{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:Z3HL7GBPPEB4MGACJLAUM42Q2C","short_pith_number":"pith:Z3HL7GBP","canonical_record":{"source":{"id":"1702.07754","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-24T20:50:36Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"9fea737d64e4c10a626af0eefbfa7d10bf4936559c816189816950d1e543568f","abstract_canon_sha256":"cfbd1379db1545d0daeb1f103041755211756dfc85d2f57f288701a89149974f"},"schema_version":"1.0"},"canonical_sha256":"cecebf982f7903c618024ac1467350d09b676c9851b4d0aeb6264f389a72ceba","source":{"kind":"arxiv","id":"1702.07754","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.07754","created_at":"2026-05-18T00:44:33Z"},{"alias_kind":"arxiv_version","alias_value":"1702.07754v3","created_at":"2026-05-18T00:44:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.07754","created_at":"2026-05-18T00:44:33Z"},{"alias_kind":"pith_short_12","alias_value":"Z3HL7GBPPEB4","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z3HL7GBPPEB4MGAC","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z3HL7GBP","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:Z3HL7GBPPEB4MGACJLAUM42Q2C","target":"record","payload":{"canonical_record":{"source":{"id":"1702.07754","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-24T20:50:36Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"9fea737d64e4c10a626af0eefbfa7d10bf4936559c816189816950d1e543568f","abstract_canon_sha256":"cfbd1379db1545d0daeb1f103041755211756dfc85d2f57f288701a89149974f"},"schema_version":"1.0"},"canonical_sha256":"cecebf982f7903c618024ac1467350d09b676c9851b4d0aeb6264f389a72ceba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:33.448476Z","signature_b64":"PIuafOXwmu/YpH6LP9ijT1CxrXPhQ6+SbcUrM8NB0kkIRYW1mhFsgkd44y/3RT0cvpm2c2eGA13UKuJiZoQTBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cecebf982f7903c618024ac1467350d09b676c9851b4d0aeb6264f389a72ceba","last_reissued_at":"2026-05-18T00:44:33.448098Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:33.448098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.07754","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":"2026-05-18T00:44:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ayj/qLeFSz5GfUyn2rZpJhc7ezLeB11LEhUVP7Hg4r7sNRT6wowcVyfQwMUt1sMyFtkTqX/bfhPJXT1o5jjwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:09:31.150805Z"},"content_sha256":"def9bac05ddd6a0ee5d72997d3ad4c8eb14e95becd07f6b1f6dd2a29fff10543","schema_version":"1.0","event_id":"sha256:def9bac05ddd6a0ee5d72997d3ad4c8eb14e95becd07f6b1f6dd2a29fff10543"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:Z3HL7GBPPEB4MGACJLAUM42Q2C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-Competitive Viruses over Static and Time--Varying Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"Angelia Nedi\\'c, Carolyn L. Beck, Ji Liu, Philip E. Par\\'e, Tamer Ba\\c{s}ar","submitted_at":"2017-02-24T20:50:36Z","abstract_excerpt":"Epidemic processes are used commonly for modeling and analysis of biological networks, computer networks, and human contact networks. The idea of competing viruses has been explored recently, motivated by the spread of different ideas along different social networks. Previous studies of competitive viruses have focused only on two viruses and on static graph structures. In this paper, we consider multiple competing viruses over static and dynamic graph structures, and investigate the eradication and propagation of diseases in these systems. Stability analysis for the class of models we conside"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07754","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":"2026-05-18T00:44:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1tEW5KWeECNVt+mWD87sFenquwXXWWgglyByvQhyfECBCWqPPOJ1aV5oUNFVnSJnGus16RFpr858Jvdfoj+7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:09:31.151143Z"},"content_sha256":"1ab19fdd34f048b610b52eb77c253823984b4cf5ad9fd04f556474f423ae8852","schema_version":"1.0","event_id":"sha256:1ab19fdd34f048b610b52eb77c253823984b4cf5ad9fd04f556474f423ae8852"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z3HL7GBPPEB4MGACJLAUM42Q2C/bundle.json","state_url":"https://pith.science/pith/Z3HL7GBPPEB4MGACJLAUM42Q2C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z3HL7GBPPEB4MGACJLAUM42Q2C/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":"2026-06-23T03:09:31Z","links":{"resolver":"https://pith.science/pith/Z3HL7GBPPEB4MGACJLAUM42Q2C","bundle":"https://pith.science/pith/Z3HL7GBPPEB4MGACJLAUM42Q2C/bundle.json","state":"https://pith.science/pith/Z3HL7GBPPEB4MGACJLAUM42Q2C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z3HL7GBPPEB4MGACJLAUM42Q2C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Z3HL7GBPPEB4MGACJLAUM42Q2C","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":"cfbd1379db1545d0daeb1f103041755211756dfc85d2f57f288701a89149974f","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-24T20:50:36Z","title_canon_sha256":"9fea737d64e4c10a626af0eefbfa7d10bf4936559c816189816950d1e543568f"},"schema_version":"1.0","source":{"id":"1702.07754","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.07754","created_at":"2026-05-18T00:44:33Z"},{"alias_kind":"arxiv_version","alias_value":"1702.07754v3","created_at":"2026-05-18T00:44:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.07754","created_at":"2026-05-18T00:44:33Z"},{"alias_kind":"pith_short_12","alias_value":"Z3HL7GBPPEB4","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z3HL7GBPPEB4MGAC","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z3HL7GBP","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:1ab19fdd34f048b610b52eb77c253823984b4cf5ad9fd04f556474f423ae8852","target":"graph","created_at":"2026-05-18T00:44:33Z","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":"Epidemic processes are used commonly for modeling and analysis of biological networks, computer networks, and human contact networks. The idea of competing viruses has been explored recently, motivated by the spread of different ideas along different social networks. Previous studies of competitive viruses have focused only on two viruses and on static graph structures. In this paper, we consider multiple competing viruses over static and dynamic graph structures, and investigate the eradication and propagation of diseases in these systems. Stability analysis for the class of models we conside","authors_text":"Angelia Nedi\\'c, Carolyn L. Beck, Ji Liu, Philip E. Par\\'e, Tamer Ba\\c{s}ar","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-24T20:50:36Z","title":"Multi-Competitive Viruses over Static and Time--Varying Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07754","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:def9bac05ddd6a0ee5d72997d3ad4c8eb14e95becd07f6b1f6dd2a29fff10543","target":"record","created_at":"2026-05-18T00:44:33Z","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":"cfbd1379db1545d0daeb1f103041755211756dfc85d2f57f288701a89149974f","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-24T20:50:36Z","title_canon_sha256":"9fea737d64e4c10a626af0eefbfa7d10bf4936559c816189816950d1e543568f"},"schema_version":"1.0","source":{"id":"1702.07754","kind":"arxiv","version":3}},"canonical_sha256":"cecebf982f7903c618024ac1467350d09b676c9851b4d0aeb6264f389a72ceba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cecebf982f7903c618024ac1467350d09b676c9851b4d0aeb6264f389a72ceba","first_computed_at":"2026-05-18T00:44:33.448098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:33.448098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PIuafOXwmu/YpH6LP9ijT1CxrXPhQ6+SbcUrM8NB0kkIRYW1mhFsgkd44y/3RT0cvpm2c2eGA13UKuJiZoQTBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:33.448476Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.07754","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:def9bac05ddd6a0ee5d72997d3ad4c8eb14e95becd07f6b1f6dd2a29fff10543","sha256:1ab19fdd34f048b610b52eb77c253823984b4cf5ad9fd04f556474f423ae8852"],"state_sha256":"f799f2a6069c9df6dfbab8533605f9ffb0b3cf794614e3768ed0dcb05717ae74"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FciuKcfw1nBzCIw1x04yiI8aRc5L+q2r2Pa5OOesF93zbMyoLE1BLAULbxVWspjyro9nw0Tx5NCpaWMt8hf3AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T03:09:31.153047Z","bundle_sha256":"023fc45dc4d52c499378b5655ec19f62b7d77133177a020bc511f812c6e8319c"}}