{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XT24DXSCQWMWMFSHHXEIUYLG33","short_pith_number":"pith:XT24DXSC","canonical_record":{"source":{"id":"1206.2427","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2012-06-12T02:43:19Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"d7fec1c9c5c64df7f9e82425af9d62cd3633deb24795ce5e39d499bb2e0ef942","abstract_canon_sha256":"48633ade520f619db28f37b2b9f12c112f50f073439ff0e6ce72210b3fbf0bfe"},"schema_version":"1.0"},"canonical_sha256":"bcf5c1de4285996616473dc88a6166def9ed6b112b2ada2855961eabfcc14632","source":{"kind":"arxiv","id":"1206.2427","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2427","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2427v2","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2427","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"pith_short_12","alias_value":"XT24DXSCQWMW","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XT24DXSCQWMWMFSH","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XT24DXSC","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XT24DXSCQWMWMFSHHXEIUYLG33","target":"record","payload":{"canonical_record":{"source":{"id":"1206.2427","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2012-06-12T02:43:19Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"d7fec1c9c5c64df7f9e82425af9d62cd3633deb24795ce5e39d499bb2e0ef942","abstract_canon_sha256":"48633ade520f619db28f37b2b9f12c112f50f073439ff0e6ce72210b3fbf0bfe"},"schema_version":"1.0"},"canonical_sha256":"bcf5c1de4285996616473dc88a6166def9ed6b112b2ada2855961eabfcc14632","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:18.902236Z","signature_b64":"YC7LZrD8+/2PBLwsad/QvNwR4GZc/q/Gs8+GsQgTNN99XCHJsm7pQVehn+BNjq3lX294W3DFIsdTPRFaq9tWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcf5c1de4285996616473dc88a6166def9ed6b112b2ada2855961eabfcc14632","last_reissued_at":"2026-05-18T03:22:18.901497Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:18.901497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.2427","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:22:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b2776+AgwJRPQzP8L2MBbkwtLPiEHOm3Q+sz5CyVzxuLXgnYav+YtSi+J2OJflpNF6qnw6bZ3v7vFkOt50HFBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:27:52.321605Z"},"content_sha256":"4d1936f02f1471c50c0f337bb1c1325dd645222f03094ea8bb692868fc3b5cf7","schema_version":"1.0","event_id":"sha256:4d1936f02f1471c50c0f337bb1c1325dd645222f03094ea8bb692868fc3b5cf7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XT24DXSCQWMWMFSHHXEIUYLG33","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Percolation of Partially Interdependent Scale-free Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"physics.data-an","authors_text":"Di Zhou, H. Eugene Stanley, Jianxi Gao, Shlomo Havlin","submitted_at":"2012-06-12T02:43:19Z","abstract_excerpt":"We study the percolation behavior of two interdependent scale-free (SF) networks under random failure of 1-$p$ fraction of nodes. Our results are based on numerical solutions of analytical expressions and simulations. We find that as the coupling strength between the two networks $q$ reduces from 1 (fully coupled) to 0 (no coupling), there exist two critical coupling strengths $q_1$ and $q_2$, which separate three different regions with different behavior of the giant component as a function of $p$. (i) For $q \\geq q_1$, an abrupt collapse transition occurs at $p=p_c$. (ii) For $q_2<q<q_1$, th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2427","kind":"arxiv","version":2},"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":"2026-05-18T03:22:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yIdiSfJELjQWAJlg1LECkA41rVyzKIHUbzJ8Tjz8zohmUa7q9t5CbqrqSLGn29f2CXrFckMChg9hp8NOZ65nBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:27:52.322044Z"},"content_sha256":"94b5ee1a3b0cbaddea40c90fd5a26443b9f7246268988582c629db393fded18c","schema_version":"1.0","event_id":"sha256:94b5ee1a3b0cbaddea40c90fd5a26443b9f7246268988582c629db393fded18c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XT24DXSCQWMWMFSHHXEIUYLG33/bundle.json","state_url":"https://pith.science/pith/XT24DXSCQWMWMFSHHXEIUYLG33/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XT24DXSCQWMWMFSHHXEIUYLG33/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":"2026-05-29T15:27:52Z","links":{"resolver":"https://pith.science/pith/XT24DXSCQWMWMFSHHXEIUYLG33","bundle":"https://pith.science/pith/XT24DXSCQWMWMFSHHXEIUYLG33/bundle.json","state":"https://pith.science/pith/XT24DXSCQWMWMFSHHXEIUYLG33/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XT24DXSCQWMWMFSHHXEIUYLG33/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XT24DXSCQWMWMFSHHXEIUYLG33","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":"48633ade520f619db28f37b2b9f12c112f50f073439ff0e6ce72210b3fbf0bfe","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2012-06-12T02:43:19Z","title_canon_sha256":"d7fec1c9c5c64df7f9e82425af9d62cd3633deb24795ce5e39d499bb2e0ef942"},"schema_version":"1.0","source":{"id":"1206.2427","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2427","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2427v2","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2427","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"pith_short_12","alias_value":"XT24DXSCQWMW","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XT24DXSCQWMWMFSH","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XT24DXSC","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:94b5ee1a3b0cbaddea40c90fd5a26443b9f7246268988582c629db393fded18c","target":"graph","created_at":"2026-05-18T03:22:18Z","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 study the percolation behavior of two interdependent scale-free (SF) networks under random failure of 1-$p$ fraction of nodes. Our results are based on numerical solutions of analytical expressions and simulations. We find that as the coupling strength between the two networks $q$ reduces from 1 (fully coupled) to 0 (no coupling), there exist two critical coupling strengths $q_1$ and $q_2$, which separate three different regions with different behavior of the giant component as a function of $p$. (i) For $q \\geq q_1$, an abrupt collapse transition occurs at $p=p_c$. (ii) For $q_2<q<q_1$, th","authors_text":"Di Zhou, H. Eugene Stanley, Jianxi Gao, Shlomo Havlin","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2012-06-12T02:43:19Z","title":"Percolation of Partially Interdependent Scale-free Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2427","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":"sha256:4d1936f02f1471c50c0f337bb1c1325dd645222f03094ea8bb692868fc3b5cf7","target":"record","created_at":"2026-05-18T03:22:18Z","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":"48633ade520f619db28f37b2b9f12c112f50f073439ff0e6ce72210b3fbf0bfe","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2012-06-12T02:43:19Z","title_canon_sha256":"d7fec1c9c5c64df7f9e82425af9d62cd3633deb24795ce5e39d499bb2e0ef942"},"schema_version":"1.0","source":{"id":"1206.2427","kind":"arxiv","version":2}},"canonical_sha256":"bcf5c1de4285996616473dc88a6166def9ed6b112b2ada2855961eabfcc14632","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcf5c1de4285996616473dc88a6166def9ed6b112b2ada2855961eabfcc14632","first_computed_at":"2026-05-18T03:22:18.901497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:18.901497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YC7LZrD8+/2PBLwsad/QvNwR4GZc/q/Gs8+GsQgTNN99XCHJsm7pQVehn+BNjq3lX294W3DFIsdTPRFaq9tWAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:18.902236Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.2427","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d1936f02f1471c50c0f337bb1c1325dd645222f03094ea8bb692868fc3b5cf7","sha256:94b5ee1a3b0cbaddea40c90fd5a26443b9f7246268988582c629db393fded18c"],"state_sha256":"6afc1ab7218af1ecd47d90b93df53aba8ab18e69f77287c79995226c6d4f4c46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IBSXCBfsdRh8KhvCAw0MVZl+BV3r513t8amzN9XfqdpgmsCcDgHNqWsTlBBoOgeR5L+RBpntc66iK1pZD6QABg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T15:27:52.325107Z","bundle_sha256":"60a00ffd5f2e06cc271efbf67023c1dab71b92ba182e43747addb14d70a03edd"}}