{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:E6U4MNHJZKFHTQH76WYCUSVTEW","short_pith_number":"pith:E6U4MNHJ","canonical_record":{"source":{"id":"0911.1022","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-11-05T13:01:58Z","cross_cats_sorted":[],"title_canon_sha256":"fbf3c220f4b8c3b098f1d4c4015fbe69aa60847aa0436c23bbf27620f14c2d05","abstract_canon_sha256":"8bf5eca678a5dfa42da3f87dc5307002ee0d13e553c78b58007c02c9d210e1b6"},"schema_version":"1.0"},"canonical_sha256":"27a9c634e9ca8a79c0fff5b02a4ab325842d8f9d335fbd348e1a3591f35efc37","source":{"kind":"arxiv","id":"0911.1022","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1022","created_at":"2026-05-18T02:10:59Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1022v2","created_at":"2026-05-18T02:10:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1022","created_at":"2026-05-18T02:10:59Z"},{"alias_kind":"pith_short_12","alias_value":"E6U4MNHJZKFH","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"E6U4MNHJZKFHTQH7","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"E6U4MNHJ","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:E6U4MNHJZKFHTQH76WYCUSVTEW","target":"record","payload":{"canonical_record":{"source":{"id":"0911.1022","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-11-05T13:01:58Z","cross_cats_sorted":[],"title_canon_sha256":"fbf3c220f4b8c3b098f1d4c4015fbe69aa60847aa0436c23bbf27620f14c2d05","abstract_canon_sha256":"8bf5eca678a5dfa42da3f87dc5307002ee0d13e553c78b58007c02c9d210e1b6"},"schema_version":"1.0"},"canonical_sha256":"27a9c634e9ca8a79c0fff5b02a4ab325842d8f9d335fbd348e1a3591f35efc37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:59.290749Z","signature_b64":"njwmNvhAo/QHt44Qa+4kpdKSWsGq6gv6ciAFPJHNYblzvbvFNNofE9CooH+GSZnZi2Z1TeU6ROAwVvGYBRWjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27a9c634e9ca8a79c0fff5b02a4ab325842d8f9d335fbd348e1a3591f35efc37","last_reissued_at":"2026-05-18T02:10:59.290039Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:59.290039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.1022","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":"2026-05-18T02:10:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0FTKI1shyuDao0ZKuiwAx2Xap84TOQ1KDPJ+Zcx0vnGSseyBFZksGq/m3r/a3cE9EDvG0B9FHW0VeTRWluPLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:19:08.977010Z"},"content_sha256":"d9708aa69de08d6f4b68db0e9b3cf2c4e39cf84605216e3deffe35426ccc8563","schema_version":"1.0","event_id":"sha256:d9708aa69de08d6f4b68db0e9b3cf2c4e39cf84605216e3deffe35426ccc8563"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:E6U4MNHJZKFHTQH76WYCUSVTEW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-gravitating Brownian particles in two dimensions: the case of N=2 particles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"P.H. Chavanis, R. Mannella","submitted_at":"2009-11-05T13:01:58Z","abstract_excerpt":"We study the motion of N=2 overdamped Brownian particles in gravitational interaction in a space of dimension d=2. This is equivalent to the simplified motion of two biological entities interacting via chemotaxis when time delay and degradation of the chemical are ignored. This problem also bears some similarities with the stochastic motion of two point vortices in viscous hydrodynamics [Agullo & Verga, Phys. Rev. E, 63, 056304 (2001)]. We analytically obtain the density probability of finding the particles at a distance r from each other at time t. We also determine the probability that the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1022","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":"2026-05-18T02:10:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3cZiVhQVhgkjWlfLRB0anyIgIkC5RwmRjJUVnPUgV1R2jv4Emy9TX1SSh4YdRV3JebzWct6e9M1UxTmtTJwpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:19:08.977371Z"},"content_sha256":"33e199b08afc98a20145e569445ffb14d181a4b819185aeb6a03ca14d2e32c35","schema_version":"1.0","event_id":"sha256:33e199b08afc98a20145e569445ffb14d181a4b819185aeb6a03ca14d2e32c35"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E6U4MNHJZKFHTQH76WYCUSVTEW/bundle.json","state_url":"https://pith.science/pith/E6U4MNHJZKFHTQH76WYCUSVTEW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E6U4MNHJZKFHTQH76WYCUSVTEW/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":"2026-05-28T05:19:08Z","links":{"resolver":"https://pith.science/pith/E6U4MNHJZKFHTQH76WYCUSVTEW","bundle":"https://pith.science/pith/E6U4MNHJZKFHTQH76WYCUSVTEW/bundle.json","state":"https://pith.science/pith/E6U4MNHJZKFHTQH76WYCUSVTEW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E6U4MNHJZKFHTQH76WYCUSVTEW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:E6U4MNHJZKFHTQH76WYCUSVTEW","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":"8bf5eca678a5dfa42da3f87dc5307002ee0d13e553c78b58007c02c9d210e1b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-11-05T13:01:58Z","title_canon_sha256":"fbf3c220f4b8c3b098f1d4c4015fbe69aa60847aa0436c23bbf27620f14c2d05"},"schema_version":"1.0","source":{"id":"0911.1022","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1022","created_at":"2026-05-18T02:10:59Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1022v2","created_at":"2026-05-18T02:10:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1022","created_at":"2026-05-18T02:10:59Z"},{"alias_kind":"pith_short_12","alias_value":"E6U4MNHJZKFH","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"E6U4MNHJZKFHTQH7","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"E6U4MNHJ","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:33e199b08afc98a20145e569445ffb14d181a4b819185aeb6a03ca14d2e32c35","target":"graph","created_at":"2026-05-18T02:10:59Z","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 study the motion of N=2 overdamped Brownian particles in gravitational interaction in a space of dimension d=2. This is equivalent to the simplified motion of two biological entities interacting via chemotaxis when time delay and degradation of the chemical are ignored. This problem also bears some similarities with the stochastic motion of two point vortices in viscous hydrodynamics [Agullo & Verga, Phys. Rev. E, 63, 056304 (2001)]. We analytically obtain the density probability of finding the particles at a distance r from each other at time t. We also determine the probability that the p","authors_text":"P.H. Chavanis, R. Mannella","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-11-05T13:01:58Z","title":"Self-gravitating Brownian particles in two dimensions: the case of N=2 particles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1022","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:d9708aa69de08d6f4b68db0e9b3cf2c4e39cf84605216e3deffe35426ccc8563","target":"record","created_at":"2026-05-18T02:10:59Z","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":"8bf5eca678a5dfa42da3f87dc5307002ee0d13e553c78b58007c02c9d210e1b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-11-05T13:01:58Z","title_canon_sha256":"fbf3c220f4b8c3b098f1d4c4015fbe69aa60847aa0436c23bbf27620f14c2d05"},"schema_version":"1.0","source":{"id":"0911.1022","kind":"arxiv","version":2}},"canonical_sha256":"27a9c634e9ca8a79c0fff5b02a4ab325842d8f9d335fbd348e1a3591f35efc37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27a9c634e9ca8a79c0fff5b02a4ab325842d8f9d335fbd348e1a3591f35efc37","first_computed_at":"2026-05-18T02:10:59.290039Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:10:59.290039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"njwmNvhAo/QHt44Qa+4kpdKSWsGq6gv6ciAFPJHNYblzvbvFNNofE9CooH+GSZnZi2Z1TeU6ROAwVvGYBRWjCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:10:59.290749Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.1022","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9708aa69de08d6f4b68db0e9b3cf2c4e39cf84605216e3deffe35426ccc8563","sha256:33e199b08afc98a20145e569445ffb14d181a4b819185aeb6a03ca14d2e32c35"],"state_sha256":"d7813a6f8d396379c012df2d5794d12f2168c279afef3c259b175066cedbcf01"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pIh5Tvrm+inD7pWLnIHIFdm5q3GqBzx4y8bn7T5wuk5xN13fAAXkbakFZPW2pFcOjdW8w/AGv+8alaBQWjI0Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T05:19:08.979473Z","bundle_sha256":"666b64e2481197359864584c900f9019b7f7324c2d26c03337251487b5ea346d"}}