{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KKO45OLNAMLWBZ65AZMJZ46IZA","short_pith_number":"pith:KKO45OLN","canonical_record":{"source":{"id":"1108.2951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-08-15T07:59:14Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6c234ced5ae212130b58adec70a55d9c8269b7baccd5a2a662eea703f63fd0e7","abstract_canon_sha256":"33a63a29b9d2251001acc22be67fd2a0127bec9dc144f2efb062c9eb0b293698"},"schema_version":"1.0"},"canonical_sha256":"529dceb96d031760e7dd06589cf3c8c801be1ef4684d805fdee6909c6343827a","source":{"kind":"arxiv","id":"1108.2951","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2951","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2951v1","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2951","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"KKO45OLNAMLW","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KKO45OLNAMLWBZ65","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KKO45OLN","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KKO45OLNAMLWBZ65AZMJZ46IZA","target":"record","payload":{"canonical_record":{"source":{"id":"1108.2951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-08-15T07:59:14Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6c234ced5ae212130b58adec70a55d9c8269b7baccd5a2a662eea703f63fd0e7","abstract_canon_sha256":"33a63a29b9d2251001acc22be67fd2a0127bec9dc144f2efb062c9eb0b293698"},"schema_version":"1.0"},"canonical_sha256":"529dceb96d031760e7dd06589cf3c8c801be1ef4684d805fdee6909c6343827a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:47.452029Z","signature_b64":"Yu3AddIxkiy8w3hr/L/w20U6DuoPG6LuOlAV8RV4smTYRNbJemELB1wE1FWa/xyiCMUeoKkrNH8kijq46ZRFDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"529dceb96d031760e7dd06589cf3c8c801be1ef4684d805fdee6909c6343827a","last_reissued_at":"2026-05-18T02:54:47.451581Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:47.451581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.2951","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":"2026-05-18T02:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sTqkSCWYudywTfnL5QZEVt52562B2R2W2G4yMIBgQy1+55WCefc8GVVUjmKdPFNkmpM/S8jdbMlnOqziC2WXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:13:27.721152Z"},"content_sha256":"bf296b65afe223082ca4245538a8cfc655d4020b2800f8ffccfad460718ed7ed","schema_version":"1.0","event_id":"sha256:bf296b65afe223082ca4245538a8cfc655d4020b2800f8ffccfad460718ed7ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KKO45OLNAMLWBZ65AZMJZ46IZA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jian-Guo Liu, Pierre Degond (IMT)","submitted_at":"2011-08-15T07:59:14Z","abstract_excerpt":"We consider a kinetic model of self-propelled particles with alignment interaction and with precession about the alignment direction. We derive a hydrodynamic system for the local density and velocity orientation of the particles. The system consists of the conservative equation for the local density and a non-conservative equation for the orientation. First, we assume that the alignment interaction is purely local and derive a first order system. However, we show that this system may lose its hyperbolicity. Under the assumption of weakly non-local interaction, we derive diffusive corrections "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2951","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":"2026-05-18T02:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LL/4hwetAcKQxYGu7fKcZDrVKKBUym8XcPh3GSGj7N1KUCDQRVAw2ZrHJw+vdle5CpXD2v7vfoBJR9qZWAduBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:13:27.721511Z"},"content_sha256":"cd81df082645f973e3942429454f0dcfc5aee5930131d0c153a4a69815588b3d","schema_version":"1.0","event_id":"sha256:cd81df082645f973e3942429454f0dcfc5aee5930131d0c153a4a69815588b3d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KKO45OLNAMLWBZ65AZMJZ46IZA/bundle.json","state_url":"https://pith.science/pith/KKO45OLNAMLWBZ65AZMJZ46IZA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KKO45OLNAMLWBZ65AZMJZ46IZA/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":"2026-06-23T18:13:27Z","links":{"resolver":"https://pith.science/pith/KKO45OLNAMLWBZ65AZMJZ46IZA","bundle":"https://pith.science/pith/KKO45OLNAMLWBZ65AZMJZ46IZA/bundle.json","state":"https://pith.science/pith/KKO45OLNAMLWBZ65AZMJZ46IZA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KKO45OLNAMLWBZ65AZMJZ46IZA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KKO45OLNAMLWBZ65AZMJZ46IZA","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":"33a63a29b9d2251001acc22be67fd2a0127bec9dc144f2efb062c9eb0b293698","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-08-15T07:59:14Z","title_canon_sha256":"6c234ced5ae212130b58adec70a55d9c8269b7baccd5a2a662eea703f63fd0e7"},"schema_version":"1.0","source":{"id":"1108.2951","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2951","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2951v1","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2951","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"KKO45OLNAMLW","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KKO45OLNAMLWBZ65","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KKO45OLN","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:cd81df082645f973e3942429454f0dcfc5aee5930131d0c153a4a69815588b3d","target":"graph","created_at":"2026-05-18T02:54:47Z","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":"We consider a kinetic model of self-propelled particles with alignment interaction and with precession about the alignment direction. We derive a hydrodynamic system for the local density and velocity orientation of the particles. The system consists of the conservative equation for the local density and a non-conservative equation for the orientation. First, we assume that the alignment interaction is purely local and derive a first order system. However, we show that this system may lose its hyperbolicity. Under the assumption of weakly non-local interaction, we derive diffusive corrections ","authors_text":"Jian-Guo Liu, Pierre Degond (IMT)","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-08-15T07:59:14Z","title":"Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2951","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:bf296b65afe223082ca4245538a8cfc655d4020b2800f8ffccfad460718ed7ed","target":"record","created_at":"2026-05-18T02:54:47Z","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":"33a63a29b9d2251001acc22be67fd2a0127bec9dc144f2efb062c9eb0b293698","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-08-15T07:59:14Z","title_canon_sha256":"6c234ced5ae212130b58adec70a55d9c8269b7baccd5a2a662eea703f63fd0e7"},"schema_version":"1.0","source":{"id":"1108.2951","kind":"arxiv","version":1}},"canonical_sha256":"529dceb96d031760e7dd06589cf3c8c801be1ef4684d805fdee6909c6343827a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"529dceb96d031760e7dd06589cf3c8c801be1ef4684d805fdee6909c6343827a","first_computed_at":"2026-05-18T02:54:47.451581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:47.451581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yu3AddIxkiy8w3hr/L/w20U6DuoPG6LuOlAV8RV4smTYRNbJemELB1wE1FWa/xyiCMUeoKkrNH8kijq46ZRFDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:47.452029Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2951","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf296b65afe223082ca4245538a8cfc655d4020b2800f8ffccfad460718ed7ed","sha256:cd81df082645f973e3942429454f0dcfc5aee5930131d0c153a4a69815588b3d"],"state_sha256":"5a4e5dfd37953ffb993ce8d69aaf53ff32aa5743c6073b170e400ff0923e440c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GBson1oXmUYREg4ylUwLl3hScbNC4GsR5VsUDlXrFxf/U8jgrajdA4qN5XRXNM13i/xx57BtOQVXB18LdwNbBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T18:13:27.723375Z","bundle_sha256":"1e413c103b9092ed86ee7d4b09db75468a100a91f924f8679ba49ffe6378d8e3"}}