{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:V2API3YATBHRFJTTWFYTTM4PFS","short_pith_number":"pith:V2API3YA","canonical_record":{"source":{"id":"1211.5937","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-11-26T12:50:43Z","cross_cats_sorted":["cs.SI","physics.soc-ph"],"title_canon_sha256":"988614f8e1d451a7c0c4c131def5d2e37df7da667b9f5cdcf327e088ab842d44","abstract_canon_sha256":"79c90d0063f57d5186577f58c152ad0bccb496e91fd35279a1a67753941c40f9"},"schema_version":"1.0"},"canonical_sha256":"ae80f46f00984f12a673b17139b38f2c8a502bd3b6b1c437881634a5eb3235af","source":{"kind":"arxiv","id":"1211.5937","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5937","created_at":"2026-05-18T02:40:04Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5937v3","created_at":"2026-05-18T02:40:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5937","created_at":"2026-05-18T02:40:04Z"},{"alias_kind":"pith_short_12","alias_value":"V2API3YATBHR","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"V2API3YATBHRFJTT","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"V2API3YA","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:V2API3YATBHRFJTTWFYTTM4PFS","target":"record","payload":{"canonical_record":{"source":{"id":"1211.5937","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-11-26T12:50:43Z","cross_cats_sorted":["cs.SI","physics.soc-ph"],"title_canon_sha256":"988614f8e1d451a7c0c4c131def5d2e37df7da667b9f5cdcf327e088ab842d44","abstract_canon_sha256":"79c90d0063f57d5186577f58c152ad0bccb496e91fd35279a1a67753941c40f9"},"schema_version":"1.0"},"canonical_sha256":"ae80f46f00984f12a673b17139b38f2c8a502bd3b6b1c437881634a5eb3235af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:04.109155Z","signature_b64":"U82/1zkBuY/Fk2wHdwwFt+/nqFYXa1pP59Epj1mg9e0Nvm+8by54PERrEtwyx70B65nl0LSruiXmPkh788swAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae80f46f00984f12a673b17139b38f2c8a502bd3b6b1c437881634a5eb3235af","last_reissued_at":"2026-05-18T02:40:04.108680Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:04.108680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.5937","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:40:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YnxnlLapxpaE4CjiPX4ERQXnPrYS30VwbNA2/wZRahSdsNlRarS6uv8Vrfl2gAzXFcGNGfe6FS2Uf5IQtyy6Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:11:57.814496Z"},"content_sha256":"a3a3a95c5208e3288f06ede07186fe22af76de5dc9e875f7134a667350205809","schema_version":"1.0","event_id":"sha256:a3a3a95c5208e3288f06ede07186fe22af76de5dc9e875f7134a667350205809"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:V2API3YATBHRFJTTWFYTTM4PFS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Comparing the reliability of networks by spectral analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Kwok Yip Szeto, Zitao Wang","submitted_at":"2012-11-26T12:50:43Z","abstract_excerpt":"We provide a method for the ranking of the reliability of two networks with the same connectance. Our method is based on the Cheeger constant linking the topological property of a network with its spectrum. We first analyze a set of twisted rings with the same connectance and degree distribution, and obtain the ranking of their reliability using their eigenvalue gaps. The results are generalized to general networks using the method of rewiring. The success of our ranking method is verified numerically for the IEEE57, the Erd\\H{o}s-R\\'enyi, and the Small-World networks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5937","kind":"arxiv","version":3},"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":"2026-05-18T02:40:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1bz5NiZbUaxvHsXHkrLeY5IUJGsZUK90UY9S9FUrMR9PclONt4jOfqzoCEgp1tZQGWQeyMLFqY7GuQDLBy9gAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:11:57.814862Z"},"content_sha256":"9cb147bf92f9f87efe76b102f425bb807e287eee7acb1fb7c40747bd75e48097","schema_version":"1.0","event_id":"sha256:9cb147bf92f9f87efe76b102f425bb807e287eee7acb1fb7c40747bd75e48097"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V2API3YATBHRFJTTWFYTTM4PFS/bundle.json","state_url":"https://pith.science/pith/V2API3YATBHRFJTTWFYTTM4PFS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V2API3YATBHRFJTTWFYTTM4PFS/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":"2026-05-28T11:11:57Z","links":{"resolver":"https://pith.science/pith/V2API3YATBHRFJTTWFYTTM4PFS","bundle":"https://pith.science/pith/V2API3YATBHRFJTTWFYTTM4PFS/bundle.json","state":"https://pith.science/pith/V2API3YATBHRFJTTWFYTTM4PFS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V2API3YATBHRFJTTWFYTTM4PFS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:V2API3YATBHRFJTTWFYTTM4PFS","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":"79c90d0063f57d5186577f58c152ad0bccb496e91fd35279a1a67753941c40f9","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-11-26T12:50:43Z","title_canon_sha256":"988614f8e1d451a7c0c4c131def5d2e37df7da667b9f5cdcf327e088ab842d44"},"schema_version":"1.0","source":{"id":"1211.5937","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5937","created_at":"2026-05-18T02:40:04Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5937v3","created_at":"2026-05-18T02:40:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5937","created_at":"2026-05-18T02:40:04Z"},{"alias_kind":"pith_short_12","alias_value":"V2API3YATBHR","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"V2API3YATBHRFJTT","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"V2API3YA","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:9cb147bf92f9f87efe76b102f425bb807e287eee7acb1fb7c40747bd75e48097","target":"graph","created_at":"2026-05-18T02:40:04Z","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 provide a method for the ranking of the reliability of two networks with the same connectance. Our method is based on the Cheeger constant linking the topological property of a network with its spectrum. We first analyze a set of twisted rings with the same connectance and degree distribution, and obtain the ranking of their reliability using their eigenvalue gaps. The results are generalized to general networks using the method of rewiring. The success of our ranking method is verified numerically for the IEEE57, the Erd\\H{o}s-R\\'enyi, and the Small-World networks.","authors_text":"Kwok Yip Szeto, Zitao Wang","cross_cats":["cs.SI","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-11-26T12:50:43Z","title":"Comparing the reliability of networks by spectral analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5937","kind":"arxiv","version":3},"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:a3a3a95c5208e3288f06ede07186fe22af76de5dc9e875f7134a667350205809","target":"record","created_at":"2026-05-18T02:40:04Z","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":"79c90d0063f57d5186577f58c152ad0bccb496e91fd35279a1a67753941c40f9","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-11-26T12:50:43Z","title_canon_sha256":"988614f8e1d451a7c0c4c131def5d2e37df7da667b9f5cdcf327e088ab842d44"},"schema_version":"1.0","source":{"id":"1211.5937","kind":"arxiv","version":3}},"canonical_sha256":"ae80f46f00984f12a673b17139b38f2c8a502bd3b6b1c437881634a5eb3235af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae80f46f00984f12a673b17139b38f2c8a502bd3b6b1c437881634a5eb3235af","first_computed_at":"2026-05-18T02:40:04.108680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:04.108680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U82/1zkBuY/Fk2wHdwwFt+/nqFYXa1pP59Epj1mg9e0Nvm+8by54PERrEtwyx70B65nl0LSruiXmPkh788swAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:04.109155Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.5937","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3a3a95c5208e3288f06ede07186fe22af76de5dc9e875f7134a667350205809","sha256:9cb147bf92f9f87efe76b102f425bb807e287eee7acb1fb7c40747bd75e48097"],"state_sha256":"9a73e29bc6a5704d065b74db164049fbc8c4cc69527ab57cee07e798d5046838"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G+XseiCd9OHJ8NPKKHtmAA6TEmsCSoJ+gYSl+WFDwShtf8oWkiIvl8ZU13BO2/4q1KcNAwnXXa5GhxxJZooTDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:11:57.816827Z","bundle_sha256":"8c9c84c2f372c10b842784ea4810e864a289720c96a3eaca788258e1a8f49a0f"}}