{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6THTYG3DQCZL5YXXWMMFD7WFBK","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":"6fab971d0b43811ce62a2f1978f41619099460c526f3d264b87933cd10169ae8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-07-12T23:47:52Z","title_canon_sha256":"ea8681cfd633e6af49f18ab94ebd44fab2ff80f41d7953ff1971813d6e004d62"},"schema_version":"1.0","source":{"id":"1007.2008","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.2008","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"1007.2008v1","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2008","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"6THTYG3DQCZL","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6THTYG3DQCZL5YXX","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6THTYG3D","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:b31ccac56cfae862870d4f0c073800ecac48dd8fd102f575a98b2eb297ab19dc","target":"graph","created_at":"2026-05-18T04:36:51Z","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 statistics of encounters of L\\'evy flights by introducing the concept of vicious L\\'evy flights - distinct groups of walkers performing independent L\\'evy flights with the process terminating upon the first encounter between walkers of different groups. We show that the probability that the process survives up to time $t$ decays as $t^{-\\alpha}$ at late times. We compute $\\alpha$ up to the second order in $\\epsilon$-expansion, where $\\epsilon=\\sigma-d$, $\\sigma$ is the L\\'evy exponent and $d$ is the spatial dimension. For $d=\\sigma$, we find the exponent of the logarithmic decay e","authors_text":"Ajay Gopinathan, Igor Goncharenko","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-07-12T23:47:52Z","title":"Vicious L\\'evy flights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2008","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:b7f602a367b206d35d98d3e2dd56375c97c70b53c47b8342dd410e03b6411ed6","target":"record","created_at":"2026-05-18T04:36:51Z","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":"6fab971d0b43811ce62a2f1978f41619099460c526f3d264b87933cd10169ae8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-07-12T23:47:52Z","title_canon_sha256":"ea8681cfd633e6af49f18ab94ebd44fab2ff80f41d7953ff1971813d6e004d62"},"schema_version":"1.0","source":{"id":"1007.2008","kind":"arxiv","version":1}},"canonical_sha256":"f4cf3c1b6380b2bee2f7b31851fec50a8f192e7238f44d7a2645d293b1becd49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4cf3c1b6380b2bee2f7b31851fec50a8f192e7238f44d7a2645d293b1becd49","first_computed_at":"2026-05-18T04:36:51.154105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:51.154105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+YAtD2i+5a7jRd8hVVOv9QH2MH75ATSsHPMymyRMoaSxRKOUxUrHsOXM7s2N6xcX4ew5c6ioAcqV4ni9UYBlAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:51.154727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.2008","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7f602a367b206d35d98d3e2dd56375c97c70b53c47b8342dd410e03b6411ed6","sha256:b31ccac56cfae862870d4f0c073800ecac48dd8fd102f575a98b2eb297ab19dc"],"state_sha256":"8a128434ea2f3fd04402413bb0ec7186e33ddbc71e744229ae224a40c7542e30"}