{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:C327PEMEPKGYYGAR6QE7KCFNEC","short_pith_number":"pith:C327PEME","canonical_record":{"source":{"id":"1612.06224","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-19T15:25:23Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"e961486aed015b2bc921124e55343f19eb0c3bdc80785604341383d9df2ddff0","abstract_canon_sha256":"fca3f60fd6ce0d5539af9c0bc3dccf965da7f4f2b4d8236d4fb5cbed3d086a37"},"schema_version":"1.0"},"canonical_sha256":"16f5f791847a8d8c1811f409f508ad208bb021f67c69457840ccddfd6284c31a","source":{"kind":"arxiv","id":"1612.06224","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06224","created_at":"2026-05-18T00:41:38Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06224v1","created_at":"2026-05-18T00:41:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06224","created_at":"2026-05-18T00:41:38Z"},{"alias_kind":"pith_short_12","alias_value":"C327PEMEPKGY","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C327PEMEPKGYYGAR","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C327PEME","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:C327PEMEPKGYYGAR6QE7KCFNEC","target":"record","payload":{"canonical_record":{"source":{"id":"1612.06224","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-19T15:25:23Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"e961486aed015b2bc921124e55343f19eb0c3bdc80785604341383d9df2ddff0","abstract_canon_sha256":"fca3f60fd6ce0d5539af9c0bc3dccf965da7f4f2b4d8236d4fb5cbed3d086a37"},"schema_version":"1.0"},"canonical_sha256":"16f5f791847a8d8c1811f409f508ad208bb021f67c69457840ccddfd6284c31a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:38.013488Z","signature_b64":"cSPB7E7VL8hpg/CZKgr2RZb1A1BW/wM4X40kMjS2mTBAmqexxdtBHv1mtQeXBaSFrSsK1228pAqgJ8gMm2V6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16f5f791847a8d8c1811f409f508ad208bb021f67c69457840ccddfd6284c31a","last_reissued_at":"2026-05-18T00:41:38.012895Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:38.012895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.06224","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":"2026-05-18T00:41:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"33x+L4ek8L7J2fIwZIyr/O1WKQBP42ZRJBPNTivBg+uqFMJgnAZQJeVA0WbOn1UdF0dfTE2ZA83iw/7zJsBMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:12:08.294507Z"},"content_sha256":"f3bcd22ac49852a18169264653137c564294274f4d261f6ea2fcef726fc3b1ba","schema_version":"1.0","event_id":"sha256:f3bcd22ac49852a18169264653137c564294274f4d261f6ea2fcef726fc3b1ba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:C327PEMEPKGYYGAR6QE7KCFNEC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cosymplectic and contact structures to resolve time-dependent and dissipative hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"C. Sard\\'on, M. De Le\\'On","submitted_at":"2016-12-19T15:25:23Z","abstract_excerpt":"In this paper, we apply the geometric Hamilton--Jacobi theory to obtain solutions of classical hamiltonian systems that are either compatible with a cosymplectic or a contact structure. As it is well known, the first structure plays a central role in the theory of time-dependent hamiltonians, whilst the second is here used to treat classical hamiltonians including dissipation terms.\n  The interest of a geometric Hamilton--Jacobi equation is the primordial observation that if a hamiltonian vector field $X_{H}$ can be projected into a configuration manifold by means of a 1-form $dW$, then the in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06224","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":""},"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":"2026-05-18T00:41:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D3LFeyx5ldr5hAOPh6pKObKGIAj8uEvqMda+UCqADQjyAzMEsCrpeTCerXyicmm0kzi5sNT80x8fOz4Ai/y0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:12:08.295140Z"},"content_sha256":"71205ef833c57c6ee1b2406adcdd4169f430fa9a02e4643530c6509541cac044","schema_version":"1.0","event_id":"sha256:71205ef833c57c6ee1b2406adcdd4169f430fa9a02e4643530c6509541cac044"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C327PEMEPKGYYGAR6QE7KCFNEC/bundle.json","state_url":"https://pith.science/pith/C327PEMEPKGYYGAR6QE7KCFNEC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C327PEMEPKGYYGAR6QE7KCFNEC/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":"2026-05-28T02:12:08Z","links":{"resolver":"https://pith.science/pith/C327PEMEPKGYYGAR6QE7KCFNEC","bundle":"https://pith.science/pith/C327PEMEPKGYYGAR6QE7KCFNEC/bundle.json","state":"https://pith.science/pith/C327PEMEPKGYYGAR6QE7KCFNEC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C327PEMEPKGYYGAR6QE7KCFNEC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C327PEMEPKGYYGAR6QE7KCFNEC","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":"fca3f60fd6ce0d5539af9c0bc3dccf965da7f4f2b4d8236d4fb5cbed3d086a37","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-19T15:25:23Z","title_canon_sha256":"e961486aed015b2bc921124e55343f19eb0c3bdc80785604341383d9df2ddff0"},"schema_version":"1.0","source":{"id":"1612.06224","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06224","created_at":"2026-05-18T00:41:38Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06224v1","created_at":"2026-05-18T00:41:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06224","created_at":"2026-05-18T00:41:38Z"},{"alias_kind":"pith_short_12","alias_value":"C327PEMEPKGY","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C327PEMEPKGYYGAR","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C327PEME","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:71205ef833c57c6ee1b2406adcdd4169f430fa9a02e4643530c6509541cac044","target":"graph","created_at":"2026-05-18T00:41:38Z","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":"In this paper, we apply the geometric Hamilton--Jacobi theory to obtain solutions of classical hamiltonian systems that are either compatible with a cosymplectic or a contact structure. As it is well known, the first structure plays a central role in the theory of time-dependent hamiltonians, whilst the second is here used to treat classical hamiltonians including dissipation terms.\n  The interest of a geometric Hamilton--Jacobi equation is the primordial observation that if a hamiltonian vector field $X_{H}$ can be projected into a configuration manifold by means of a 1-form $dW$, then the in","authors_text":"C. Sard\\'on, M. De Le\\'On","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-19T15:25:23Z","title":"Cosymplectic and contact structures to resolve time-dependent and dissipative hamiltonian systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06224","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:f3bcd22ac49852a18169264653137c564294274f4d261f6ea2fcef726fc3b1ba","target":"record","created_at":"2026-05-18T00:41:38Z","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":"fca3f60fd6ce0d5539af9c0bc3dccf965da7f4f2b4d8236d4fb5cbed3d086a37","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-19T15:25:23Z","title_canon_sha256":"e961486aed015b2bc921124e55343f19eb0c3bdc80785604341383d9df2ddff0"},"schema_version":"1.0","source":{"id":"1612.06224","kind":"arxiv","version":1}},"canonical_sha256":"16f5f791847a8d8c1811f409f508ad208bb021f67c69457840ccddfd6284c31a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16f5f791847a8d8c1811f409f508ad208bb021f67c69457840ccddfd6284c31a","first_computed_at":"2026-05-18T00:41:38.012895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:38.012895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cSPB7E7VL8hpg/CZKgr2RZb1A1BW/wM4X40kMjS2mTBAmqexxdtBHv1mtQeXBaSFrSsK1228pAqgJ8gMm2V6AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:38.013488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06224","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3bcd22ac49852a18169264653137c564294274f4d261f6ea2fcef726fc3b1ba","sha256:71205ef833c57c6ee1b2406adcdd4169f430fa9a02e4643530c6509541cac044"],"state_sha256":"9b92f03a0a5e5828055e5cf5f36e55a904d0e9512e077b85cca99af70ea28487"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JvUWDH46a5H89mRKPyHW7cNUIuqAxEsmV6e4dzf3Bvc3GEMdEeUHwREmfzFEy86GLvw2UvwwCZ23xzqB25J/DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:12:08.298511Z","bundle_sha256":"5dd4b1a11ae1ea4c4a8c71014fea5a3dbd55143bf48a057aaed8262510e6e1af"}}