{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:Z376OPAGMVTVSUCE5NK6LMPRU4","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":"d5ccfe89b9df2ed925c74c2762dcbae0e4cb499940dc7136cc304b7d0c20924c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2008-01-13T22:04:49Z","title_canon_sha256":"3cb4dd4096f68414708458720cd785467c8e8b1e81adcc445e752961a68598a0"},"schema_version":"1.0","source":{"id":"0801.1987","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.1987","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"arxiv_version","alias_value":"0801.1987v2","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.1987","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"pith_short_12","alias_value":"Z376OPAGMVTV","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"Z376OPAGMVTVSUCE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"Z376OPAG","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:d8a7930d6aae29303041b830bc2645bf097e6a138326a539478084e04b8c7337","target":"graph","created_at":"2026-05-18T01:59:59Z","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":"We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual solutions whose costs are within a factor of 1+eps of the optimal cost in time O((r+c)log(n)/eps^2 + n).","authors_text":"Christos Koufogiannakis, Neal E. Young","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2008-01-13T22:04:49Z","title":"A Nearly Linear-Time PTAS for Explicit Fractional Packing and Covering Linear Programs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.1987","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":"sha256:2741ac69d799159ef56b05f2e238d1365f605963d5bd312e16cccc46f2a86906","target":"record","created_at":"2026-05-18T01:59:59Z","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":"d5ccfe89b9df2ed925c74c2762dcbae0e4cb499940dc7136cc304b7d0c20924c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2008-01-13T22:04:49Z","title_canon_sha256":"3cb4dd4096f68414708458720cd785467c8e8b1e81adcc445e752961a68598a0"},"schema_version":"1.0","source":{"id":"0801.1987","kind":"arxiv","version":2}},"canonical_sha256":"ceffe73c066567595044eb55e5b1f1a72c6aa98e8c1ad1425183c78fe5ce5521","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ceffe73c066567595044eb55e5b1f1a72c6aa98e8c1ad1425183c78fe5ce5521","first_computed_at":"2026-05-18T01:59:59.457158Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:59.457158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nXuHw4+LlYKjI87eZ0xXse1qupaqyvBs76Yy2Z4ZNZ5f0i503AqTNvgmBxzcJGgAcQTGAxZJ7YS2agX6u6g0Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:59.457769Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.1987","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2741ac69d799159ef56b05f2e238d1365f605963d5bd312e16cccc46f2a86906","sha256:d8a7930d6aae29303041b830bc2645bf097e6a138326a539478084e04b8c7337"],"state_sha256":"3d1f7e2b8cf3e910c01d7f32ccf56b3ea38c7285ef29cb754ee7640f8d92f0d8"}