{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TE3PDMHEA576DSQQ6XLZOGKLLV","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":"85adec742c1da646976b5fa50a5ed856a581edf9af9a4cad89e3180cd0d87b68","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2013-08-06T09:13:03Z","title_canon_sha256":"3ae30784ef0242ff4c17770262f657ec500569aa6c30999a7eaa80431b657ae4"},"schema_version":"1.0","source":{"id":"1308.1210","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1210","created_at":"2026-05-18T02:59:34Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1210v2","created_at":"2026-05-18T02:59:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1210","created_at":"2026-05-18T02:59:34Z"},{"alias_kind":"pith_short_12","alias_value":"TE3PDMHEA576","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TE3PDMHEA576DSQQ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TE3PDMHE","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:3af90452fbee69c117631c8e8961e138d98454229fcab1cd6e2796fcf5d8be6a","target":"graph","created_at":"2026-05-18T02:59:34Z","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 develop a methodology for analyzing the percolation phenomena of two mutually coupled (interdependent) networks based on the cavity method of statistical mechanics. In particular, we take into account the influence of degree-degree correlations inside and between the networks on the network robustness against targeted attacks and random failures. We show that the developed methodology is reduced to the well-known generating function formalism in the absence of degree-degree correlations. The validity of the developed methodology is confirmed by a comparison with the results of numerical exp","authors_text":"Shunsuke Watanabe, Yoshiyuki Kabashima","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2013-08-06T09:13:03Z","title":"Cavity-based robustness analysis of interdependent networks: Influences of intranetwork and internetwork degree-degree correlations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1210","kind":"arxiv","version":2},"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:a729111beae2b4476d2dc1b5182765247c0ff841b787025c262d2a99fedfaf59","target":"record","created_at":"2026-05-18T02:59:34Z","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":"85adec742c1da646976b5fa50a5ed856a581edf9af9a4cad89e3180cd0d87b68","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2013-08-06T09:13:03Z","title_canon_sha256":"3ae30784ef0242ff4c17770262f657ec500569aa6c30999a7eaa80431b657ae4"},"schema_version":"1.0","source":{"id":"1308.1210","kind":"arxiv","version":2}},"canonical_sha256":"9936f1b0e4077fe1ca10f5d797194b5d405f63d90b7dd989773be3620a0dfd71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9936f1b0e4077fe1ca10f5d797194b5d405f63d90b7dd989773be3620a0dfd71","first_computed_at":"2026-05-18T02:59:34.784513Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:34.784513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cGAj3t/rXQ3+LKdTG9I/kyt9uX4CMhQKxOfOzjSV+oklcVS9rnz6OuxrqutL+UDmQn+LwnyO6CHouHTH1TJEAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:34.789358Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.1210","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a729111beae2b4476d2dc1b5182765247c0ff841b787025c262d2a99fedfaf59","sha256:3af90452fbee69c117631c8e8961e138d98454229fcab1cd6e2796fcf5d8be6a"],"state_sha256":"ed2069982e700be54c7ae485cca19fc98e76ee0e4d339b0fc6d6bf1cf268404a"}