{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:6THTYG3DQCZL5YXXWMMFD7WFBK","short_pith_number":"pith:6THTYG3D","canonical_record":{"source":{"id":"1007.2008","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-07-12T23:47:52Z","cross_cats_sorted":[],"title_canon_sha256":"ea8681cfd633e6af49f18ab94ebd44fab2ff80f41d7953ff1971813d6e004d62","abstract_canon_sha256":"6fab971d0b43811ce62a2f1978f41619099460c526f3d264b87933cd10169ae8"},"schema_version":"1.0"},"canonical_sha256":"f4cf3c1b6380b2bee2f7b31851fec50a8f192e7238f44d7a2645d293b1becd49","source":{"kind":"arxiv","id":"1007.2008","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:6THTYG3DQCZL5YXXWMMFD7WFBK","target":"record","payload":{"canonical_record":{"source":{"id":"1007.2008","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-07-12T23:47:52Z","cross_cats_sorted":[],"title_canon_sha256":"ea8681cfd633e6af49f18ab94ebd44fab2ff80f41d7953ff1971813d6e004d62","abstract_canon_sha256":"6fab971d0b43811ce62a2f1978f41619099460c526f3d264b87933cd10169ae8"},"schema_version":"1.0"},"canonical_sha256":"f4cf3c1b6380b2bee2f7b31851fec50a8f192e7238f44d7a2645d293b1becd49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:51.154727Z","signature_b64":"+YAtD2i+5a7jRd8hVVOv9QH2MH75ATSsHPMymyRMoaSxRKOUxUrHsOXM7s2N6xcX4ew5c6ioAcqV4ni9UYBlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4cf3c1b6380b2bee2f7b31851fec50a8f192e7238f44d7a2645d293b1becd49","last_reissued_at":"2026-05-18T04:36:51.154105Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:51.154105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.2008","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":"2026-05-18T04:36:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wtq7x9L7yt/wnESM50QstI5/SgbWaqmyOHLMAzc6d1LOSa1xkfUTAFkuKaG1/x1eQyxo20Nwokxu+ekSeEreBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T23:15:40.924642Z"},"content_sha256":"b7f602a367b206d35d98d3e2dd56375c97c70b53c47b8342dd410e03b6411ed6","schema_version":"1.0","event_id":"sha256:b7f602a367b206d35d98d3e2dd56375c97c70b53c47b8342dd410e03b6411ed6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:6THTYG3DQCZL5YXXWMMFD7WFBK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vicious L\\'evy flights","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Ajay Gopinathan, Igor Goncharenko","submitted_at":"2010-07-12T23:47:52Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2008","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":"2026-05-18T04:36:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kib4mZq5+9cl3Gdg3Dq1z5p53K2mMMk32Po+JWpAlA2bd4KCJDX4HNEh+4Q/fxqNmP1kweCTkaQVbhFQNk6fBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T23:15:40.924978Z"},"content_sha256":"b31ccac56cfae862870d4f0c073800ecac48dd8fd102f575a98b2eb297ab19dc","schema_version":"1.0","event_id":"sha256:b31ccac56cfae862870d4f0c073800ecac48dd8fd102f575a98b2eb297ab19dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6THTYG3DQCZL5YXXWMMFD7WFBK/bundle.json","state_url":"https://pith.science/pith/6THTYG3DQCZL5YXXWMMFD7WFBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6THTYG3DQCZL5YXXWMMFD7WFBK/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":"2026-06-03T23:15:40Z","links":{"resolver":"https://pith.science/pith/6THTYG3DQCZL5YXXWMMFD7WFBK","bundle":"https://pith.science/pith/6THTYG3DQCZL5YXXWMMFD7WFBK/bundle.json","state":"https://pith.science/pith/6THTYG3DQCZL5YXXWMMFD7WFBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6THTYG3DQCZL5YXXWMMFD7WFBK/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T98aYyRSwQVazNbudhE2xsr2lDiDMVYh/IQ5ivwHTVLLwqoDBylszK8V7YgrlaLzvv/Prd1iXpHPeXVcKXPGDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T23:15:40.926973Z","bundle_sha256":"43e9709a92619c188a474884de5d84d57014878da7cc7156ab9e0f989662f2e6"}}