{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6ET7UBYZR3YYPDDMDETJBVPALM","short_pith_number":"pith:6ET7UBYZ","canonical_record":{"source":{"id":"1711.00784","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-11-02T15:33:31Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"2e152b70b30935701aae20421c92039fe958e2b8c57138178286c2b3191bbed1","abstract_canon_sha256":"f69fbef77663926d452488bdb0a0d151cf2d38941c3ac0c8781e9405f4c45fa2"},"schema_version":"1.0"},"canonical_sha256":"f127fa07198ef1878c6c192690d5e05b1bc0d76a37433285850f033cd0574602","source":{"kind":"arxiv","id":"1711.00784","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.00784","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"arxiv_version","alias_value":"1711.00784v1","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00784","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"pith_short_12","alias_value":"6ET7UBYZR3YY","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6ET7UBYZR3YYPDDM","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6ET7UBYZ","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6ET7UBYZR3YYPDDMDETJBVPALM","target":"record","payload":{"canonical_record":{"source":{"id":"1711.00784","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-11-02T15:33:31Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"2e152b70b30935701aae20421c92039fe958e2b8c57138178286c2b3191bbed1","abstract_canon_sha256":"f69fbef77663926d452488bdb0a0d151cf2d38941c3ac0c8781e9405f4c45fa2"},"schema_version":"1.0"},"canonical_sha256":"f127fa07198ef1878c6c192690d5e05b1bc0d76a37433285850f033cd0574602","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:29.554689Z","signature_b64":"r+wgvBCpPyK7xaln5+we75hFyQlCo7MoLReKfUPkI/OvhuTh01W+oPxMyOvPkmxpJSmsNLA/07hxa4fiTnQTAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f127fa07198ef1878c6c192690d5e05b1bc0d76a37433285850f033cd0574602","last_reissued_at":"2026-05-18T00:31:29.554135Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:29.554135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.00784","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":"2026-05-18T00:31:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aEFFxWnL3xTAlV1clPwaCyqw1thvWHsfEXeHSoKwBqKBdydNNR97azi3QXttqVIS37Jm2kD2b0ZTV8mauE9WAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:14:19.927518Z"},"content_sha256":"1b0707a004cc4b8ab2c9aac3074e27774415b109da03f46e9cd47989b871bc02","schema_version":"1.0","event_id":"sha256:1b0707a004cc4b8ab2c9aac3074e27774415b109da03f46e9cd47989b871bc02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6ET7UBYZR3YYPDDMDETJBVPALM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scalable Approximation Algorithm for Network Immunization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"cs.DM","authors_text":"Imdadullah Khan, Juvaria Tariq, Mudassir Shabbir, Muhammad Ahmad","submitted_at":"2017-11-02T15:33:31Z","abstract_excerpt":"The problem of identifying important players in a given network is of pivotal importance for viral marketing, public health management, network security and various other fields of social network analysis. In this work we find the most important vertices in a graph G = (V,E) to immunize so as the chances of an epidemic outbreak is minimized. This problem is directly relevant to minimizing the impact of a contagion spread (e.g. flu virus, computer virus and rumor) in a graph (e.g. social network, computer network) with a limited budget (e.g. the number of available vaccines, antivirus software,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00784","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":"2026-05-18T00:31:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pG6xiwkoAMrFFxzMEPCcF5L28eV9Vh9+Nqimnsqcsw1Y2AYMNQkv56PXIu6f8FAYdqGQ5dkN8Lsh1DoEVY8kDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:14:19.927861Z"},"content_sha256":"16af5ed183ee1aa46d97f49605cc1b9109065c8903aeccc61ca320e541eefe22","schema_version":"1.0","event_id":"sha256:16af5ed183ee1aa46d97f49605cc1b9109065c8903aeccc61ca320e541eefe22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ET7UBYZR3YYPDDMDETJBVPALM/bundle.json","state_url":"https://pith.science/pith/6ET7UBYZR3YYPDDMDETJBVPALM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ET7UBYZR3YYPDDMDETJBVPALM/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":"2026-06-03T10:14:19Z","links":{"resolver":"https://pith.science/pith/6ET7UBYZR3YYPDDMDETJBVPALM","bundle":"https://pith.science/pith/6ET7UBYZR3YYPDDMDETJBVPALM/bundle.json","state":"https://pith.science/pith/6ET7UBYZR3YYPDDMDETJBVPALM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ET7UBYZR3YYPDDMDETJBVPALM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6ET7UBYZR3YYPDDMDETJBVPALM","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":"f69fbef77663926d452488bdb0a0d151cf2d38941c3ac0c8781e9405f4c45fa2","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-11-02T15:33:31Z","title_canon_sha256":"2e152b70b30935701aae20421c92039fe958e2b8c57138178286c2b3191bbed1"},"schema_version":"1.0","source":{"id":"1711.00784","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.00784","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"arxiv_version","alias_value":"1711.00784v1","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00784","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"pith_short_12","alias_value":"6ET7UBYZR3YY","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6ET7UBYZR3YYPDDM","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6ET7UBYZ","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:16af5ed183ee1aa46d97f49605cc1b9109065c8903aeccc61ca320e541eefe22","target":"graph","created_at":"2026-05-18T00:31:29Z","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":"The problem of identifying important players in a given network is of pivotal importance for viral marketing, public health management, network security and various other fields of social network analysis. In this work we find the most important vertices in a graph G = (V,E) to immunize so as the chances of an epidemic outbreak is minimized. This problem is directly relevant to minimizing the impact of a contagion spread (e.g. flu virus, computer virus and rumor) in a graph (e.g. social network, computer network) with a limited budget (e.g. the number of available vaccines, antivirus software,","authors_text":"Imdadullah Khan, Juvaria Tariq, Mudassir Shabbir, Muhammad Ahmad","cross_cats":["cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-11-02T15:33:31Z","title":"Scalable Approximation Algorithm for Network Immunization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00784","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":"sha256:1b0707a004cc4b8ab2c9aac3074e27774415b109da03f46e9cd47989b871bc02","target":"record","created_at":"2026-05-18T00:31:29Z","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":"f69fbef77663926d452488bdb0a0d151cf2d38941c3ac0c8781e9405f4c45fa2","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-11-02T15:33:31Z","title_canon_sha256":"2e152b70b30935701aae20421c92039fe958e2b8c57138178286c2b3191bbed1"},"schema_version":"1.0","source":{"id":"1711.00784","kind":"arxiv","version":1}},"canonical_sha256":"f127fa07198ef1878c6c192690d5e05b1bc0d76a37433285850f033cd0574602","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f127fa07198ef1878c6c192690d5e05b1bc0d76a37433285850f033cd0574602","first_computed_at":"2026-05-18T00:31:29.554135Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:29.554135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r+wgvBCpPyK7xaln5+we75hFyQlCo7MoLReKfUPkI/OvhuTh01W+oPxMyOvPkmxpJSmsNLA/07hxa4fiTnQTAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:29.554689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.00784","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b0707a004cc4b8ab2c9aac3074e27774415b109da03f46e9cd47989b871bc02","sha256:16af5ed183ee1aa46d97f49605cc1b9109065c8903aeccc61ca320e541eefe22"],"state_sha256":"6625a496d6338ff720370be7d211410ae2129b763555320bdef905d3279c4014"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GXMd90cgGvSBmbJKhfv2NTIlvkCJ/oQdcTy9ea711EMoriOxQOzo+MoJsA2asfaE9ikt7ZXUKDNEQp6eIljOCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T10:14:19.929774Z","bundle_sha256":"fb4b93bfcbca33c41c91af96d914efa752f76d14071efef1e2a9abf9d6492e4c"}}