{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EM45WAQTVVBFP5GY5OEWN4T3GJ","short_pith_number":"pith:EM45WAQT","canonical_record":{"source":{"id":"1603.08307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2016-03-28T04:52:04Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"0111a1771f17e242f179687b868f24066ac0df96d2d679db02de3ed7b530a651","abstract_canon_sha256":"c461dbe90ac96cde135ce1eb4366e0e36609d7e337965eb32244c0b836ee669e"},"schema_version":"1.0"},"canonical_sha256":"2339db0213ad4257f4d8eb8966f27b327a5efd89d73bd40c69b4bcdd1e41ce56","source":{"kind":"arxiv","id":"1603.08307","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08307","created_at":"2026-05-18T01:18:11Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08307v1","created_at":"2026-05-18T01:18:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08307","created_at":"2026-05-18T01:18:11Z"},{"alias_kind":"pith_short_12","alias_value":"EM45WAQTVVBF","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EM45WAQTVVBFP5GY","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EM45WAQT","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EM45WAQTVVBFP5GY5OEWN4T3GJ","target":"record","payload":{"canonical_record":{"source":{"id":"1603.08307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2016-03-28T04:52:04Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"0111a1771f17e242f179687b868f24066ac0df96d2d679db02de3ed7b530a651","abstract_canon_sha256":"c461dbe90ac96cde135ce1eb4366e0e36609d7e337965eb32244c0b836ee669e"},"schema_version":"1.0"},"canonical_sha256":"2339db0213ad4257f4d8eb8966f27b327a5efd89d73bd40c69b4bcdd1e41ce56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:11.063198Z","signature_b64":"rwSbFVvi/W7IrcKEW6GyWc9SoFN2WhOSdZOfrkFpPGmhXyViv2jEJrqhfGtTINFAFKYZNKBo5uBpoFMgMC/0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2339db0213ad4257f4d8eb8966f27b327a5efd89d73bd40c69b4bcdd1e41ce56","last_reissued_at":"2026-05-18T01:18:11.062620Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:11.062620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.08307","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":"2026-05-18T01:18:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5/VdIV2x/DvLlckKcp9FasU+gYKNB6puFrM5ccHfhc/H6UgySHU6oHvdmuAZ5klWkM0tKGhrBo4D+pwccgKOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:00:30.736692Z"},"content_sha256":"afe2842dd0ba01f2b12876cb3aa312121d9a9e96f9ed1e078170b461d7f59162","schema_version":"1.0","event_id":"sha256:afe2842dd0ba01f2b12876cb3aa312121d9a9e96f9ed1e078170b461d7f59162"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EM45WAQTVVBFP5GY5OEWN4T3GJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cyber Epidemic Models with Dependences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"cs.CR","authors_text":"Gaofeng Da, Maochao Xu, Shouhuai Xu","submitted_at":"2016-03-28T04:52:04Z","abstract_excerpt":"Studying models of cyber epidemics over arbitrary complex networks can deepen our understanding of cyber security from a whole-system perspective. In this paper, we initiate the investigation of cyber epidemic models that accommodate the {\\em dependences} between the cyber attack events. Due to the notorious difficulty in dealing with such dependences, essentially all existing cyber epidemic models have assumed them away. Specifically, we introduce the idea of Copulas into cyber epidemic models for accommodating the dependences between the cyber attack events. We investigate the epidemic equil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08307","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":"2026-05-18T01:18:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"do33HKTDFr+jJ2pW0uy3oFdpJ3CQ37Fz0BZClsC5qV3hz5TEJKZH0djztrDa7HBGvLTycii5ou7/zYHG+j4MBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:00:30.737036Z"},"content_sha256":"06a8826f369c6231171ccdf3ed95dd2e8bcae74665aaba9b7a6c9c2bca5fe2fd","schema_version":"1.0","event_id":"sha256:06a8826f369c6231171ccdf3ed95dd2e8bcae74665aaba9b7a6c9c2bca5fe2fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EM45WAQTVVBFP5GY5OEWN4T3GJ/bundle.json","state_url":"https://pith.science/pith/EM45WAQTVVBFP5GY5OEWN4T3GJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EM45WAQTVVBFP5GY5OEWN4T3GJ/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":"2026-06-03T21:00:30Z","links":{"resolver":"https://pith.science/pith/EM45WAQTVVBFP5GY5OEWN4T3GJ","bundle":"https://pith.science/pith/EM45WAQTVVBFP5GY5OEWN4T3GJ/bundle.json","state":"https://pith.science/pith/EM45WAQTVVBFP5GY5OEWN4T3GJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EM45WAQTVVBFP5GY5OEWN4T3GJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EM45WAQTVVBFP5GY5OEWN4T3GJ","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":"c461dbe90ac96cde135ce1eb4366e0e36609d7e337965eb32244c0b836ee669e","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2016-03-28T04:52:04Z","title_canon_sha256":"0111a1771f17e242f179687b868f24066ac0df96d2d679db02de3ed7b530a651"},"schema_version":"1.0","source":{"id":"1603.08307","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08307","created_at":"2026-05-18T01:18:11Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08307v1","created_at":"2026-05-18T01:18:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08307","created_at":"2026-05-18T01:18:11Z"},{"alias_kind":"pith_short_12","alias_value":"EM45WAQTVVBF","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EM45WAQTVVBFP5GY","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EM45WAQT","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:06a8826f369c6231171ccdf3ed95dd2e8bcae74665aaba9b7a6c9c2bca5fe2fd","target":"graph","created_at":"2026-05-18T01:18:11Z","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":"Studying models of cyber epidemics over arbitrary complex networks can deepen our understanding of cyber security from a whole-system perspective. In this paper, we initiate the investigation of cyber epidemic models that accommodate the {\\em dependences} between the cyber attack events. Due to the notorious difficulty in dealing with such dependences, essentially all existing cyber epidemic models have assumed them away. Specifically, we introduce the idea of Copulas into cyber epidemic models for accommodating the dependences between the cyber attack events. We investigate the epidemic equil","authors_text":"Gaofeng Da, Maochao Xu, Shouhuai Xu","cross_cats":["cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2016-03-28T04:52:04Z","title":"Cyber Epidemic Models with Dependences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08307","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:afe2842dd0ba01f2b12876cb3aa312121d9a9e96f9ed1e078170b461d7f59162","target":"record","created_at":"2026-05-18T01:18:11Z","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":"c461dbe90ac96cde135ce1eb4366e0e36609d7e337965eb32244c0b836ee669e","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2016-03-28T04:52:04Z","title_canon_sha256":"0111a1771f17e242f179687b868f24066ac0df96d2d679db02de3ed7b530a651"},"schema_version":"1.0","source":{"id":"1603.08307","kind":"arxiv","version":1}},"canonical_sha256":"2339db0213ad4257f4d8eb8966f27b327a5efd89d73bd40c69b4bcdd1e41ce56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2339db0213ad4257f4d8eb8966f27b327a5efd89d73bd40c69b4bcdd1e41ce56","first_computed_at":"2026-05-18T01:18:11.062620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:11.062620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rwSbFVvi/W7IrcKEW6GyWc9SoFN2WhOSdZOfrkFpPGmhXyViv2jEJrqhfGtTINFAFKYZNKBo5uBpoFMgMC/0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:11.063198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08307","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afe2842dd0ba01f2b12876cb3aa312121d9a9e96f9ed1e078170b461d7f59162","sha256:06a8826f369c6231171ccdf3ed95dd2e8bcae74665aaba9b7a6c9c2bca5fe2fd"],"state_sha256":"afa0eb2b45d6b754434271d2a70664fd2185b4282a40057fffcef847e59aee97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bnrHEXq+3WY4sed3PmZNdY3yKqnFOPokI03mg0uJaqKr6TxfWaJ5m+yNhrh8eu3T0hlBG9AEh5NqKGFD6LPGBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T21:00:30.739038Z","bundle_sha256":"a8b1bfd4232352730d957d3d1eb52067bf057bae2325b311ebceb08ed53fab4e"}}