{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GLS422L3YJZYYHEYUVMWQD3TUD","short_pith_number":"pith:GLS422L3","canonical_record":{"source":{"id":"1409.3161","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-09-10T17:39:48Z","cross_cats_sorted":[],"title_canon_sha256":"13058715bdf09dea9e6dac874e066e796b0147f73e7df5d3ae02142cac27ff09","abstract_canon_sha256":"9d00c44999b803684edb2f4ed15f1875e0c6ff2c2556bb9f67f1b5b1689a2b04"},"schema_version":"1.0"},"canonical_sha256":"32e5cd697bc2738c1c98a559680f73a0f0c3f3900aa282f310f6ef98d631e80e","source":{"kind":"arxiv","id":"1409.3161","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3161","created_at":"2026-05-18T02:26:38Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3161v2","created_at":"2026-05-18T02:26:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3161","created_at":"2026-05-18T02:26:38Z"},{"alias_kind":"pith_short_12","alias_value":"GLS422L3YJZY","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GLS422L3YJZYYHEY","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GLS422L3","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GLS422L3YJZYYHEYUVMWQD3TUD","target":"record","payload":{"canonical_record":{"source":{"id":"1409.3161","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-09-10T17:39:48Z","cross_cats_sorted":[],"title_canon_sha256":"13058715bdf09dea9e6dac874e066e796b0147f73e7df5d3ae02142cac27ff09","abstract_canon_sha256":"9d00c44999b803684edb2f4ed15f1875e0c6ff2c2556bb9f67f1b5b1689a2b04"},"schema_version":"1.0"},"canonical_sha256":"32e5cd697bc2738c1c98a559680f73a0f0c3f3900aa282f310f6ef98d631e80e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:38.769449Z","signature_b64":"9GUeYQ3L7TmFQ43JkBjZtkoGSW5gR2lnrVGYPLpd40mUNLkWcyxHUekOFSPJXpyOIGvgFEbsxA8Zf4JhnRQuBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32e5cd697bc2738c1c98a559680f73a0f0c3f3900aa282f310f6ef98d631e80e","last_reissued_at":"2026-05-18T02:26:38.768947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:38.768947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.3161","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:26:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H98ZN+tFKdTPAVi61TxBAeTf5UxG2N82m5Ubb3iPnaazI2IDBbN3PzNagvCCmuOQU0fPikvWw6ndzeKgf5wIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:46:21.980368Z"},"content_sha256":"7eff781e81284e2c86fd65fa173eba441e9866fff3cb70b0d9546bcfba74ab59","schema_version":"1.0","event_id":"sha256:7eff781e81284e2c86fd65fa173eba441e9866fff3cb70b0d9546bcfba74ab59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GLS422L3YJZYYHEYUVMWQD3TUD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Thomas Ihle, Yen-Liang Chou","submitted_at":"2014-09-10T17:39:48Z","abstract_excerpt":"A ring-kinetic theory for Vicsek-style models of self-propelled agents is derived from the exact N-particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle pre-collisional correlations and cluster formation which both seem important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small density expansion of the collision operator and derive the first two equations of the BBGKY-hierarchy. An algorithm is presented that numerically solves "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3161","kind":"arxiv","version":2},"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":"2026-05-18T02:26:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qMMjmiQ6VZBjMRUYGxjd0heqFIWWrccK5Qr+ZS3tSPPuyxY/rtY2j09lTAXbw2FsqYouu9A2nkW2P+JkwMTfAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:46:21.980963Z"},"content_sha256":"ed544689bd20c118d54249041a5af96576fbd8ec0e779efec1fccb936ce05cee","schema_version":"1.0","event_id":"sha256:ed544689bd20c118d54249041a5af96576fbd8ec0e779efec1fccb936ce05cee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GLS422L3YJZYYHEYUVMWQD3TUD/bundle.json","state_url":"https://pith.science/pith/GLS422L3YJZYYHEYUVMWQD3TUD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GLS422L3YJZYYHEYUVMWQD3TUD/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":"2026-05-26T13:46:21Z","links":{"resolver":"https://pith.science/pith/GLS422L3YJZYYHEYUVMWQD3TUD","bundle":"https://pith.science/pith/GLS422L3YJZYYHEYUVMWQD3TUD/bundle.json","state":"https://pith.science/pith/GLS422L3YJZYYHEYUVMWQD3TUD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GLS422L3YJZYYHEYUVMWQD3TUD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GLS422L3YJZYYHEYUVMWQD3TUD","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":"9d00c44999b803684edb2f4ed15f1875e0c6ff2c2556bb9f67f1b5b1689a2b04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-09-10T17:39:48Z","title_canon_sha256":"13058715bdf09dea9e6dac874e066e796b0147f73e7df5d3ae02142cac27ff09"},"schema_version":"1.0","source":{"id":"1409.3161","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3161","created_at":"2026-05-18T02:26:38Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3161v2","created_at":"2026-05-18T02:26:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3161","created_at":"2026-05-18T02:26:38Z"},{"alias_kind":"pith_short_12","alias_value":"GLS422L3YJZY","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GLS422L3YJZYYHEY","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GLS422L3","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:ed544689bd20c118d54249041a5af96576fbd8ec0e779efec1fccb936ce05cee","target":"graph","created_at":"2026-05-18T02:26:38Z","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":"A ring-kinetic theory for Vicsek-style models of self-propelled agents is derived from the exact N-particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle pre-collisional correlations and cluster formation which both seem important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small density expansion of the collision operator and derive the first two equations of the BBGKY-hierarchy. An algorithm is presented that numerically solves ","authors_text":"Thomas Ihle, Yen-Liang Chou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-09-10T17:39:48Z","title":"Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3161","kind":"arxiv","version":2},"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":"sha256:7eff781e81284e2c86fd65fa173eba441e9866fff3cb70b0d9546bcfba74ab59","target":"record","created_at":"2026-05-18T02:26:38Z","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":"9d00c44999b803684edb2f4ed15f1875e0c6ff2c2556bb9f67f1b5b1689a2b04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-09-10T17:39:48Z","title_canon_sha256":"13058715bdf09dea9e6dac874e066e796b0147f73e7df5d3ae02142cac27ff09"},"schema_version":"1.0","source":{"id":"1409.3161","kind":"arxiv","version":2}},"canonical_sha256":"32e5cd697bc2738c1c98a559680f73a0f0c3f3900aa282f310f6ef98d631e80e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32e5cd697bc2738c1c98a559680f73a0f0c3f3900aa282f310f6ef98d631e80e","first_computed_at":"2026-05-18T02:26:38.768947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:38.768947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9GUeYQ3L7TmFQ43JkBjZtkoGSW5gR2lnrVGYPLpd40mUNLkWcyxHUekOFSPJXpyOIGvgFEbsxA8Zf4JhnRQuBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:38.769449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.3161","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7eff781e81284e2c86fd65fa173eba441e9866fff3cb70b0d9546bcfba74ab59","sha256:ed544689bd20c118d54249041a5af96576fbd8ec0e779efec1fccb936ce05cee"],"state_sha256":"226c7f71c7544346432fc8af0b68079487107da13647e25631a34a6281f228e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SUXGSkTR9xXMkVoZclfZOt6bGn+EH+zMMULnvjnxuheh1onajbWxc3VPCfWcB2/+q6wBoB60EiFQINeh9AuKCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:46:21.984154Z","bundle_sha256":"4af4158e248bb1215dcb59871a927f13d4812136356240cfe9feb5fb358cfd61"}}