{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:O4WMILUIAJAJIBUN3GC5JT2EGR","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":"ce9dec4ebfb574a3a18c59d2b302a7306534fb388adf1493d693f9c3019eebe5","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-05-25T13:38:31Z","title_canon_sha256":"82160cc2da0725371a549e912422e339d72bbfaf0d61f25f32166ba00ec73fbf"},"schema_version":"1.0","source":{"id":"1805.10284","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10284","created_at":"2026-05-18T00:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10284v1","created_at":"2026-05-18T00:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10284","created_at":"2026-05-18T00:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"O4WMILUIAJAJ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"O4WMILUIAJAJIBUN","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"O4WMILUI","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:a8b11ca5f6cce0b835b0425cefe1628b0954786cd7185584bc960966d9582864","target":"graph","created_at":"2026-05-18T00:06:20Z","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":"The first return time (FRT) is the time it takes a random walker to first return to its original site, and the global first passage time (GFPT) is the first passage time for a random walker to move from a randomly selected site to a given site. We find that in finite networks the variance of FRT, Var(FRT), can be expressed Var(FRT)~$=2\\langle$FRT$ \\rangle \\langle $GFPT$ \\rangle -\\langle $FRT$ \\rangle^2-\\langle $FRT$ \\rangle$, where $\\langle \\cdot \\rangle$ is the mean of the random variable. Therefore a method of calculating the variance of FRT on general finite networks is presented. We then c","authors_text":"Guoai Xu, H. Eugene Stanley, Junhao Peng, Lin Chen, Renxiang Shao","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-05-25T13:38:31Z","title":"Analysis of fluctuations in the first return times of random walks on regular branched networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10284","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":"sha256:98272f5aeb337aaacd94fa74cff2fdd1b5c9f378ee6f4fa76815591e233a5e67","target":"record","created_at":"2026-05-18T00:06:20Z","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":"ce9dec4ebfb574a3a18c59d2b302a7306534fb388adf1493d693f9c3019eebe5","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-05-25T13:38:31Z","title_canon_sha256":"82160cc2da0725371a549e912422e339d72bbfaf0d61f25f32166ba00ec73fbf"},"schema_version":"1.0","source":{"id":"1805.10284","kind":"arxiv","version":1}},"canonical_sha256":"772cc42e88024094068dd985d4cf4434775202ca6aec5970ae745c65a485a3a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"772cc42e88024094068dd985d4cf4434775202ca6aec5970ae745c65a485a3a8","first_computed_at":"2026-05-18T00:06:20.199688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:20.199688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"09KTDTdtG+FjpqRQdx11iNkdaYEPMEgLiSTwKfsBU9Z7D3XILwBtWMjXKSoeK/F49dhbJz42FVoIOo9XIFYrAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:20.200298Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.10284","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98272f5aeb337aaacd94fa74cff2fdd1b5c9f378ee6f4fa76815591e233a5e67","sha256:a8b11ca5f6cce0b835b0425cefe1628b0954786cd7185584bc960966d9582864"],"state_sha256":"6a0a8dfd47543d43cfbc015f9f1114b627ca1f5e6e66264851b0d2a11fe83ddc"}