{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AC6GAV7EMKQTEA2HQQTH6NBBQG","short_pith_number":"pith:AC6GAV7E","canonical_record":{"source":{"id":"1508.04005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-17T12:53:01Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"87324c126727ec363f9861ba0c676eb76e2a78343cbbdcac4d5d3993e2e8a6d7","abstract_canon_sha256":"455bf0c59da3da533dc5f0a67d9d7453f3bd0e38a90fddea6c5681699fff18a0"},"schema_version":"1.0"},"canonical_sha256":"00bc6057e462a132034784267f342181926977db49edc3936bdf1a8d1ed5379b","source":{"kind":"arxiv","id":"1508.04005","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04005","created_at":"2026-05-18T01:35:13Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04005v1","created_at":"2026-05-18T01:35:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04005","created_at":"2026-05-18T01:35:13Z"},{"alias_kind":"pith_short_12","alias_value":"AC6GAV7EMKQT","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AC6GAV7EMKQTEA2H","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AC6GAV7E","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AC6GAV7EMKQTEA2HQQTH6NBBQG","target":"record","payload":{"canonical_record":{"source":{"id":"1508.04005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-17T12:53:01Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"87324c126727ec363f9861ba0c676eb76e2a78343cbbdcac4d5d3993e2e8a6d7","abstract_canon_sha256":"455bf0c59da3da533dc5f0a67d9d7453f3bd0e38a90fddea6c5681699fff18a0"},"schema_version":"1.0"},"canonical_sha256":"00bc6057e462a132034784267f342181926977db49edc3936bdf1a8d1ed5379b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:13.087881Z","signature_b64":"jEgBZuhOWx/WkllfVIS+3ye6Jmfd8hVgr7b1PNNz8sRGvtrPkNg24MXtu/MFN0L1b2krbPfT0suryhgISxp4Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00bc6057e462a132034784267f342181926977db49edc3936bdf1a8d1ed5379b","last_reissued_at":"2026-05-18T01:35:13.083305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:13.083305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.04005","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":"2026-05-18T01:35:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IJ5oeCIg5IA2m1hVOmIYYiGVKQaLCl7kIX2zWUXgrgF7pa+cZrYr352jAjyB9ahLtY0ybFEVZv8UpRBnVNoABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:05:34.004141Z"},"content_sha256":"4fd0b322cb7e5c2113e4fb8719663cc80c0dc5ae6cbf1c5566b5585ed77cd819","schema_version":"1.0","event_id":"sha256:4fd0b322cb7e5c2113e4fb8719663cc80c0dc5ae6cbf1c5566b5585ed77cd819"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AC6GAV7EMKQTEA2HQQTH6NBBQG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quaternions in Hamiltonian dynamics of a rigid body -- Part II. Relation of canonical Poisson and Lie-Poisson structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Sergiy I. Zub, Stanislav S. Zub","submitted_at":"2015-08-17T12:53:01Z","abstract_excerpt":"It was proposed the Lie group such that symplectic structure of orbits of co-adjoint representation of the group is revealed symplectic structure of a rigid body dynamics in quaternion variables. It is shown that Poisson brackets of corresponding Lie-Poisson structure coincide with canonical Poisson brackets on cotangent bundle of group unit quaternions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04005","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":"2026-05-18T01:35:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IClpTMSkvOx8v4/15CFWW2jEtE7+9CK833wM1MB6nWlpW8pvQJALvW8fGEq3fsKlysy6FCSNzmzoN2oX7ufJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:05:34.004512Z"},"content_sha256":"ed691e943c373ed25e14e1c1253d31ed8982cf475ea89080a87605b476bbde7a","schema_version":"1.0","event_id":"sha256:ed691e943c373ed25e14e1c1253d31ed8982cf475ea89080a87605b476bbde7a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AC6GAV7EMKQTEA2HQQTH6NBBQG/bundle.json","state_url":"https://pith.science/pith/AC6GAV7EMKQTEA2HQQTH6NBBQG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AC6GAV7EMKQTEA2HQQTH6NBBQG/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":"2026-06-22T16:05:34Z","links":{"resolver":"https://pith.science/pith/AC6GAV7EMKQTEA2HQQTH6NBBQG","bundle":"https://pith.science/pith/AC6GAV7EMKQTEA2HQQTH6NBBQG/bundle.json","state":"https://pith.science/pith/AC6GAV7EMKQTEA2HQQTH6NBBQG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AC6GAV7EMKQTEA2HQQTH6NBBQG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AC6GAV7EMKQTEA2HQQTH6NBBQG","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":"455bf0c59da3da533dc5f0a67d9d7453f3bd0e38a90fddea6c5681699fff18a0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-17T12:53:01Z","title_canon_sha256":"87324c126727ec363f9861ba0c676eb76e2a78343cbbdcac4d5d3993e2e8a6d7"},"schema_version":"1.0","source":{"id":"1508.04005","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04005","created_at":"2026-05-18T01:35:13Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04005v1","created_at":"2026-05-18T01:35:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04005","created_at":"2026-05-18T01:35:13Z"},{"alias_kind":"pith_short_12","alias_value":"AC6GAV7EMKQT","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AC6GAV7EMKQTEA2H","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AC6GAV7E","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:ed691e943c373ed25e14e1c1253d31ed8982cf475ea89080a87605b476bbde7a","target":"graph","created_at":"2026-05-18T01:35:13Z","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":"It was proposed the Lie group such that symplectic structure of orbits of co-adjoint representation of the group is revealed symplectic structure of a rigid body dynamics in quaternion variables. It is shown that Poisson brackets of corresponding Lie-Poisson structure coincide with canonical Poisson brackets on cotangent bundle of group unit quaternions.","authors_text":"Sergiy I. Zub, Stanislav S. Zub","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-17T12:53:01Z","title":"Quaternions in Hamiltonian dynamics of a rigid body -- Part II. Relation of canonical Poisson and Lie-Poisson structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04005","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":"sha256:4fd0b322cb7e5c2113e4fb8719663cc80c0dc5ae6cbf1c5566b5585ed77cd819","target":"record","created_at":"2026-05-18T01:35:13Z","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":"455bf0c59da3da533dc5f0a67d9d7453f3bd0e38a90fddea6c5681699fff18a0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-17T12:53:01Z","title_canon_sha256":"87324c126727ec363f9861ba0c676eb76e2a78343cbbdcac4d5d3993e2e8a6d7"},"schema_version":"1.0","source":{"id":"1508.04005","kind":"arxiv","version":1}},"canonical_sha256":"00bc6057e462a132034784267f342181926977db49edc3936bdf1a8d1ed5379b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00bc6057e462a132034784267f342181926977db49edc3936bdf1a8d1ed5379b","first_computed_at":"2026-05-18T01:35:13.083305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:13.083305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jEgBZuhOWx/WkllfVIS+3ye6Jmfd8hVgr7b1PNNz8sRGvtrPkNg24MXtu/MFN0L1b2krbPfT0suryhgISxp4Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:13.087881Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.04005","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fd0b322cb7e5c2113e4fb8719663cc80c0dc5ae6cbf1c5566b5585ed77cd819","sha256:ed691e943c373ed25e14e1c1253d31ed8982cf475ea89080a87605b476bbde7a"],"state_sha256":"6d6c16840ef6cb2a9c6c39f9d60589eaa92d87d0e3dc23fbcb606b19a03f4ea4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EQDQv57Zb32Hvpmjksrn0zvimu7fnwjvNuI/Juw/4+gaZmXSkZDOhQU8EIUh8sCaX2mAbHmme/wNQlj4FAIfDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:05:34.006402Z","bundle_sha256":"c125fe78f4689498b540a2acf64db6f77bffca6cb7b1284548a18bae0d45ecb2"}}