{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:7MK6Z73MJPWNGO25D2ET7HMTLW","short_pith_number":"pith:7MK6Z73M","canonical_record":{"source":{"id":"cs/0205042","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.DS","submitted_at":"2002-05-18T16:12:53Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"28647361d4f1493fb6679d5cb4733494bbb73f1e08853701327a12dfa629c7b7","abstract_canon_sha256":"18da54997d0c9dc226bf5615f98963f742b374311f4e9eaf40579b79a6b5691b"},"schema_version":"1.0"},"canonical_sha256":"fb15ecff6c4becd33b5d1e893f9d935d9bc321ccd770940d285e0663938a687e","source":{"kind":"arxiv","id":"cs/0205042","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0205042","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0205042v1","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0205042","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"pith_short_12","alias_value":"7MK6Z73MJPWN","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"7MK6Z73MJPWNGO25","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"7MK6Z73M","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:7MK6Z73MJPWNGO25D2ET7HMTLW","target":"record","payload":{"canonical_record":{"source":{"id":"cs/0205042","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.DS","submitted_at":"2002-05-18T16:12:53Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"28647361d4f1493fb6679d5cb4733494bbb73f1e08853701327a12dfa629c7b7","abstract_canon_sha256":"18da54997d0c9dc226bf5615f98963f742b374311f4e9eaf40579b79a6b5691b"},"schema_version":"1.0"},"canonical_sha256":"fb15ecff6c4becd33b5d1e893f9d935d9bc321ccd770940d285e0663938a687e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:53.936350Z","signature_b64":"HQZX//rgmgs4GZWzVXf2uqpgYm2IIAQxjVQcJjbvi0THseqiiji9fWmMotLrSuZ4G0Uc3g94fHeBPIX5tb3wCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb15ecff6c4becd33b5d1e893f9d935d9bc321ccd770940d285e0663938a687e","last_reissued_at":"2026-05-18T01:59:53.935796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:53.935796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cs/0205042","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":"2026-05-18T01:59:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K9UhbQbbkEys6FyKLiTDD+tjY4T5d1QH8yhkrQ7izS5hCrIwmqYuegLalXy5EJz2DCPME3SahY8IpAKBp7jyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:34:51.560691Z"},"content_sha256":"d26fd30666c675161939d4d478de79dfd844137020f6f4fd8cef59b4c02eae08","schema_version":"1.0","event_id":"sha256:d26fd30666c675161939d4d478de79dfd844137020f6f4fd8cef59b4c02eae08"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:7MK6Z73MJPWNGO25D2ET7HMTLW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orienting Graphs to Optimize Reachability","license":"","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"E. Schmeichel, Neal E. Young, S. L. Hakimi","submitted_at":"2002-05-18T16:12:53Z","abstract_excerpt":"The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to minimize the number of such pairs. The paper describes a quadratic-time algorithm for the first problem, and a proof that the second problem is NP-hard to approximate within some constant 1+epsilon > 1. The latter proof also shows that the second problem is equivalent to ``comparability graph completion''; neither problem was previously known to be NP-hard."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0205042","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":"2026-05-18T01:59:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QvP8Kq9vvpPNuRrZxV8hcgb6j4LeKmuqPsV9Li2I2KfDuHoODHHYW9nBTgkRMDFjMhVues+1alMwFbI5tqbfDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:34:51.561037Z"},"content_sha256":"3d8184e6cc2dd0aa16560ad2199bccea1cfacc0fa0937d0733d6059066ade503","schema_version":"1.0","event_id":"sha256:3d8184e6cc2dd0aa16560ad2199bccea1cfacc0fa0937d0733d6059066ade503"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7MK6Z73MJPWNGO25D2ET7HMTLW/bundle.json","state_url":"https://pith.science/pith/7MK6Z73MJPWNGO25D2ET7HMTLW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7MK6Z73MJPWNGO25D2ET7HMTLW/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":"2026-06-12T01:34:51Z","links":{"resolver":"https://pith.science/pith/7MK6Z73MJPWNGO25D2ET7HMTLW","bundle":"https://pith.science/pith/7MK6Z73MJPWNGO25D2ET7HMTLW/bundle.json","state":"https://pith.science/pith/7MK6Z73MJPWNGO25D2ET7HMTLW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7MK6Z73MJPWNGO25D2ET7HMTLW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:7MK6Z73MJPWNGO25D2ET7HMTLW","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":"18da54997d0c9dc226bf5615f98963f742b374311f4e9eaf40579b79a6b5691b","cross_cats_sorted":["cs.DM"],"license":"","primary_cat":"cs.DS","submitted_at":"2002-05-18T16:12:53Z","title_canon_sha256":"28647361d4f1493fb6679d5cb4733494bbb73f1e08853701327a12dfa629c7b7"},"schema_version":"1.0","source":{"id":"cs/0205042","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0205042","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0205042v1","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0205042","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"pith_short_12","alias_value":"7MK6Z73MJPWN","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"7MK6Z73MJPWNGO25","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"7MK6Z73M","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:3d8184e6cc2dd0aa16560ad2199bccea1cfacc0fa0937d0733d6059066ade503","target":"graph","created_at":"2026-05-18T01:59:53Z","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 paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to minimize the number of such pairs. The paper describes a quadratic-time algorithm for the first problem, and a proof that the second problem is NP-hard to approximate within some constant 1+epsilon > 1. The latter proof also shows that the second problem is equivalent to ``comparability graph completion''; neither problem was previously known to be NP-hard.","authors_text":"E. Schmeichel, Neal E. Young, S. L. Hakimi","cross_cats":["cs.DM"],"headline":"","license":"","primary_cat":"cs.DS","submitted_at":"2002-05-18T16:12:53Z","title":"Orienting Graphs to Optimize Reachability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0205042","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:d26fd30666c675161939d4d478de79dfd844137020f6f4fd8cef59b4c02eae08","target":"record","created_at":"2026-05-18T01:59:53Z","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":"18da54997d0c9dc226bf5615f98963f742b374311f4e9eaf40579b79a6b5691b","cross_cats_sorted":["cs.DM"],"license":"","primary_cat":"cs.DS","submitted_at":"2002-05-18T16:12:53Z","title_canon_sha256":"28647361d4f1493fb6679d5cb4733494bbb73f1e08853701327a12dfa629c7b7"},"schema_version":"1.0","source":{"id":"cs/0205042","kind":"arxiv","version":1}},"canonical_sha256":"fb15ecff6c4becd33b5d1e893f9d935d9bc321ccd770940d285e0663938a687e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb15ecff6c4becd33b5d1e893f9d935d9bc321ccd770940d285e0663938a687e","first_computed_at":"2026-05-18T01:59:53.935796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:53.935796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HQZX//rgmgs4GZWzVXf2uqpgYm2IIAQxjVQcJjbvi0THseqiiji9fWmMotLrSuZ4G0Uc3g94fHeBPIX5tb3wCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:53.936350Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0205042","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d26fd30666c675161939d4d478de79dfd844137020f6f4fd8cef59b4c02eae08","sha256:3d8184e6cc2dd0aa16560ad2199bccea1cfacc0fa0937d0733d6059066ade503"],"state_sha256":"5a7287a98d8b42bb43a6a93c313872a9b266e342248b5e95740a115b49722a45"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"srAFcCH1qI+k+QC/I1yVKUQOyKlpDYliahph69oPdjbfdncaHt8yQc+GBENT+h/epLByfTUqQ79wQlJj3AkBAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T01:34:51.562883Z","bundle_sha256":"d36edefacbe32e0dbb4b6fc13d897002f3a0061f1e4df1b79e16f578bb2c8441"}}