{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7AUNNLH3SZIJSOIY6MFADD2LPC","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":"529826d0a0cf6f08a58edc12b38f59953af5ca9648180096aecad59cbbd99d69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-10-10T00:40:28Z","title_canon_sha256":"6d3b42e0b96ae127e44efa05423b07dd76e459b46d13dbb9c5813dcf191e19fc"},"schema_version":"1.0","source":{"id":"1110.1896","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1896","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1896v1","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1896","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"7AUNNLH3SZIJ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7AUNNLH3SZIJSOIY","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7AUNNLH3","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:870d8c9bddb44359fbe7ad8db9ce8afb85b2fc7ecb1a55d477c8eec8b83180db","target":"graph","created_at":"2026-05-18T04:11:19Z","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":"Let $({\\bf U},{\\bf S},d)$ be an instance of Set Cover Problem, where ${\\bf U}=\\{u_1,...,u_n\\}$ is a $n$ element ground set, ${\\bf S}=\\{S_1,...,S_m\\}$ is a set of $m$ subsets of ${\\bf U}$ satisfying $\\bigcup_{i=1}^m S_i={\\bf U}$ and $d$ is a positive integer. In STOC 1993 M. Bellare, S. Goldwasser, C. Lund and A. Russell proved the NP-hardness to distinguish the following two cases of ${\\bf GapSetCover_{\\eta}}$ for any constant $\\eta > 1$. The Yes case is the instance for which there is an exact cover of size $d$ and the No case is the instance for which any cover of ${\\bf U}$ from ${\\bf S}$ ha","authors_text":"Hao Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-10-10T00:40:28Z","title":"Restricted Parameter Range Promise Set Cover Problems Are Easy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1896","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:cd0be067aa5206e41c6cffde954edd49027aa169b7b59f9096397e8b81c2b25e","target":"record","created_at":"2026-05-18T04:11:19Z","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":"529826d0a0cf6f08a58edc12b38f59953af5ca9648180096aecad59cbbd99d69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-10-10T00:40:28Z","title_canon_sha256":"6d3b42e0b96ae127e44efa05423b07dd76e459b46d13dbb9c5813dcf191e19fc"},"schema_version":"1.0","source":{"id":"1110.1896","kind":"arxiv","version":1}},"canonical_sha256":"f828d6acfb9650993918f30a018f4b7894b74c43f962b98abe0f3d65aea2a61b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f828d6acfb9650993918f30a018f4b7894b74c43f962b98abe0f3d65aea2a61b","first_computed_at":"2026-05-18T04:11:19.387187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:19.387187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o6LXEd//c1mrTO4GPEyxlDoHL3IZJG6gbSWwPV1gvypSYz2fxeC4/O0fYLU3l7chggXH4PQoG8y8v3NInU12BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:19.387642Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1896","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd0be067aa5206e41c6cffde954edd49027aa169b7b59f9096397e8b81c2b25e","sha256:870d8c9bddb44359fbe7ad8db9ce8afb85b2fc7ecb1a55d477c8eec8b83180db"],"state_sha256":"8f78c9a9ce958c2be0aad110f115e398089d794fb1f689fa9cce952f1dbbca9b"}