{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:JVBZ2LHVOX7YVBMUXFACAJFSDV","short_pith_number":"pith:JVBZ2LHV","canonical_record":{"source":{"id":"1112.1055","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-05T20:43:54Z","cross_cats_sorted":["nlin.AO","physics.bio-ph"],"title_canon_sha256":"73b3533ee0235d36e0b452a29da4e12b5f9f6ca0284c325f890bd092901b71a2","abstract_canon_sha256":"018a5f072ecd646ceae01b49aec963d88df1fc8dd103d90a68b75990e14f5ed3"},"schema_version":"1.0"},"canonical_sha256":"4d439d2cf575ff8a8594b9402024b21d4fa9c51c5a545cb1b1a6061292121220","source":{"kind":"arxiv","id":"1112.1055","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1055","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1055v2","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1055","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"pith_short_12","alias_value":"JVBZ2LHVOX7Y","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JVBZ2LHVOX7YVBMU","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JVBZ2LHV","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:JVBZ2LHVOX7YVBMUXFACAJFSDV","target":"record","payload":{"canonical_record":{"source":{"id":"1112.1055","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-05T20:43:54Z","cross_cats_sorted":["nlin.AO","physics.bio-ph"],"title_canon_sha256":"73b3533ee0235d36e0b452a29da4e12b5f9f6ca0284c325f890bd092901b71a2","abstract_canon_sha256":"018a5f072ecd646ceae01b49aec963d88df1fc8dd103d90a68b75990e14f5ed3"},"schema_version":"1.0"},"canonical_sha256":"4d439d2cf575ff8a8594b9402024b21d4fa9c51c5a545cb1b1a6061292121220","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:50.756464Z","signature_b64":"TrlQYqE6zGaMYlq5oqL23h4eG0ZEx3/IW3TMLal5+MYn2WhE3mLVTiC4HiZa28/XkqVcc78KjbGNFag3Xd95Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d439d2cf575ff8a8594b9402024b21d4fa9c51c5a545cb1b1a6061292121220","last_reissued_at":"2026-05-18T04:01:50.755807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:50.755807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.1055","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":"2026-05-18T04:01:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UI1cMg31UymaAgfLGMGskP8JjqO7z3dctK6BZmbQ8qZGQ0oRBwtxvnPixWIurJXpT9lqrJJJRH/5CUU6hHcDAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:33:00.708225Z"},"content_sha256":"89f53dfe1be52c9dc1a0975c25a63dfae9e8138c11ade0435feec9fb8ba28a6a","schema_version":"1.0","event_id":"sha256:89f53dfe1be52c9dc1a0975c25a63dfae9e8138c11ade0435feec9fb8ba28a6a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:JVBZ2LHVOX7YVBMUXFACAJFSDV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Individual based and mean-field modelling of direct aggregation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO","physics.bio-ph"],"primary_cat":"math.DS","authors_text":"Jan Haskovec, Marie-Therese Wolfram, Martin Burger","submitted_at":"2011-12-05T20:43:54Z","abstract_excerpt":"We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighbourhood. In the first-order model the location of each individual is subject to a density-dependent random walk, while in the second-order model the density-dependent random walk acts on the velocity variable, together with a density-dependent damping term. The main novelty of our models is that we do not assume any explicit aggregative force acting on the individuals; instead, aggregation is obtained exclusivel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1055","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":"2026-05-18T04:01:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hci1NrA+9GG8M70+lI6205bqnKk7r4ndBTH5B/PAZsSMdg7eAMzYJgxeA2X0eO3jYKqpb2Fx5vjgFlsB6j1+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:33:00.709005Z"},"content_sha256":"364b67e1a499a8999dcc6ff11a8b0c0a36e7c96a7ae09a151baff06809069dc7","schema_version":"1.0","event_id":"sha256:364b67e1a499a8999dcc6ff11a8b0c0a36e7c96a7ae09a151baff06809069dc7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JVBZ2LHVOX7YVBMUXFACAJFSDV/bundle.json","state_url":"https://pith.science/pith/JVBZ2LHVOX7YVBMUXFACAJFSDV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JVBZ2LHVOX7YVBMUXFACAJFSDV/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":"2026-05-31T16:33:00Z","links":{"resolver":"https://pith.science/pith/JVBZ2LHVOX7YVBMUXFACAJFSDV","bundle":"https://pith.science/pith/JVBZ2LHVOX7YVBMUXFACAJFSDV/bundle.json","state":"https://pith.science/pith/JVBZ2LHVOX7YVBMUXFACAJFSDV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JVBZ2LHVOX7YVBMUXFACAJFSDV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JVBZ2LHVOX7YVBMUXFACAJFSDV","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":"018a5f072ecd646ceae01b49aec963d88df1fc8dd103d90a68b75990e14f5ed3","cross_cats_sorted":["nlin.AO","physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-05T20:43:54Z","title_canon_sha256":"73b3533ee0235d36e0b452a29da4e12b5f9f6ca0284c325f890bd092901b71a2"},"schema_version":"1.0","source":{"id":"1112.1055","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1055","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1055v2","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1055","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"pith_short_12","alias_value":"JVBZ2LHVOX7Y","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JVBZ2LHVOX7YVBMU","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JVBZ2LHV","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:364b67e1a499a8999dcc6ff11a8b0c0a36e7c96a7ae09a151baff06809069dc7","target":"graph","created_at":"2026-05-18T04:01:50Z","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 introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighbourhood. In the first-order model the location of each individual is subject to a density-dependent random walk, while in the second-order model the density-dependent random walk acts on the velocity variable, together with a density-dependent damping term. The main novelty of our models is that we do not assume any explicit aggregative force acting on the individuals; instead, aggregation is obtained exclusivel","authors_text":"Jan Haskovec, Marie-Therese Wolfram, Martin Burger","cross_cats":["nlin.AO","physics.bio-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-05T20:43:54Z","title":"Individual based and mean-field modelling of direct aggregation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1055","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":"sha256:89f53dfe1be52c9dc1a0975c25a63dfae9e8138c11ade0435feec9fb8ba28a6a","target":"record","created_at":"2026-05-18T04:01:50Z","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":"018a5f072ecd646ceae01b49aec963d88df1fc8dd103d90a68b75990e14f5ed3","cross_cats_sorted":["nlin.AO","physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-05T20:43:54Z","title_canon_sha256":"73b3533ee0235d36e0b452a29da4e12b5f9f6ca0284c325f890bd092901b71a2"},"schema_version":"1.0","source":{"id":"1112.1055","kind":"arxiv","version":2}},"canonical_sha256":"4d439d2cf575ff8a8594b9402024b21d4fa9c51c5a545cb1b1a6061292121220","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d439d2cf575ff8a8594b9402024b21d4fa9c51c5a545cb1b1a6061292121220","first_computed_at":"2026-05-18T04:01:50.755807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:50.755807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TrlQYqE6zGaMYlq5oqL23h4eG0ZEx3/IW3TMLal5+MYn2WhE3mLVTiC4HiZa28/XkqVcc78KjbGNFag3Xd95Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:50.756464Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1055","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89f53dfe1be52c9dc1a0975c25a63dfae9e8138c11ade0435feec9fb8ba28a6a","sha256:364b67e1a499a8999dcc6ff11a8b0c0a36e7c96a7ae09a151baff06809069dc7"],"state_sha256":"205b2e56c1924dcf9ade64a56e013c5fb0dca185bebe2f3824ca53673388983c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zjjMIn49Y8zCnnVbcQgUVwifMLhPRPfyaPZYevscB3SA5laK7DHSZnDbBzY3ZJwK8YcL/fjmhhOTf3w0nmJvAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T16:33:00.713479Z","bundle_sha256":"697c1670f36c31a212693508903f6a52cc48bba9c76483aeba1ec4189d530967"}}