{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2YPJTQ2VCP3FLZXYVFCQ5BHO7U","short_pith_number":"pith:2YPJTQ2V","canonical_record":{"source":{"id":"1508.01352","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-08-06T10:34:44Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"e334396ac7f6b6b46aa375bd69d430b450df6a3b4fe8db6467857202fa9e495b","abstract_canon_sha256":"f083f83d3ca3fb523ccaf37f89e3a15c9fe05f1f6bbc0977cdbc75c4069775da"},"schema_version":"1.0"},"canonical_sha256":"d61e99c35513f655e6f8a9450e84eefd3b944e2d90271748baf1ae55a736a6d5","source":{"kind":"arxiv","id":"1508.01352","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01352","created_at":"2026-05-18T01:22:20Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01352v1","created_at":"2026-05-18T01:22:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01352","created_at":"2026-05-18T01:22:20Z"},{"alias_kind":"pith_short_12","alias_value":"2YPJTQ2VCP3F","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2YPJTQ2VCP3FLZXY","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2YPJTQ2V","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2YPJTQ2VCP3FLZXYVFCQ5BHO7U","target":"record","payload":{"canonical_record":{"source":{"id":"1508.01352","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-08-06T10:34:44Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"e334396ac7f6b6b46aa375bd69d430b450df6a3b4fe8db6467857202fa9e495b","abstract_canon_sha256":"f083f83d3ca3fb523ccaf37f89e3a15c9fe05f1f6bbc0977cdbc75c4069775da"},"schema_version":"1.0"},"canonical_sha256":"d61e99c35513f655e6f8a9450e84eefd3b944e2d90271748baf1ae55a736a6d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:20.619396Z","signature_b64":"eYHAZJkIRRdDLikYDhFSZPp0Gc0o9Bb696F9UqZZhRxTfH9LRuJ/9CNITFdkK9xyU2KhdPgcgOfcGygvpx0ADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d61e99c35513f655e6f8a9450e84eefd3b944e2d90271748baf1ae55a736a6d5","last_reissued_at":"2026-05-18T01:22:20.618677Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:20.618677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.01352","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":"2026-05-18T01:22:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1SGjVwEWlHY0iJ97B95ZfEVMEtPI0TlnT+pVpAR7CTaUY1ndyBEWeJEy9BQYW1YCj00xTh8oRE2dmfX43H/4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T23:39:22.632626Z"},"content_sha256":"4f05ffaeeff2b2b703c4b5519364efb5a5acb5f6f27570e43c827b0daea7c402","schema_version":"1.0","event_id":"sha256:4f05ffaeeff2b2b703c4b5519364efb5a5acb5f6f27570e43c827b0daea7c402"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2YPJTQ2VCP3FLZXYVFCQ5BHO7U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Resilience of Networks Formed of Interdependent Modular Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"Louis Shekhtman, Saray Shai, Shlomo Havlin","submitted_at":"2015-08-06T10:34:44Z","abstract_excerpt":"Many infrastructure networks have a modular structure and are also interdependent. While significant research has explored the resilience of interdependent networks, there has been no analysis of the effects of modularity. Here we develop a theoretical framework for attacks on interdependent modular networks and support our results by simulations. We focus on the case where each network has the same number of communities and the dependency links are restricted to be between pairs of communities of different networks. This is very realistic for infrastructure across cities. Each city has its ow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01352","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":"2026-05-18T01:22:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Kr9L52AYCTjKxOxEUs+yoELMSkoPMy3zVXwVZr8La5yo/lC21xljS6e7iDyp+1Gbp/dF3+i77kpwvGv34skBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T23:39:22.633358Z"},"content_sha256":"03b8d33ec02ac1177ab1d0d6bd5c6dd9ac4700e21620a83f216073f482d7446f","schema_version":"1.0","event_id":"sha256:03b8d33ec02ac1177ab1d0d6bd5c6dd9ac4700e21620a83f216073f482d7446f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2YPJTQ2VCP3FLZXYVFCQ5BHO7U/bundle.json","state_url":"https://pith.science/pith/2YPJTQ2VCP3FLZXYVFCQ5BHO7U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2YPJTQ2VCP3FLZXYVFCQ5BHO7U/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":"2026-05-23T23:39:22Z","links":{"resolver":"https://pith.science/pith/2YPJTQ2VCP3FLZXYVFCQ5BHO7U","bundle":"https://pith.science/pith/2YPJTQ2VCP3FLZXYVFCQ5BHO7U/bundle.json","state":"https://pith.science/pith/2YPJTQ2VCP3FLZXYVFCQ5BHO7U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2YPJTQ2VCP3FLZXYVFCQ5BHO7U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2YPJTQ2VCP3FLZXYVFCQ5BHO7U","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":"f083f83d3ca3fb523ccaf37f89e3a15c9fe05f1f6bbc0977cdbc75c4069775da","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-08-06T10:34:44Z","title_canon_sha256":"e334396ac7f6b6b46aa375bd69d430b450df6a3b4fe8db6467857202fa9e495b"},"schema_version":"1.0","source":{"id":"1508.01352","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01352","created_at":"2026-05-18T01:22:20Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01352v1","created_at":"2026-05-18T01:22:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01352","created_at":"2026-05-18T01:22:20Z"},{"alias_kind":"pith_short_12","alias_value":"2YPJTQ2VCP3F","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2YPJTQ2VCP3FLZXY","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2YPJTQ2V","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:03b8d33ec02ac1177ab1d0d6bd5c6dd9ac4700e21620a83f216073f482d7446f","target":"graph","created_at":"2026-05-18T01:22:20Z","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":"Many infrastructure networks have a modular structure and are also interdependent. While significant research has explored the resilience of interdependent networks, there has been no analysis of the effects of modularity. Here we develop a theoretical framework for attacks on interdependent modular networks and support our results by simulations. We focus on the case where each network has the same number of communities and the dependency links are restricted to be between pairs of communities of different networks. This is very realistic for infrastructure across cities. Each city has its ow","authors_text":"Louis Shekhtman, Saray Shai, Shlomo Havlin","cross_cats":["cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-08-06T10:34:44Z","title":"Resilience of Networks Formed of Interdependent Modular Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01352","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":"sha256:4f05ffaeeff2b2b703c4b5519364efb5a5acb5f6f27570e43c827b0daea7c402","target":"record","created_at":"2026-05-18T01:22:20Z","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":"f083f83d3ca3fb523ccaf37f89e3a15c9fe05f1f6bbc0977cdbc75c4069775da","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-08-06T10:34:44Z","title_canon_sha256":"e334396ac7f6b6b46aa375bd69d430b450df6a3b4fe8db6467857202fa9e495b"},"schema_version":"1.0","source":{"id":"1508.01352","kind":"arxiv","version":1}},"canonical_sha256":"d61e99c35513f655e6f8a9450e84eefd3b944e2d90271748baf1ae55a736a6d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d61e99c35513f655e6f8a9450e84eefd3b944e2d90271748baf1ae55a736a6d5","first_computed_at":"2026-05-18T01:22:20.618677Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:20.618677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eYHAZJkIRRdDLikYDhFSZPp0Gc0o9Bb696F9UqZZhRxTfH9LRuJ/9CNITFdkK9xyU2KhdPgcgOfcGygvpx0ADg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:20.619396Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01352","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f05ffaeeff2b2b703c4b5519364efb5a5acb5f6f27570e43c827b0daea7c402","sha256:03b8d33ec02ac1177ab1d0d6bd5c6dd9ac4700e21620a83f216073f482d7446f"],"state_sha256":"8c414acc9f98c9a70b4ff476ecb682ebffca74bbe007e941225b2a3764a5040e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jzV7QmVBsxVRZzDHC3MP4sBItuv2jGrBlL51+WMbGCB+hQdDTpzgYgY7sst/sG2m5Ty+s/tSSpEGCdG2+8vaCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T23:39:22.637106Z","bundle_sha256":"a2a84060c5120e629f8cf4dc6be441d2d41ecbdf8392371a4dfe56ad93c18589"}}