{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:O4WMILUIAJAJIBUN3GC5JT2EGR","short_pith_number":"pith:O4WMILUI","canonical_record":{"source":{"id":"1805.10284","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-05-25T13:38:31Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"82160cc2da0725371a549e912422e339d72bbfaf0d61f25f32166ba00ec73fbf","abstract_canon_sha256":"ce9dec4ebfb574a3a18c59d2b302a7306534fb388adf1493d693f9c3019eebe5"},"schema_version":"1.0"},"canonical_sha256":"772cc42e88024094068dd985d4cf4434775202ca6aec5970ae745c65a485a3a8","source":{"kind":"arxiv","id":"1805.10284","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:O4WMILUIAJAJIBUN3GC5JT2EGR","target":"record","payload":{"canonical_record":{"source":{"id":"1805.10284","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-05-25T13:38:31Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"82160cc2da0725371a549e912422e339d72bbfaf0d61f25f32166ba00ec73fbf","abstract_canon_sha256":"ce9dec4ebfb574a3a18c59d2b302a7306534fb388adf1493d693f9c3019eebe5"},"schema_version":"1.0"},"canonical_sha256":"772cc42e88024094068dd985d4cf4434775202ca6aec5970ae745c65a485a3a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:20.200298Z","signature_b64":"09KTDTdtG+FjpqRQdx11iNkdaYEPMEgLiSTwKfsBU9Z7D3XILwBtWMjXKSoeK/F49dhbJz42FVoIOo9XIFYrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"772cc42e88024094068dd985d4cf4434775202ca6aec5970ae745c65a485a3a8","last_reissued_at":"2026-05-18T00:06:20.199688Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:20.199688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.10284","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":"2026-05-18T00:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qPtlr0dkcuK+BPoclEzOCbHXJBd6AnfhR49//9YuGA8iT4Dl9VmsU54rqEwSRaILxjwkSzlyaXEbtsBWPdU0Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:30:46.689581Z"},"content_sha256":"98272f5aeb337aaacd94fa74cff2fdd1b5c9f378ee6f4fa76815591e233a5e67","schema_version":"1.0","event_id":"sha256:98272f5aeb337aaacd94fa74cff2fdd1b5c9f378ee6f4fa76815591e233a5e67"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:O4WMILUIAJAJIBUN3GC5JT2EGR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of fluctuations in the first return times of random walks on regular branched networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"cond-mat.stat-mech","authors_text":"Guoai Xu, H. Eugene Stanley, Junhao Peng, Lin Chen, Renxiang Shao","submitted_at":"2018-05-25T13:38:31Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10284","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":"2026-05-18T00:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y3sQECYQQW0xVIh8VW2P2PqZ300tLx9UkAsGYjmWOzH8yaecUxKNs/OMlQCVcmr9IsQHo86e4M2ZGW2+VqQcCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:30:46.690002Z"},"content_sha256":"a8b11ca5f6cce0b835b0425cefe1628b0954786cd7185584bc960966d9582864","schema_version":"1.0","event_id":"sha256:a8b11ca5f6cce0b835b0425cefe1628b0954786cd7185584bc960966d9582864"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O4WMILUIAJAJIBUN3GC5JT2EGR/bundle.json","state_url":"https://pith.science/pith/O4WMILUIAJAJIBUN3GC5JT2EGR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O4WMILUIAJAJIBUN3GC5JT2EGR/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":"2026-05-29T20:30:46Z","links":{"resolver":"https://pith.science/pith/O4WMILUIAJAJIBUN3GC5JT2EGR","bundle":"https://pith.science/pith/O4WMILUIAJAJIBUN3GC5JT2EGR/bundle.json","state":"https://pith.science/pith/O4WMILUIAJAJIBUN3GC5JT2EGR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O4WMILUIAJAJIBUN3GC5JT2EGR/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vdFn6IrQAqb4tXQxi6g+im0vJuUGBctyCW73rPm1ReyHwXcnwkfsUQzAutbvGrKo5Ty6U+YZI7n0QrMBHp4wDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T20:30:46.693351Z","bundle_sha256":"582a81397a06f4a7ed5da2ba7b57670da0d982ac5d36c23ba9c7222d6bf01290"}}