{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QM2EOVPOBCBDPCB7BSGERRJP5F","short_pith_number":"pith:QM2EOVPO","canonical_record":{"source":{"id":"1609.03822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-09-13T13:32:03Z","cross_cats_sorted":["q-bio.PE","q-bio.QM"],"title_canon_sha256":"31669d0abae7f929766625970d04d2fe9749fe5a98a440c5ecf7d554da7da3c3","abstract_canon_sha256":"a4f42e2b9a5780e23c262e5f3e2ca87d19cb26bf2c46abbf4b4015b0d1f2c61c"},"schema_version":"1.0"},"canonical_sha256":"83344755ee088237883f0c8c48c52fe95f33231b94e65a9edacf43e80a1486de","source":{"kind":"arxiv","id":"1609.03822","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03822","created_at":"2026-05-18T01:04:40Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03822v1","created_at":"2026-05-18T01:04:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03822","created_at":"2026-05-18T01:04:40Z"},{"alias_kind":"pith_short_12","alias_value":"QM2EOVPOBCBD","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QM2EOVPOBCBDPCB7","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QM2EOVPO","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QM2EOVPOBCBDPCB7BSGERRJP5F","target":"record","payload":{"canonical_record":{"source":{"id":"1609.03822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-09-13T13:32:03Z","cross_cats_sorted":["q-bio.PE","q-bio.QM"],"title_canon_sha256":"31669d0abae7f929766625970d04d2fe9749fe5a98a440c5ecf7d554da7da3c3","abstract_canon_sha256":"a4f42e2b9a5780e23c262e5f3e2ca87d19cb26bf2c46abbf4b4015b0d1f2c61c"},"schema_version":"1.0"},"canonical_sha256":"83344755ee088237883f0c8c48c52fe95f33231b94e65a9edacf43e80a1486de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:40.888108Z","signature_b64":"6C6QWCeR/yO8gwYK+b7tn6Bdj6+EwEo4P4qanPZWFdQANYVqLwGfwGn35gMU2NderOniaC6Tlz+ioo5ASQcFBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83344755ee088237883f0c8c48c52fe95f33231b94e65a9edacf43e80a1486de","last_reissued_at":"2026-05-18T01:04:40.887506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:40.887506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.03822","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":"2026-05-18T01:04:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R/iNr3l1r7YAWqYNjMsvUjC8sH5/tRzBIrDJpBO8D5X8t8BBz5cRgVeM9VdRWbzIRjcUpctTdkPWdHfsbLahAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T23:13:59.466149Z"},"content_sha256":"491c9c5e875683906a936ff60104c7db97ddb5102053b0a5cbf82973a9b9f313","schema_version":"1.0","event_id":"sha256:491c9c5e875683906a936ff60104c7db97ddb5102053b0a5cbf82973a9b9f313"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QM2EOVPOBCBDPCB7BSGERRJP5F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Search reliability and search efficiency of combined L\\'evy-Brownian motion: long relocations mingled with thorough local exploration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE","q-bio.QM"],"primary_cat":"cond-mat.stat-mech","authors_text":"(2) Akhiezer Inst. for Theoret. Physics NSC KIPT, 3, (3) MPIPKS Dresden (4) Dept. of Physics, 4) R. Klages (3, 5), (5) School of Math. Sci., (6) Inst. for Physics, 7) ((1) Physics Dept., (7) Dept. of Physics, Astronomy, A.V. Chechkin (2, Kharkov, Queen Mary U. of London, R. Metzler (6, Tampere U. of Technology), TU Munich, U. of Padova, U. of Potsdam, V.V. Palyulin (1)","submitted_at":"2016-09-13T13:32:03Z","abstract_excerpt":"A combined dynamics consisting of Brownian motion and L\\'evy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economically of such dynamics thus poses an important problem. Here we model this dynamics by a one-dimensional fractional Fokker-Planck equation combining unbiased Brownian motion and L\\'evy flights. By solving this equation both analytically and numerically we show that the superposition of recurrent Brownian motion and L\\'evy flights with stable expo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03822","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":"2026-05-18T01:04:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vVSvr3nr9sLGD73/tEVCt9k7UhUk3SC0SUgbjMm2uL2H3+4Z22eSR3KLAFa8HSVgOG2OJTPcOIJl+04GrxB/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T23:13:59.466522Z"},"content_sha256":"23ece2111f279aa13f09052850e02e36b12f81b58a8ebe2d1a4b2cc74568b896","schema_version":"1.0","event_id":"sha256:23ece2111f279aa13f09052850e02e36b12f81b58a8ebe2d1a4b2cc74568b896"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QM2EOVPOBCBDPCB7BSGERRJP5F/bundle.json","state_url":"https://pith.science/pith/QM2EOVPOBCBDPCB7BSGERRJP5F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QM2EOVPOBCBDPCB7BSGERRJP5F/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":"2026-06-03T23:13:59Z","links":{"resolver":"https://pith.science/pith/QM2EOVPOBCBDPCB7BSGERRJP5F","bundle":"https://pith.science/pith/QM2EOVPOBCBDPCB7BSGERRJP5F/bundle.json","state":"https://pith.science/pith/QM2EOVPOBCBDPCB7BSGERRJP5F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QM2EOVPOBCBDPCB7BSGERRJP5F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QM2EOVPOBCBDPCB7BSGERRJP5F","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":"a4f42e2b9a5780e23c262e5f3e2ca87d19cb26bf2c46abbf4b4015b0d1f2c61c","cross_cats_sorted":["q-bio.PE","q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-09-13T13:32:03Z","title_canon_sha256":"31669d0abae7f929766625970d04d2fe9749fe5a98a440c5ecf7d554da7da3c3"},"schema_version":"1.0","source":{"id":"1609.03822","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03822","created_at":"2026-05-18T01:04:40Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03822v1","created_at":"2026-05-18T01:04:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03822","created_at":"2026-05-18T01:04:40Z"},{"alias_kind":"pith_short_12","alias_value":"QM2EOVPOBCBD","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QM2EOVPOBCBDPCB7","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QM2EOVPO","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:23ece2111f279aa13f09052850e02e36b12f81b58a8ebe2d1a4b2cc74568b896","target":"graph","created_at":"2026-05-18T01:04:40Z","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 combined dynamics consisting of Brownian motion and L\\'evy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economically of such dynamics thus poses an important problem. Here we model this dynamics by a one-dimensional fractional Fokker-Planck equation combining unbiased Brownian motion and L\\'evy flights. By solving this equation both analytically and numerically we show that the superposition of recurrent Brownian motion and L\\'evy flights with stable expo","authors_text":"(2) Akhiezer Inst. for Theoret. Physics NSC KIPT, 3, (3) MPIPKS Dresden (4) Dept. of Physics, 4) R. Klages (3, 5), (5) School of Math. Sci., (6) Inst. for Physics, 7) ((1) Physics Dept., (7) Dept. of Physics, Astronomy, A.V. Chechkin (2, Kharkov, Queen Mary U. of London, R. Metzler (6, Tampere U. of Technology), TU Munich, U. of Padova, U. of Potsdam, V.V. Palyulin (1)","cross_cats":["q-bio.PE","q-bio.QM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-09-13T13:32:03Z","title":"Search reliability and search efficiency of combined L\\'evy-Brownian motion: long relocations mingled with thorough local exploration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03822","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":"sha256:491c9c5e875683906a936ff60104c7db97ddb5102053b0a5cbf82973a9b9f313","target":"record","created_at":"2026-05-18T01:04:40Z","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":"a4f42e2b9a5780e23c262e5f3e2ca87d19cb26bf2c46abbf4b4015b0d1f2c61c","cross_cats_sorted":["q-bio.PE","q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-09-13T13:32:03Z","title_canon_sha256":"31669d0abae7f929766625970d04d2fe9749fe5a98a440c5ecf7d554da7da3c3"},"schema_version":"1.0","source":{"id":"1609.03822","kind":"arxiv","version":1}},"canonical_sha256":"83344755ee088237883f0c8c48c52fe95f33231b94e65a9edacf43e80a1486de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83344755ee088237883f0c8c48c52fe95f33231b94e65a9edacf43e80a1486de","first_computed_at":"2026-05-18T01:04:40.887506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:40.887506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6C6QWCeR/yO8gwYK+b7tn6Bdj6+EwEo4P4qanPZWFdQANYVqLwGfwGn35gMU2NderOniaC6Tlz+ioo5ASQcFBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:40.888108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03822","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:491c9c5e875683906a936ff60104c7db97ddb5102053b0a5cbf82973a9b9f313","sha256:23ece2111f279aa13f09052850e02e36b12f81b58a8ebe2d1a4b2cc74568b896"],"state_sha256":"38b04f6f2b686fc7561b9ceef49b91b5d83c8d98f635b8264a83925e26535abf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TpTBIYuWtJxxKV/HHCQmdRjUOikXYX0JWhzWuL4QEyvNXRT1kVpQ8RgoJoUphgWDpmBAMpC5GCcZvKPahgyIDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T23:13:59.468678Z","bundle_sha256":"e7555b31d6da92ce86619a5c037987caf5a20a576c6c323e72a5eb0f06d76cc8"}}