{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FEQHKLNBE57VNJKWOSVXONLCVN","short_pith_number":"pith:FEQHKLNB","canonical_record":{"source":{"id":"1609.08403","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-27T13:20:49Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"84896836e09b3f5c11fc4cc26380d41a75a300b718ef0a986dc050b377ed7f6d","abstract_canon_sha256":"dc44c6ef58e574b6b420b5d42f09e8ea1574c4d978ead131b079d6ea63438053"},"schema_version":"1.0"},"canonical_sha256":"2920752da1277f56a55674ab773562ab7d9e0b90f10d59132ea870859c330932","source":{"kind":"arxiv","id":"1609.08403","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08403","created_at":"2026-05-18T00:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08403v2","created_at":"2026-05-18T00:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08403","created_at":"2026-05-18T00:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"FEQHKLNBE57V","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FEQHKLNBE57VNJKW","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FEQHKLNB","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FEQHKLNBE57VNJKWOSVXONLCVN","target":"record","payload":{"canonical_record":{"source":{"id":"1609.08403","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-27T13:20:49Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"84896836e09b3f5c11fc4cc26380d41a75a300b718ef0a986dc050b377ed7f6d","abstract_canon_sha256":"dc44c6ef58e574b6b420b5d42f09e8ea1574c4d978ead131b079d6ea63438053"},"schema_version":"1.0"},"canonical_sha256":"2920752da1277f56a55674ab773562ab7d9e0b90f10d59132ea870859c330932","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:04.320507Z","signature_b64":"qwuS7o91uOKkGtPDPj0y4zFTz5sPP2Mi1Rm5jRvezYY3KnD3xO/adHQ2Tx8+kuuavr9gAJinHGkbEthqguxEBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2920752da1277f56a55674ab773562ab7d9e0b90f10d59132ea870859c330932","last_reissued_at":"2026-05-18T00:46:04.320029Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:04.320029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.08403","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gt96OJIqC5ojDNsQgaVxBhrgbdEPPKCWpZm21P6KH2gSscM/Qt6CB0ogD1GJGmB9ZGi5tjUbwK/JbBbOG3r7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:25:39.226653Z"},"content_sha256":"f43d676bd51c7513cff3a0ab7e4d15f2baec54549d915d32ee172315ca55a34b","schema_version":"1.0","event_id":"sha256:f43d676bd51c7513cff3a0ab7e4d15f2baec54549d915d32ee172315ca55a34b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FEQHKLNBE57VNJKWOSVXONLCVN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tight Hardness Results for Distance and Centrality Problems in Constant Degree Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Jacob Evald, S{\\o}ren Dahlgaard","submitted_at":"2016-09-27T13:20:49Z","abstract_excerpt":"Finding important nodes in a graph and measuring their importance is a fundamental problem in the analysis of social networks, transportation networks, biological systems, etc. Among popular such metrics are graph centrality, betweenness centrality (BC), and reach centrality (RC). These measures are also very related to classic notions like diameter and radius. Roditty and Vassilevska Williams~[STOC'13] showed that no algorithm can compute a (3/2-\\delta)-approximation of the diameter in sparse and unweighted graphs faster that n^{2-o(1)} time unless the widely believed strong exponential time "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08403","kind":"arxiv","version":2},"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":"2026-05-18T00:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BXcLesm/8d2b1Jg067ezyeAkH7e9YuHJHEKEbNssfI3LdYOf/sGUyTxjMRa1yCkr0Lnep7c5MFzeO4DyjiiABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:25:39.226984Z"},"content_sha256":"20d27d24c0e4cdc375cca17f5538cfbb8fc0ede0b8e498c0045187aabc5984b3","schema_version":"1.0","event_id":"sha256:20d27d24c0e4cdc375cca17f5538cfbb8fc0ede0b8e498c0045187aabc5984b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FEQHKLNBE57VNJKWOSVXONLCVN/bundle.json","state_url":"https://pith.science/pith/FEQHKLNBE57VNJKWOSVXONLCVN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FEQHKLNBE57VNJKWOSVXONLCVN/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":"2026-06-27T01:25:39Z","links":{"resolver":"https://pith.science/pith/FEQHKLNBE57VNJKWOSVXONLCVN","bundle":"https://pith.science/pith/FEQHKLNBE57VNJKWOSVXONLCVN/bundle.json","state":"https://pith.science/pith/FEQHKLNBE57VNJKWOSVXONLCVN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FEQHKLNBE57VNJKWOSVXONLCVN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FEQHKLNBE57VNJKWOSVXONLCVN","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":"dc44c6ef58e574b6b420b5d42f09e8ea1574c4d978ead131b079d6ea63438053","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-27T13:20:49Z","title_canon_sha256":"84896836e09b3f5c11fc4cc26380d41a75a300b718ef0a986dc050b377ed7f6d"},"schema_version":"1.0","source":{"id":"1609.08403","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08403","created_at":"2026-05-18T00:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08403v2","created_at":"2026-05-18T00:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08403","created_at":"2026-05-18T00:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"FEQHKLNBE57V","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FEQHKLNBE57VNJKW","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FEQHKLNB","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:20d27d24c0e4cdc375cca17f5538cfbb8fc0ede0b8e498c0045187aabc5984b3","target":"graph","created_at":"2026-05-18T00:46:04Z","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":"Finding important nodes in a graph and measuring their importance is a fundamental problem in the analysis of social networks, transportation networks, biological systems, etc. Among popular such metrics are graph centrality, betweenness centrality (BC), and reach centrality (RC). These measures are also very related to classic notions like diameter and radius. Roditty and Vassilevska Williams~[STOC'13] showed that no algorithm can compute a (3/2-\\delta)-approximation of the diameter in sparse and unweighted graphs faster that n^{2-o(1)} time unless the widely believed strong exponential time ","authors_text":"Jacob Evald, S{\\o}ren Dahlgaard","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-27T13:20:49Z","title":"Tight Hardness Results for Distance and Centrality Problems in Constant Degree Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08403","kind":"arxiv","version":2},"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:f43d676bd51c7513cff3a0ab7e4d15f2baec54549d915d32ee172315ca55a34b","target":"record","created_at":"2026-05-18T00:46:04Z","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":"dc44c6ef58e574b6b420b5d42f09e8ea1574c4d978ead131b079d6ea63438053","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-27T13:20:49Z","title_canon_sha256":"84896836e09b3f5c11fc4cc26380d41a75a300b718ef0a986dc050b377ed7f6d"},"schema_version":"1.0","source":{"id":"1609.08403","kind":"arxiv","version":2}},"canonical_sha256":"2920752da1277f56a55674ab773562ab7d9e0b90f10d59132ea870859c330932","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2920752da1277f56a55674ab773562ab7d9e0b90f10d59132ea870859c330932","first_computed_at":"2026-05-18T00:46:04.320029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:04.320029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qwuS7o91uOKkGtPDPj0y4zFTz5sPP2Mi1Rm5jRvezYY3KnD3xO/adHQ2Tx8+kuuavr9gAJinHGkbEthqguxEBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:04.320507Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.08403","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f43d676bd51c7513cff3a0ab7e4d15f2baec54549d915d32ee172315ca55a34b","sha256:20d27d24c0e4cdc375cca17f5538cfbb8fc0ede0b8e498c0045187aabc5984b3"],"state_sha256":"e5d02d19e9df2bf674ec8a9b575397a98f144ef8cfac6a2a3b552c58601d6bde"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KAFILpPRuFzcTngPGNSHdV7Ct9k3NxuNHOO7ELBDhuHFSdEBaSntSWhDYv7ggKuQ5cm9b3pKzvy4qZ/xTINzAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T01:25:39.228773Z","bundle_sha256":"56cb3155f7e771c6ee990e45663d66e312791c56a0876f558b7dde04b854320b"}}