{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:NVPONUISIYZUZLZ3FXOHT5P4B7","short_pith_number":"pith:NVPONUIS","canonical_record":{"source":{"id":"2304.10071","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.QM","submitted_at":"2023-04-20T03:51:58Z","cross_cats_sorted":["physics.bio-ph"],"title_canon_sha256":"7ca88311ab96fc5cef587997543b15578150daa0393ea61f0ca53c32ab7158ed","abstract_canon_sha256":"0786c9bf64ee22f0ddddf81a8e486f7ed79d2e9075c8ee679afe2a692c2bb12a"},"schema_version":"1.0"},"canonical_sha256":"6d5ee6d11246334caf3b2ddc79f5fc0ffb5df0ba8ed7ad390c0f307e4cb47eba","source":{"kind":"arxiv","id":"2304.10071","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.10071","created_at":"2026-07-05T06:53:06Z"},{"alias_kind":"arxiv_version","alias_value":"2304.10071v1","created_at":"2026-07-05T06:53:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.10071","created_at":"2026-07-05T06:53:06Z"},{"alias_kind":"pith_short_12","alias_value":"NVPONUISIYZU","created_at":"2026-07-05T06:53:06Z"},{"alias_kind":"pith_short_16","alias_value":"NVPONUISIYZUZLZ3","created_at":"2026-07-05T06:53:06Z"},{"alias_kind":"pith_short_8","alias_value":"NVPONUIS","created_at":"2026-07-05T06:53:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:NVPONUISIYZUZLZ3FXOHT5P4B7","target":"record","payload":{"canonical_record":{"source":{"id":"2304.10071","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.QM","submitted_at":"2023-04-20T03:51:58Z","cross_cats_sorted":["physics.bio-ph"],"title_canon_sha256":"7ca88311ab96fc5cef587997543b15578150daa0393ea61f0ca53c32ab7158ed","abstract_canon_sha256":"0786c9bf64ee22f0ddddf81a8e486f7ed79d2e9075c8ee679afe2a692c2bb12a"},"schema_version":"1.0"},"canonical_sha256":"6d5ee6d11246334caf3b2ddc79f5fc0ffb5df0ba8ed7ad390c0f307e4cb47eba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:53:06.817984Z","signature_b64":"B3yYiTX4hTfs2J4vOLP0EtcvfBICHluPDDQwyOI1l1Pw0eMl1zgCDu9EnMmm4xeEA/wrOqwXv27JqubkK6v5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d5ee6d11246334caf3b2ddc79f5fc0ffb5df0ba8ed7ad390c0f307e4cb47eba","last_reissued_at":"2026-07-05T06:53:06.817492Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:53:06.817492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.10071","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":"2026-07-05T06:53:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cP3OfbNjiapGwT19ydv+/I1pL4FFKekCgQL7860/UtqUIjVFTWr0UmFxGHo4P7Buaxw8dhFoo0bR8meukfXqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T09:20:21.189151Z"},"content_sha256":"95c688df1462975d3b5c297fd86fb1bda99a0dc89f9ee09cb09743a4d246cc17","schema_version":"1.0","event_id":"sha256:95c688df1462975d3b5c297fd86fb1bda99a0dc89f9ee09cb09743a4d246cc17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:NVPONUISIYZUZLZ3FXOHT5P4B7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Data-driven discovery of stochastic dynamical equations of collective motion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.bio-ph"],"primary_cat":"q-bio.QM","authors_text":"Arshed Nabeel, Cl\\'ement Sire, Danny Raj M, Guy Theraulaz, Ram\\'on Escobedo, Srikanth K. Iyer, Vishwesha Guttal, Vivek Jadhav","submitted_at":"2023-04-20T03:51:58Z","abstract_excerpt":"Coarse-grained descriptions of collective motion of flocking systems are often derived for the macroscopic or the thermodynamic limit. However, many real flocks are small sized (10 to 100 individuals), called the mesoscopic scales, where stochasticity arising from the finite flock sizes is important. Developing mesoscopic scale equations, typically in the form of stochastic differential equations, can be challenging even for the simplest of the collective motion models. Here, we take a novel data-driven equation learning approach to construct the stochastic mesoscopic descriptions of a simple "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.10071","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.10071/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:53:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y6nze1pDXjZmD6oxhpL6SirvC00aApgipbsR/crxaKz7SwBZ7lOIRUd4NeglloNlhj5LVgdCa1bkdwI/cByqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T09:20:21.189549Z"},"content_sha256":"4bcb47ec1deabb7e16e80f415476e51f3b61e6eb1ab206c0c3602358553ecf02","schema_version":"1.0","event_id":"sha256:4bcb47ec1deabb7e16e80f415476e51f3b61e6eb1ab206c0c3602358553ecf02"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NVPONUISIYZUZLZ3FXOHT5P4B7/bundle.json","state_url":"https://pith.science/pith/NVPONUISIYZUZLZ3FXOHT5P4B7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NVPONUISIYZUZLZ3FXOHT5P4B7/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":"2026-07-07T09:20:21Z","links":{"resolver":"https://pith.science/pith/NVPONUISIYZUZLZ3FXOHT5P4B7","bundle":"https://pith.science/pith/NVPONUISIYZUZLZ3FXOHT5P4B7/bundle.json","state":"https://pith.science/pith/NVPONUISIYZUZLZ3FXOHT5P4B7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NVPONUISIYZUZLZ3FXOHT5P4B7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:NVPONUISIYZUZLZ3FXOHT5P4B7","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":"0786c9bf64ee22f0ddddf81a8e486f7ed79d2e9075c8ee679afe2a692c2bb12a","cross_cats_sorted":["physics.bio-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.QM","submitted_at":"2023-04-20T03:51:58Z","title_canon_sha256":"7ca88311ab96fc5cef587997543b15578150daa0393ea61f0ca53c32ab7158ed"},"schema_version":"1.0","source":{"id":"2304.10071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.10071","created_at":"2026-07-05T06:53:06Z"},{"alias_kind":"arxiv_version","alias_value":"2304.10071v1","created_at":"2026-07-05T06:53:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.10071","created_at":"2026-07-05T06:53:06Z"},{"alias_kind":"pith_short_12","alias_value":"NVPONUISIYZU","created_at":"2026-07-05T06:53:06Z"},{"alias_kind":"pith_short_16","alias_value":"NVPONUISIYZUZLZ3","created_at":"2026-07-05T06:53:06Z"},{"alias_kind":"pith_short_8","alias_value":"NVPONUIS","created_at":"2026-07-05T06:53:06Z"}],"graph_snapshots":[{"event_id":"sha256:4bcb47ec1deabb7e16e80f415476e51f3b61e6eb1ab206c0c3602358553ecf02","target":"graph","created_at":"2026-07-05T06:53:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2304.10071/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Coarse-grained descriptions of collective motion of flocking systems are often derived for the macroscopic or the thermodynamic limit. However, many real flocks are small sized (10 to 100 individuals), called the mesoscopic scales, where stochasticity arising from the finite flock sizes is important. Developing mesoscopic scale equations, typically in the form of stochastic differential equations, can be challenging even for the simplest of the collective motion models. Here, we take a novel data-driven equation learning approach to construct the stochastic mesoscopic descriptions of a simple ","authors_text":"Arshed Nabeel, Cl\\'ement Sire, Danny Raj M, Guy Theraulaz, Ram\\'on Escobedo, Srikanth K. Iyer, Vishwesha Guttal, Vivek Jadhav","cross_cats":["physics.bio-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.QM","submitted_at":"2023-04-20T03:51:58Z","title":"Data-driven discovery of stochastic dynamical equations of collective motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.10071","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":"sha256:95c688df1462975d3b5c297fd86fb1bda99a0dc89f9ee09cb09743a4d246cc17","target":"record","created_at":"2026-07-05T06:53:06Z","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":"0786c9bf64ee22f0ddddf81a8e486f7ed79d2e9075c8ee679afe2a692c2bb12a","cross_cats_sorted":["physics.bio-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.QM","submitted_at":"2023-04-20T03:51:58Z","title_canon_sha256":"7ca88311ab96fc5cef587997543b15578150daa0393ea61f0ca53c32ab7158ed"},"schema_version":"1.0","source":{"id":"2304.10071","kind":"arxiv","version":1}},"canonical_sha256":"6d5ee6d11246334caf3b2ddc79f5fc0ffb5df0ba8ed7ad390c0f307e4cb47eba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d5ee6d11246334caf3b2ddc79f5fc0ffb5df0ba8ed7ad390c0f307e4cb47eba","first_computed_at":"2026-07-05T06:53:06.817492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:53:06.817492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B3yYiTX4hTfs2J4vOLP0EtcvfBICHluPDDQwyOI1l1Pw0eMl1zgCDu9EnMmm4xeEA/wrOqwXv27JqubkK6v5BA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:53:06.817984Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.10071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95c688df1462975d3b5c297fd86fb1bda99a0dc89f9ee09cb09743a4d246cc17","sha256:4bcb47ec1deabb7e16e80f415476e51f3b61e6eb1ab206c0c3602358553ecf02"],"state_sha256":"176f81fd1d384f1d130e1ceda5b60a694b2816df61dd2635e391424560157950"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9tdqi4a6xCijBCwmtGZV1+hWMSIbzXAA4/5OwnygscbIRdCQ6yDEXzU9ZnAb7iBQ/yBAHSUay6CyyMRRFAXoBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T09:20:21.191529Z","bundle_sha256":"e19a7b9f6cbb1698fe2ef04868aad0f3078bf5320a4733fea24f261b5eb4c00e"}}