{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:ELOHDCVMUCH4HXUOO6EYKJEPW4","short_pith_number":"pith:ELOHDCVM","canonical_record":{"source":{"id":"nlin/0602013","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.CD","submitted_at":"2006-02-07T12:52:28Z","cross_cats_sorted":[],"title_canon_sha256":"d3de13e7f207ae4a2c11112f53d296fc41a3fe548bfe56b7431533961c032b50","abstract_canon_sha256":"b4b62e701ab135c3a82c3e6721a232c7de9235673edc562ae895c35580c474f3"},"schema_version":"1.0"},"canonical_sha256":"22dc718aaca08fc3de8e778985248fb73fac6df19a217139a87874f292d4bfb1","source":{"kind":"arxiv","id":"nlin/0602013","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0602013","created_at":"2026-05-18T04:00:16Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0602013v1","created_at":"2026-05-18T04:00:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0602013","created_at":"2026-05-18T04:00:16Z"},{"alias_kind":"pith_short_12","alias_value":"ELOHDCVMUCH4","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"ELOHDCVMUCH4HXUO","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"ELOHDCVM","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:ELOHDCVMUCH4HXUOO6EYKJEPW4","target":"record","payload":{"canonical_record":{"source":{"id":"nlin/0602013","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.CD","submitted_at":"2006-02-07T12:52:28Z","cross_cats_sorted":[],"title_canon_sha256":"d3de13e7f207ae4a2c11112f53d296fc41a3fe548bfe56b7431533961c032b50","abstract_canon_sha256":"b4b62e701ab135c3a82c3e6721a232c7de9235673edc562ae895c35580c474f3"},"schema_version":"1.0"},"canonical_sha256":"22dc718aaca08fc3de8e778985248fb73fac6df19a217139a87874f292d4bfb1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:16.353225Z","signature_b64":"5wMFF4chlDSNF0+h0gxCdQhC8s8qamE2uSRmZi8nkv5Fu8qWUPGmii+OeTTZY+MfIL4r1OgzxyfH+ew3XE9lCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22dc718aaca08fc3de8e778985248fb73fac6df19a217139a87874f292d4bfb1","last_reissued_at":"2026-05-18T04:00:16.352536Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:16.352536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"nlin/0602013","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":"2026-05-18T04:00:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K7qLGrOY0iXd99H46xg9YZFCn8mG1IAP6dIWMcXAaRCi7xEj06mX0HcrznAIxOj58oibqzqqjz5Uhqb1m0YDCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:21:59.307917Z"},"content_sha256":"26e5534a515fb0c06e287d6f466309a2e36dfa69122fa01c33874a7f4102f301","schema_version":"1.0","event_id":"sha256:26e5534a515fb0c06e287d6f466309a2e36dfa69122fa01c33874a7f4102f301"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:ELOHDCVMUCH4HXUOO6EYKJEPW4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Absorbing processes in Richardson diffusion: analytical results","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Angelo Vulpiani, Mogens H. Jensen, Simone Pigolotti","submitted_at":"2006-02-07T12:52:28Z","abstract_excerpt":"We consider the recently addressed problem of a passive particle (a predator), being the center of a ``sphere of interception'' of radius $R$ and able to absorb other passive particles (the preys) entering into the sphere. Assuming that all the particles are advected by a turbulent flow and that, in particular, the Richardson equation properly describes the relative dispersion, we calculate an analytical expression for the flux into the sphere as a function of time, assuming an initial constant density of preys outside the sphere. In the same framework, we show that the distribution of times o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0602013","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":""},"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":"2026-05-18T04:00:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OgONKnXzcfu/SynL58F1kxSTAFPDfNA5JMsioO3ZCYaZpqsjA7dr/KqXxIolwGkXYIDBR0U4E6rAVTuKzxgEBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:21:59.308255Z"},"content_sha256":"b3eaf4505e200f2f507e612b9a2e2c2dcf3dc1aa28de96dcaba30408463fefba","schema_version":"1.0","event_id":"sha256:b3eaf4505e200f2f507e612b9a2e2c2dcf3dc1aa28de96dcaba30408463fefba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ELOHDCVMUCH4HXUOO6EYKJEPW4/bundle.json","state_url":"https://pith.science/pith/ELOHDCVMUCH4HXUOO6EYKJEPW4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ELOHDCVMUCH4HXUOO6EYKJEPW4/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":"2026-06-02T22:21:59Z","links":{"resolver":"https://pith.science/pith/ELOHDCVMUCH4HXUOO6EYKJEPW4","bundle":"https://pith.science/pith/ELOHDCVMUCH4HXUOO6EYKJEPW4/bundle.json","state":"https://pith.science/pith/ELOHDCVMUCH4HXUOO6EYKJEPW4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ELOHDCVMUCH4HXUOO6EYKJEPW4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:ELOHDCVMUCH4HXUOO6EYKJEPW4","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":"b4b62e701ab135c3a82c3e6721a232c7de9235673edc562ae895c35580c474f3","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2006-02-07T12:52:28Z","title_canon_sha256":"d3de13e7f207ae4a2c11112f53d296fc41a3fe548bfe56b7431533961c032b50"},"schema_version":"1.0","source":{"id":"nlin/0602013","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0602013","created_at":"2026-05-18T04:00:16Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0602013v1","created_at":"2026-05-18T04:00:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0602013","created_at":"2026-05-18T04:00:16Z"},{"alias_kind":"pith_short_12","alias_value":"ELOHDCVMUCH4","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"ELOHDCVMUCH4HXUO","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"ELOHDCVM","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:b3eaf4505e200f2f507e612b9a2e2c2dcf3dc1aa28de96dcaba30408463fefba","target":"graph","created_at":"2026-05-18T04:00:16Z","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 consider the recently addressed problem of a passive particle (a predator), being the center of a ``sphere of interception'' of radius $R$ and able to absorb other passive particles (the preys) entering into the sphere. Assuming that all the particles are advected by a turbulent flow and that, in particular, the Richardson equation properly describes the relative dispersion, we calculate an analytical expression for the flux into the sphere as a function of time, assuming an initial constant density of preys outside the sphere. In the same framework, we show that the distribution of times o","authors_text":"Angelo Vulpiani, Mogens H. Jensen, Simone Pigolotti","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.CD","submitted_at":"2006-02-07T12:52:28Z","title":"Absorbing processes in Richardson diffusion: analytical results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0602013","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":"sha256:26e5534a515fb0c06e287d6f466309a2e36dfa69122fa01c33874a7f4102f301","target":"record","created_at":"2026-05-18T04:00:16Z","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":"b4b62e701ab135c3a82c3e6721a232c7de9235673edc562ae895c35580c474f3","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2006-02-07T12:52:28Z","title_canon_sha256":"d3de13e7f207ae4a2c11112f53d296fc41a3fe548bfe56b7431533961c032b50"},"schema_version":"1.0","source":{"id":"nlin/0602013","kind":"arxiv","version":1}},"canonical_sha256":"22dc718aaca08fc3de8e778985248fb73fac6df19a217139a87874f292d4bfb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22dc718aaca08fc3de8e778985248fb73fac6df19a217139a87874f292d4bfb1","first_computed_at":"2026-05-18T04:00:16.352536Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:16.352536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5wMFF4chlDSNF0+h0gxCdQhC8s8qamE2uSRmZi8nkv5Fu8qWUPGmii+OeTTZY+MfIL4r1OgzxyfH+ew3XE9lCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:16.353225Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0602013","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26e5534a515fb0c06e287d6f466309a2e36dfa69122fa01c33874a7f4102f301","sha256:b3eaf4505e200f2f507e612b9a2e2c2dcf3dc1aa28de96dcaba30408463fefba"],"state_sha256":"66783530a9d0021e5103c1716fb7c11c7a966618620955fe339d08d272aea579"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t6ArrsgVDL4Q17qsOY25u4Byrh92kft4HQsVedEUYCEbWek6olOkq6DtyNS5colqqAAf8H0zw+iODWGatue0DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:21:59.310135Z","bundle_sha256":"9ab731caf9e52538e9b26de5351263bb67da3ba924f0c3ef666495857521753a"}}