{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:EOGMYSHSHGDZT6KZNYBUNF5KJI","short_pith_number":"pith:EOGMYSHS","canonical_record":{"source":{"id":"1211.7233","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-11-30T12:55:49Z","cross_cats_sorted":["cond-mat.stat-mech","physics.flu-dyn"],"title_canon_sha256":"c318ec8f354df180d68c7a2eccda97100936652a5deb8cd421eb48049154aefe","abstract_canon_sha256":"784de193c89793dd5f3fa2ef3838f503fd5ee02ce47969bf3ed20f6abb2a59be"},"schema_version":"1.0"},"canonical_sha256":"238ccc48f2398799f9596e034697aa4a372acacf08fcdcdf0a98b4039658ba05","source":{"kind":"arxiv","id":"1211.7233","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.7233","created_at":"2026-05-18T01:52:52Z"},{"alias_kind":"arxiv_version","alias_value":"1211.7233v2","created_at":"2026-05-18T01:52:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.7233","created_at":"2026-05-18T01:52:52Z"},{"alias_kind":"pith_short_12","alias_value":"EOGMYSHSHGDZ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EOGMYSHSHGDZT6KZ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EOGMYSHS","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:EOGMYSHSHGDZT6KZNYBUNF5KJI","target":"record","payload":{"canonical_record":{"source":{"id":"1211.7233","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-11-30T12:55:49Z","cross_cats_sorted":["cond-mat.stat-mech","physics.flu-dyn"],"title_canon_sha256":"c318ec8f354df180d68c7a2eccda97100936652a5deb8cd421eb48049154aefe","abstract_canon_sha256":"784de193c89793dd5f3fa2ef3838f503fd5ee02ce47969bf3ed20f6abb2a59be"},"schema_version":"1.0"},"canonical_sha256":"238ccc48f2398799f9596e034697aa4a372acacf08fcdcdf0a98b4039658ba05","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:52:52.916869Z","signature_b64":"Z51C9+zxDUHoPsWFos6cYyYx7evo0CT/BxYG0VFeMXybPNyO565zokNIpXAlOe19bUbLh4QE6KsGEyS9rA+RDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"238ccc48f2398799f9596e034697aa4a372acacf08fcdcdf0a98b4039658ba05","last_reissued_at":"2026-05-18T01:52:52.916228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:52:52.916228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.7233","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":"2026-05-18T01:52:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BJkdE1dIyP4+xy/h7NlGoLypAhBh6muyIdV1cdQ/OPWo+4EFIaNJp/FSPvwLZygz8e1kKznj0Ri8h/hIrcDIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:41:58.242122Z"},"content_sha256":"e34bd2683282b1e167b8ae60bf3f7d17b05a381b7ad5869471e4429ea22a13db","schema_version":"1.0","event_id":"sha256:e34bd2683282b1e167b8ae60bf3f7d17b05a381b7ad5869471e4429ea22a13db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:EOGMYSHSHGDZT6KZNYBUNF5KJI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effective rates in dilute reaction-advection systems for the annihilation process $A + A \\to \\varnothing$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","physics.flu-dyn"],"primary_cat":"nlin.CD","authors_text":"Giorgio Krstulovic, Jeremie Bec, Massimo Cencini","submitted_at":"2012-11-30T12:55:49Z","abstract_excerpt":"A dilute system of reacting particles transported by fluid flows is considered. The particles react as $A + A \\to \\varnothing$ with a given rate when they are within a finite radius of interaction. The system is described in terms of the joint n-point number spatial density that it is shown to obey a hierarchy of transport equations. An analytic solution is obtained in either the dilute or the long-time limit by using a Lagrangian approach where statistical averages are performed along non- reacting trajectories. In this limit, it is shown that the moments of the number of particles have an ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.7233","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":"2026-05-18T01:52:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oLfwIQ4aUVr3VTKSxggrCG5QA4yyXEJQ7Azb6nZvrRrvATfjIu5Ei0XBsZey/SwJXnamb9X1QRg1YoKn7CJQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:41:58.242782Z"},"content_sha256":"77f8b2451da75df19e53111563ed814b280f5993b49664fff67660e1cc941fd8","schema_version":"1.0","event_id":"sha256:77f8b2451da75df19e53111563ed814b280f5993b49664fff67660e1cc941fd8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EOGMYSHSHGDZT6KZNYBUNF5KJI/bundle.json","state_url":"https://pith.science/pith/EOGMYSHSHGDZT6KZNYBUNF5KJI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EOGMYSHSHGDZT6KZNYBUNF5KJI/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":"2026-05-26T18:41:58Z","links":{"resolver":"https://pith.science/pith/EOGMYSHSHGDZT6KZNYBUNF5KJI","bundle":"https://pith.science/pith/EOGMYSHSHGDZT6KZNYBUNF5KJI/bundle.json","state":"https://pith.science/pith/EOGMYSHSHGDZT6KZNYBUNF5KJI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EOGMYSHSHGDZT6KZNYBUNF5KJI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EOGMYSHSHGDZT6KZNYBUNF5KJI","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":"784de193c89793dd5f3fa2ef3838f503fd5ee02ce47969bf3ed20f6abb2a59be","cross_cats_sorted":["cond-mat.stat-mech","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-11-30T12:55:49Z","title_canon_sha256":"c318ec8f354df180d68c7a2eccda97100936652a5deb8cd421eb48049154aefe"},"schema_version":"1.0","source":{"id":"1211.7233","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.7233","created_at":"2026-05-18T01:52:52Z"},{"alias_kind":"arxiv_version","alias_value":"1211.7233v2","created_at":"2026-05-18T01:52:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.7233","created_at":"2026-05-18T01:52:52Z"},{"alias_kind":"pith_short_12","alias_value":"EOGMYSHSHGDZ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EOGMYSHSHGDZT6KZ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EOGMYSHS","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:77f8b2451da75df19e53111563ed814b280f5993b49664fff67660e1cc941fd8","target":"graph","created_at":"2026-05-18T01:52:52Z","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 dilute system of reacting particles transported by fluid flows is considered. The particles react as $A + A \\to \\varnothing$ with a given rate when they are within a finite radius of interaction. The system is described in terms of the joint n-point number spatial density that it is shown to obey a hierarchy of transport equations. An analytic solution is obtained in either the dilute or the long-time limit by using a Lagrangian approach where statistical averages are performed along non- reacting trajectories. In this limit, it is shown that the moments of the number of particles have an ex","authors_text":"Giorgio Krstulovic, Jeremie Bec, Massimo Cencini","cross_cats":["cond-mat.stat-mech","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-11-30T12:55:49Z","title":"Effective rates in dilute reaction-advection systems for the annihilation process $A + A \\to \\varnothing$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.7233","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:e34bd2683282b1e167b8ae60bf3f7d17b05a381b7ad5869471e4429ea22a13db","target":"record","created_at":"2026-05-18T01:52:52Z","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":"784de193c89793dd5f3fa2ef3838f503fd5ee02ce47969bf3ed20f6abb2a59be","cross_cats_sorted":["cond-mat.stat-mech","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-11-30T12:55:49Z","title_canon_sha256":"c318ec8f354df180d68c7a2eccda97100936652a5deb8cd421eb48049154aefe"},"schema_version":"1.0","source":{"id":"1211.7233","kind":"arxiv","version":2}},"canonical_sha256":"238ccc48f2398799f9596e034697aa4a372acacf08fcdcdf0a98b4039658ba05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"238ccc48f2398799f9596e034697aa4a372acacf08fcdcdf0a98b4039658ba05","first_computed_at":"2026-05-18T01:52:52.916228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:52:52.916228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z51C9+zxDUHoPsWFos6cYyYx7evo0CT/BxYG0VFeMXybPNyO565zokNIpXAlOe19bUbLh4QE6KsGEyS9rA+RDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:52:52.916869Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.7233","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e34bd2683282b1e167b8ae60bf3f7d17b05a381b7ad5869471e4429ea22a13db","sha256:77f8b2451da75df19e53111563ed814b280f5993b49664fff67660e1cc941fd8"],"state_sha256":"da67f15470fa0d7f3144765c547e40b1cfecafaf8a11c5ebb6a389bab4fce41d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iRLpHR2q6eLdRpIrhpz4XdDTgiY/AUXJGfUOo3vt5JLoKwciHgvEgoSBC/PePvfxURCsjg059qxNedIZALW5CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T18:41:58.246065Z","bundle_sha256":"8ecbba006be18da034c966583ed26e82685ff08f4a6994279373f76ab8a55ad9"}}