{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SRLI32QKGTC33R7E72RPYUXMQT","short_pith_number":"pith:SRLI32QK","canonical_record":{"source":{"id":"1606.06308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-20T20:05:13Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"1e6a14977b8ef8d5b3f84e81debe487129a9d77acf80c2a449f0fb431b20b779","abstract_canon_sha256":"d78a6f6c375d2d75319ee33eeead1bd47bddd5d169134b3a158ecb7effcd17d4"},"schema_version":"1.0"},"canonical_sha256":"94568dea0a34c5bdc7e4fea2fc52ec84fb9832f8bb7179b894555573494320b3","source":{"kind":"arxiv","id":"1606.06308","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06308","created_at":"2026-05-18T01:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06308v1","created_at":"2026-05-18T01:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06308","created_at":"2026-05-18T01:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"SRLI32QKGTC3","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SRLI32QKGTC33R7E","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SRLI32QK","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SRLI32QKGTC33R7E72RPYUXMQT","target":"record","payload":{"canonical_record":{"source":{"id":"1606.06308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-20T20:05:13Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"1e6a14977b8ef8d5b3f84e81debe487129a9d77acf80c2a449f0fb431b20b779","abstract_canon_sha256":"d78a6f6c375d2d75319ee33eeead1bd47bddd5d169134b3a158ecb7effcd17d4"},"schema_version":"1.0"},"canonical_sha256":"94568dea0a34c5bdc7e4fea2fc52ec84fb9832f8bb7179b894555573494320b3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:11.257532Z","signature_b64":"i0hbxW/ZIGaelfCaDo20es6oudZ1KjsAMYi0jRy9/lDheE0BMsTuVAkAyAh1Y26vkR8oxDMG+iPt7K9c9XHIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94568dea0a34c5bdc7e4fea2fc52ec84fb9832f8bb7179b894555573494320b3","last_reissued_at":"2026-05-18T01:12:11.257122Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:11.257122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.06308","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":"2026-05-18T01:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7lYwbbjfNhbVnQ6Peu8BTaZcyCdcFzxhaueRoysUTQc4JaL+h/vPocpCN2TqOgjpIDDPEWuONCPL8ZAN/hXKBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:52:18.070270Z"},"content_sha256":"de42d533c0d94050c8914ce9045a3f39572d6e5f41c0cf85ab11aea748228a76","schema_version":"1.0","event_id":"sha256:de42d533c0d94050c8914ce9045a3f39572d6e5f41c0cf85ab11aea748228a76"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SRLI32QKGTC33R7E72RPYUXMQT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noise and dissipation in rigid body motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"math.DS","authors_text":"Alexis Arnaudon, Alex L. De Castro, Darryl D. Holm","submitted_at":"2016-06-20T20:05:13Z","abstract_excerpt":"Using the rigid body as an example, we illustrate some features of stochastic geometric mechanics. These features include: i) a geometric variational motivation for the noise structure involving Lie-Poisson brackets and momentum maps, ii) stochastic coadjoint motion with double bracket dissipation, iii) the Lie-Poisson Fokker-Planck description and its stationary solutions, iv) random dynamical systems, random attractors and SRB measures connected to statistical physics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06308","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":"2026-05-18T01:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"82Eul4mJUtbghTrr8vhmr+Unylgi3MC+4DBdhsVlhqOKy9HpxESTRse83zP5sb02xcJpe+W3vRD73Z4pi29pCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:52:18.070631Z"},"content_sha256":"6527ff989f89b7ce92a275a9b3742099b3aa74b7b9702a7840d1ef86b0fb5763","schema_version":"1.0","event_id":"sha256:6527ff989f89b7ce92a275a9b3742099b3aa74b7b9702a7840d1ef86b0fb5763"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SRLI32QKGTC33R7E72RPYUXMQT/bundle.json","state_url":"https://pith.science/pith/SRLI32QKGTC33R7E72RPYUXMQT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SRLI32QKGTC33R7E72RPYUXMQT/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":"2026-06-05T09:52:18Z","links":{"resolver":"https://pith.science/pith/SRLI32QKGTC33R7E72RPYUXMQT","bundle":"https://pith.science/pith/SRLI32QKGTC33R7E72RPYUXMQT/bundle.json","state":"https://pith.science/pith/SRLI32QKGTC33R7E72RPYUXMQT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SRLI32QKGTC33R7E72RPYUXMQT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SRLI32QKGTC33R7E72RPYUXMQT","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":"d78a6f6c375d2d75319ee33eeead1bd47bddd5d169134b3a158ecb7effcd17d4","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-20T20:05:13Z","title_canon_sha256":"1e6a14977b8ef8d5b3f84e81debe487129a9d77acf80c2a449f0fb431b20b779"},"schema_version":"1.0","source":{"id":"1606.06308","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06308","created_at":"2026-05-18T01:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06308v1","created_at":"2026-05-18T01:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06308","created_at":"2026-05-18T01:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"SRLI32QKGTC3","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SRLI32QKGTC33R7E","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SRLI32QK","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:6527ff989f89b7ce92a275a9b3742099b3aa74b7b9702a7840d1ef86b0fb5763","target":"graph","created_at":"2026-05-18T01:12:11Z","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":"Using the rigid body as an example, we illustrate some features of stochastic geometric mechanics. These features include: i) a geometric variational motivation for the noise structure involving Lie-Poisson brackets and momentum maps, ii) stochastic coadjoint motion with double bracket dissipation, iii) the Lie-Poisson Fokker-Planck description and its stationary solutions, iv) random dynamical systems, random attractors and SRB measures connected to statistical physics.","authors_text":"Alexis Arnaudon, Alex L. De Castro, Darryl D. Holm","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-20T20:05:13Z","title":"Noise and dissipation in rigid body motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06308","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:de42d533c0d94050c8914ce9045a3f39572d6e5f41c0cf85ab11aea748228a76","target":"record","created_at":"2026-05-18T01:12:11Z","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":"d78a6f6c375d2d75319ee33eeead1bd47bddd5d169134b3a158ecb7effcd17d4","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-20T20:05:13Z","title_canon_sha256":"1e6a14977b8ef8d5b3f84e81debe487129a9d77acf80c2a449f0fb431b20b779"},"schema_version":"1.0","source":{"id":"1606.06308","kind":"arxiv","version":1}},"canonical_sha256":"94568dea0a34c5bdc7e4fea2fc52ec84fb9832f8bb7179b894555573494320b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94568dea0a34c5bdc7e4fea2fc52ec84fb9832f8bb7179b894555573494320b3","first_computed_at":"2026-05-18T01:12:11.257122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:11.257122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i0hbxW/ZIGaelfCaDo20es6oudZ1KjsAMYi0jRy9/lDheE0BMsTuVAkAyAh1Y26vkR8oxDMG+iPt7K9c9XHIDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:11.257532Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.06308","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de42d533c0d94050c8914ce9045a3f39572d6e5f41c0cf85ab11aea748228a76","sha256:6527ff989f89b7ce92a275a9b3742099b3aa74b7b9702a7840d1ef86b0fb5763"],"state_sha256":"d7abcc3fa3026cdbcc1a7a9756dffdfc99d64e7cd0526d8e321a57f281e48b52"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uHIdOEFo7d1YsxBy6vGxD0fymGj1dhS7LfLhHvGBd1hZ9CQCiWW2+HyIxTv+bTT9/69fmeTRD9gF+sOP0CruAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:52:18.072547Z","bundle_sha256":"5f33a326f79a312e18014927bd926d175bc8abacf839e32132963c501cddd0a9"}}