_short_12","alias_value":"T24QG7GWREL3","created_at":"2026-07-05T11:21:12Z"},{"alias_kind":"pith_short_16","alias_value":"T24QG7GWREL3RZIN","created_at":"2026-07-05T11:21:12Z"},{"alias_kind":"pith_short_8","alias_value":"T24QG7GW","created_at":"2026-07-05T11:21:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:T24QG7GWREL3RZINVPGFLXIVBA","target":"record","payload":{"canonical_record":{"source":{"id":"2506.11873","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math-ph","submitted_at":"2025-06-13T15:26:02Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a1fc8e088afec8da69d312e6e1ac1ec03f8e68c0fe4a07f0e3591f9dc4b89301","abstract_canon_sha256":"6b657ffe2b55e18a49c79472c02b1e5a0178b82b6eee52f8e5e3130319faa07b"},"schema_version":"1.0"},"canonical_sha256":"9eb9037cd68917b8e50dabcc55dd1508036b62ec0aa8214ef4cd5ec1bd6226ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:21:12.056188Z","signature_b64":"x8J8bWvWqNhvlFWEH+ix4VjBvN16pGEVBfSGI1I+Vxz9ki003e4Gc5oP5R19VMsYAVUD4XCvdw2qf1/hfy1OAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9eb9037cd68917b8e50dabcc55dd1508036b62ec0aa8214ef4cd5ec1bd6226ac","last_reissued_at":"2026-07-05T11:21:12.055568Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:21:12.055568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.11873","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:21:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G42/tRVMESLuJ55mTevh8YKjfOjtBxLpCHtlH5NUBBH4Dk1SEHFlkr68qPlGFKFD3dLFU9g2UiXdjks5fEqlDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T15:34:04.562361Z"},"content_sha256":"1284e022d5f6739b3fab5a9792ae61e41096c157aee56a6b03b7dfe38157c521","schema_version":"1.0","event_id":"sha256:1284e022d5f6739b3fab5a9792ae61e41096c157aee56a6b03b7dfe38157c521"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:T24QG7GWREL3RZINVPGFLXIVBA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A relation between k-symplectic and k-contact Hamiltonian systems","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"S. Vilari\\~no","submitted_at":"2025-06-13T15:26:02Z","abstract_excerpt":"Systems of partial differential equations which appear in classical field theories can be studied geometrically using different geometrical structures, for example, k-symplectic geometry, k-cosymplectic geometry, multisymplectic geometry, etc. In recent years, there has been a notable increase in the study of k-contact Hamiltonian systems. These are based on the description of the dynamics of field theories using the so-called k-contact manifolds. Such structures are generalizations of contact structures and k-symplectic structures. The relation between k-symplectic manifolds and k-contact man"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11873","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/2506.11873/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:21:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qe1wMzUQO2x5/e5cxkWlwB4J88LvACfUkWVY2pft0bQcS+AY5dXPTNe+qFXKbIpnzCxsvrDcnjNxvcvVq5chCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T15:34:04.563998Z"},"content_sha256":"471f6d32e139a5430ff4b518a8c9d8c8d6661acb0cdf8a788944a4ca2c22dfc7","schema_version":"1.0","event_id":"sha256:471f6d32e139a5430ff4b518a8c9d8c8d6661acb0cdf8a788944a4ca2c22dfc7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T24QG7GWREL3RZINVPGFLXIVBA/bundle.json","state_url":"https://pith.science/pith/T24QG7GWREL3RZINVPGFLXIVBA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T24QG7GWREL3RZINVPGFLXIVBA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-14T15:34:04Z","links":{"resolver":"https://pith.science/pith/T24QG7GWREL3RZINVPGFLXIVBA","bundle":"https://pith.science/pith/T24QG7GWREL3RZINVPGFLXIVBA/bundle.json","state":"https://pith.science/pith/T24QG7GWREL3RZINVPGFLXIVBA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T24QG7GWREL3RZINVPGFLXIVBA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:T24QG7GWREL3RZINVPGFLXIVBA","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":"6b657ffe2b55e18a49c79472c02b1e5a0178b82b6eee52f8e5e3130319faa07b","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math-ph","submitted_at":"2025-06-13T15:26:02Z","title_canon_sha256":"a1fc8e088afec8da69d312e6e1ac1ec03f8e68c0fe4a07f0e3591f9dc4b89301"},"schema_version":"1.0","source":{"id":"2506.11873","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.11873","created_at":"2026-07-05T11:21:12Z"},{"alias_kind":"arxiv_version","alias_value":"2506.11873v1","created_at":"2026-07-05T11:21:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11873","created_at":"2026-07-05T11:21:12Z"},{"alias_kind":"pith_short_12","alias_value":"T24QG7GWREL3","created_at":"2026-07-05T11:21:12Z"},{"alias_kind":"pith_short_16","alias_value":"T24QG7GWREL3RZIN","created_at":"2026-07-05T11:21:12Z"},{"alias_kind":"pith_short_8","alias_value":"T24QG7GW","created_at":"2026-07-05T11:21:12Z"}],"graph_snapshots":[{"event_id":"sha256:471f6d32e139a5430ff4b518a8c9d8c8d6661acb0cdf8a788944a4ca2c22dfc7","target":"graph","created_at":"2026-07-05T11:21:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.11873/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Systems of partial differential equations which appear in classical field theories can be studied geometrically using different geometrical structures, for example, k-symplectic geometry, k-cosymplectic geometry, multisymplectic geometry, etc. In recent years, there has been a notable increase in the study of k-contact Hamiltonian systems. These are based on the description of the dynamics of field theories using the so-called k-contact manifolds. Such structures are generalizations of contact structures and k-symplectic structures. The relation between k-symplectic manifolds and k-contact man","authors_text":"S. Vilari\\~no","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math-ph","submitted_at":"2025-06-13T15:26:02Z","title":"A relation between k-symplectic and k-contact Hamiltonian systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11873","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":"sha256:1284e022d5f6739b3fab5a9792ae61e41096c157aee56a6b03b7dfe38157c521","target":"record","created_at":"2026-07-05T11:21:12Z","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":"6b657ffe2b55e18a49c79472c02b1e5a0178b82b6eee52f8e5e3130319faa07b","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math-ph","submitted_at":"2025-06-13T15:26:02Z","title_canon_sha256":"a1fc8e088afec8da69d312e6e1ac1ec03f8e68c0fe4a07f0e3591f9dc4b89301"},"schema_version":"1.0","source":{"id":"2506.11873","kind":"arxiv","version":1}},"canonical_sha256":"9eb9037cd68917b8e50dabcc55dd1508036b62ec0aa8214ef4cd5ec1bd6226ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9eb9037cd68917b8e50dabcc55dd1508036b62ec0aa8214ef4cd5ec1bd6226ac","first_computed_at":"2026-07-05T11:21:12.055568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:21:12.055568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x8J8bWvWqNhvlFWEH+ix4VjBvN16pGEVBfSGI1I+Vxz9ki003e4Gc5oP5R19VMsYAVUD4XCvdw2qf1/hfy1OAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:21:12.056188Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.11873","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1284e022d5f6739b3fab5a9792ae61e41096c157aee56a6b03b7dfe38157c521","sha256:471f6d32e139a5430ff4b518a8c9d8c8d6661acb0cdf8a788944a4ca2c22dfc7"],"state_sha256":"3cb105e27bf42054dc8d63257a72f0dddb1c91fe2f9f2254de5247c75d62e8ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t/uZMCcTdCJW4T7WEN3LNX5IIOQUH38OleMxHeSq12TlNDHfcw6Y7yo4DKn1/m1Xu/6RE98aIPZwev/5R+2bBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T15:34:04.570600Z","bundle_sha256":"b5214c0825d0c4fb20c23d0f7cc6baf83406347167f5268d4252fb1b1da22593"}}