{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SQXG2FBIEU7V4H6ULFH7HDHLOG","short_pith_number":"pith:SQXG2FBI","canonical_record":{"source":{"id":"1502.00400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-02-02T08:55:44Z","cross_cats_sorted":["cs.DM","cs.SI","math.CO","math.PR"],"title_canon_sha256":"3e7d970399fa62b1bd3e91c6538a0ed411930b91d3926eaea8f1856bded1d8d0","abstract_canon_sha256":"c5b75f0e4412bca236d6e5990601deb48228f042a44d4a8347dc45a9582e2856"},"schema_version":"1.0"},"canonical_sha256":"942e6d1428253f5e1fd4594ff38ceb718e1f5e2c48d5cf220d49cc1a652f83f1","source":{"kind":"arxiv","id":"1502.00400","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00400","created_at":"2026-05-18T02:28:06Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00400v1","created_at":"2026-05-18T02:28:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00400","created_at":"2026-05-18T02:28:06Z"},{"alias_kind":"pith_short_12","alias_value":"SQXG2FBIEU7V","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SQXG2FBIEU7V4H6U","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SQXG2FBI","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SQXG2FBIEU7V4H6ULFH7HDHLOG","target":"record","payload":{"canonical_record":{"source":{"id":"1502.00400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-02-02T08:55:44Z","cross_cats_sorted":["cs.DM","cs.SI","math.CO","math.PR"],"title_canon_sha256":"3e7d970399fa62b1bd3e91c6538a0ed411930b91d3926eaea8f1856bded1d8d0","abstract_canon_sha256":"c5b75f0e4412bca236d6e5990601deb48228f042a44d4a8347dc45a9582e2856"},"schema_version":"1.0"},"canonical_sha256":"942e6d1428253f5e1fd4594ff38ceb718e1f5e2c48d5cf220d49cc1a652f83f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:06.061639Z","signature_b64":"efpSCS7fbmJsC7A6oAQJ96lN+u7s5dnxCDgX7ITCgBli/j7vlDYH6zp3RxXRGQVlLVRDsjLatE9ROGH4QxG5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"942e6d1428253f5e1fd4594ff38ceb718e1f5e2c48d5cf220d49cc1a652f83f1","last_reissued_at":"2026-05-18T02:28:06.061268Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:06.061268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.00400","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":"2026-05-18T02:28:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XvNcflpjqjLRVqZNSnqnNcMS6vWDGkybVYMiQPqugvjlqm1NSejQlARk1PnMjoMtp9GyigcbMj9sz/4pST6XCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:23:41.134785Z"},"content_sha256":"481058df135acae2ca09ee7f17caeafa9865e552474cda932caf2051045d453a","schema_version":"1.0","event_id":"sha256:481058df135acae2ca09ee7f17caeafa9865e552474cda932caf2051045d453a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SQXG2FBIEU7V4H6ULFH7HDHLOG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"k-Connectivity of Random Key Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.SI","math.CO","math.PR"],"primary_cat":"physics.soc-ph","authors_text":"Jun Zhao, Osman Ya\\u{g}an, Virgil Gligor","submitted_at":"2015-02-02T08:55:44Z","abstract_excerpt":"Random key graphs represent topologies of secure wireless sensor networks that apply the seminal Eschenauer-Gligor random key predistribution scheme to secure communication between sensors. These graphs have received much attention and also been used in diverse application areas beyond secure sensor networks; e.g., cryptanalysis, social networks, and recommender systems. Formally, a random key graph with $n$ nodes is constructed by assigning each node $X_n$ keys selected uniformly at random from a pool of $Y_n$ keys and then putting an undirected edge between any two nodes sharing at least one"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00400","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":"2026-05-18T02:28:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EFXkHECJsFTw0Zcrc0OL9GOFnOQ/El4IuNZVDsC5lI6IWAUDQzz4Xzt8hp1v6Vcxp7AkSYMCjnUVxHqtke7mBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:23:41.135547Z"},"content_sha256":"7ab1d95ac611df608915b130895f69f3cfeccfb9baaecbfa3b2978b3138d2318","schema_version":"1.0","event_id":"sha256:7ab1d95ac611df608915b130895f69f3cfeccfb9baaecbfa3b2978b3138d2318"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SQXG2FBIEU7V4H6ULFH7HDHLOG/bundle.json","state_url":"https://pith.science/pith/SQXG2FBIEU7V4H6ULFH7HDHLOG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SQXG2FBIEU7V4H6ULFH7HDHLOG/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":"2026-06-12T02:23:41Z","links":{"resolver":"https://pith.science/pith/SQXG2FBIEU7V4H6ULFH7HDHLOG","bundle":"https://pith.science/pith/SQXG2FBIEU7V4H6ULFH7HDHLOG/bundle.json","state":"https://pith.science/pith/SQXG2FBIEU7V4H6ULFH7HDHLOG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SQXG2FBIEU7V4H6ULFH7HDHLOG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SQXG2FBIEU7V4H6ULFH7HDHLOG","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":"c5b75f0e4412bca236d6e5990601deb48228f042a44d4a8347dc45a9582e2856","cross_cats_sorted":["cs.DM","cs.SI","math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-02-02T08:55:44Z","title_canon_sha256":"3e7d970399fa62b1bd3e91c6538a0ed411930b91d3926eaea8f1856bded1d8d0"},"schema_version":"1.0","source":{"id":"1502.00400","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00400","created_at":"2026-05-18T02:28:06Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00400v1","created_at":"2026-05-18T02:28:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00400","created_at":"2026-05-18T02:28:06Z"},{"alias_kind":"pith_short_12","alias_value":"SQXG2FBIEU7V","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SQXG2FBIEU7V4H6U","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SQXG2FBI","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:7ab1d95ac611df608915b130895f69f3cfeccfb9baaecbfa3b2978b3138d2318","target":"graph","created_at":"2026-05-18T02:28:06Z","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":"Random key graphs represent topologies of secure wireless sensor networks that apply the seminal Eschenauer-Gligor random key predistribution scheme to secure communication between sensors. These graphs have received much attention and also been used in diverse application areas beyond secure sensor networks; e.g., cryptanalysis, social networks, and recommender systems. Formally, a random key graph with $n$ nodes is constructed by assigning each node $X_n$ keys selected uniformly at random from a pool of $Y_n$ keys and then putting an undirected edge between any two nodes sharing at least one","authors_text":"Jun Zhao, Osman Ya\\u{g}an, Virgil Gligor","cross_cats":["cs.DM","cs.SI","math.CO","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-02-02T08:55:44Z","title":"k-Connectivity of Random Key Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00400","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":"sha256:481058df135acae2ca09ee7f17caeafa9865e552474cda932caf2051045d453a","target":"record","created_at":"2026-05-18T02:28:06Z","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":"c5b75f0e4412bca236d6e5990601deb48228f042a44d4a8347dc45a9582e2856","cross_cats_sorted":["cs.DM","cs.SI","math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-02-02T08:55:44Z","title_canon_sha256":"3e7d970399fa62b1bd3e91c6538a0ed411930b91d3926eaea8f1856bded1d8d0"},"schema_version":"1.0","source":{"id":"1502.00400","kind":"arxiv","version":1}},"canonical_sha256":"942e6d1428253f5e1fd4594ff38ceb718e1f5e2c48d5cf220d49cc1a652f83f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"942e6d1428253f5e1fd4594ff38ceb718e1f5e2c48d5cf220d49cc1a652f83f1","first_computed_at":"2026-05-18T02:28:06.061268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:06.061268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"efpSCS7fbmJsC7A6oAQJ96lN+u7s5dnxCDgX7ITCgBli/j7vlDYH6zp3RxXRGQVlLVRDsjLatE9ROGH4QxG5Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:06.061639Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.00400","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:481058df135acae2ca09ee7f17caeafa9865e552474cda932caf2051045d453a","sha256:7ab1d95ac611df608915b130895f69f3cfeccfb9baaecbfa3b2978b3138d2318"],"state_sha256":"62be05dbfcfe35d9979b8bf0fcf1a2de8384d604773b2f0f7c290fffdcc3e459"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5HRKzDez3T5DzP/Xxe+qXgerpnEGz8V0i866O/mfNygBX2iP3bkpheh2utgnQkOojy3/irxb6wvKIPN72ClaCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T02:23:41.140377Z","bundle_sha256":"770288bac8fcbb2d87a129d7e337c5b13a67a4049d9df33ff007618d2912a1ae"}}