{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:AI2ESVZGLKBXWXPNKMA6ZMACS7","short_pith_number":"pith:AI2ESVZG","canonical_record":{"source":{"id":"2008.05374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-08-12T15:14:57Z","cross_cats_sorted":[],"title_canon_sha256":"6cb3e8392c1766c5008b3ec697e34b3010c9d816db4316172bacaefee84f096c","abstract_canon_sha256":"f686e24d3549eb47a952df56218a1d564aa808c9a393cf992d2d9f1ed6552234"},"schema_version":"1.0"},"canonical_sha256":"02344957265a837b5ded5301ecb00297ebe627d5b12cfcada8833fa97fb6f41b","source":{"kind":"arxiv","id":"2008.05374","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.05374","created_at":"2026-07-05T01:26:46Z"},{"alias_kind":"arxiv_version","alias_value":"2008.05374v1","created_at":"2026-07-05T01:26:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.05374","created_at":"2026-07-05T01:26:46Z"},{"alias_kind":"pith_short_12","alias_value":"AI2ESVZGLKBX","created_at":"2026-07-05T01:26:46Z"},{"alias_kind":"pith_short_16","alias_value":"AI2ESVZGLKBXWXPN","created_at":"2026-07-05T01:26:46Z"},{"alias_kind":"pith_short_8","alias_value":"AI2ESVZG","created_at":"2026-07-05T01:26:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:AI2ESVZGLKBXWXPNKMA6ZMACS7","target":"record","payload":{"canonical_record":{"source":{"id":"2008.05374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-08-12T15:14:57Z","cross_cats_sorted":[],"title_canon_sha256":"6cb3e8392c1766c5008b3ec697e34b3010c9d816db4316172bacaefee84f096c","abstract_canon_sha256":"f686e24d3549eb47a952df56218a1d564aa808c9a393cf992d2d9f1ed6552234"},"schema_version":"1.0"},"canonical_sha256":"02344957265a837b5ded5301ecb00297ebe627d5b12cfcada8833fa97fb6f41b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:26:46.107980Z","signature_b64":"PT09aabHgTAVe59+lWvLYC8TNxGeAZXKSrP2eUnuAk2dOpLTOxIPPZ/DxG1NDcoBpu636d3q38LMSKisKWW1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02344957265a837b5ded5301ecb00297ebe627d5b12cfcada8833fa97fb6f41b","last_reissued_at":"2026-07-05T01:26:46.107581Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:26:46.107581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.05374","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":"2026-07-05T01:26:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZuREezvvgeuMY/5UG4EaBIrDlBHIDiaFqn+D44xlu0/6a10lbqMj/4JMJIlKqVy6eRShs3YEuq9TscsouF+pDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T23:10:25.654994Z"},"content_sha256":"fb47dfc12c62763c3fcd9b0249227a4e21742ea18b835e347a684b0894f9e108","schema_version":"1.0","event_id":"sha256:fb47dfc12c62763c3fcd9b0249227a4e21742ea18b835e347a684b0894f9e108"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:AI2ESVZGLKBXWXPNKMA6ZMACS7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tight Bounds on Subexponential Time Approximation of Set Cover and Related Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Guy Kortsarz, Magn\\'us M. Halld\\'orsson, Marek Cygan","submitted_at":"2020-08-12T15:14:57Z","abstract_excerpt":"We show that Set Cover on instances with $N$ elements cannot be approximated within $(1-\\gamma)\\ln N$-factor in time exp($N^{\\gamma-\\delta})$, for any $0 < \\gamma < 1$ and any $\\delta > 0$, assuming the Exponential Time Hypothesis. This essentially matches the best upper bound known by Cygan et al.\\ (IPL, 2009) of $(1-\\gamma)\\ln N$-factor in time $exp(O(N^\\gamma))$.\n  The lower bound is obtained by extracting a standalone reduction from Label Cover to Set Cover from the work of Moshkovitz (Theory of Computing, 2015), and applying it to a different PCP theorem than done there. We also obtain a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.05374","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.05374/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:26:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nGI0vyzR21zl3N/NAhG68pry0XJ+jaYzQTAror7EZHnfCJZDqvOUJX5pUz481YE1lnbYmoolsJcaGWqk06XqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T23:10:25.655374Z"},"content_sha256":"54e687754d5c4f42ceeabb31e37988cbd6cee17c8dc188469fe4ba2ee913ba76","schema_version":"1.0","event_id":"sha256:54e687754d5c4f42ceeabb31e37988cbd6cee17c8dc188469fe4ba2ee913ba76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AI2ESVZGLKBXWXPNKMA6ZMACS7/bundle.json","state_url":"https://pith.science/pith/AI2ESVZGLKBXWXPNKMA6ZMACS7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AI2ESVZGLKBXWXPNKMA6ZMACS7/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":"2026-07-06T23:10:25Z","links":{"resolver":"https://pith.science/pith/AI2ESVZGLKBXWXPNKMA6ZMACS7","bundle":"https://pith.science/pith/AI2ESVZGLKBXWXPNKMA6ZMACS7/bundle.json","state":"https://pith.science/pith/AI2ESVZGLKBXWXPNKMA6ZMACS7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AI2ESVZGLKBXWXPNKMA6ZMACS7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:AI2ESVZGLKBXWXPNKMA6ZMACS7","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":"f686e24d3549eb47a952df56218a1d564aa808c9a393cf992d2d9f1ed6552234","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-08-12T15:14:57Z","title_canon_sha256":"6cb3e8392c1766c5008b3ec697e34b3010c9d816db4316172bacaefee84f096c"},"schema_version":"1.0","source":{"id":"2008.05374","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.05374","created_at":"2026-07-05T01:26:46Z"},{"alias_kind":"arxiv_version","alias_value":"2008.05374v1","created_at":"2026-07-05T01:26:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.05374","created_at":"2026-07-05T01:26:46Z"},{"alias_kind":"pith_short_12","alias_value":"AI2ESVZGLKBX","created_at":"2026-07-05T01:26:46Z"},{"alias_kind":"pith_short_16","alias_value":"AI2ESVZGLKBXWXPN","created_at":"2026-07-05T01:26:46Z"},{"alias_kind":"pith_short_8","alias_value":"AI2ESVZG","created_at":"2026-07-05T01:26:46Z"}],"graph_snapshots":[{"event_id":"sha256:54e687754d5c4f42ceeabb31e37988cbd6cee17c8dc188469fe4ba2ee913ba76","target":"graph","created_at":"2026-07-05T01:26:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2008.05374/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that Set Cover on instances with $N$ elements cannot be approximated within $(1-\\gamma)\\ln N$-factor in time exp($N^{\\gamma-\\delta})$, for any $0 < \\gamma < 1$ and any $\\delta > 0$, assuming the Exponential Time Hypothesis. This essentially matches the best upper bound known by Cygan et al.\\ (IPL, 2009) of $(1-\\gamma)\\ln N$-factor in time $exp(O(N^\\gamma))$.\n  The lower bound is obtained by extracting a standalone reduction from Label Cover to Set Cover from the work of Moshkovitz (Theory of Computing, 2015), and applying it to a different PCP theorem than done there. We also obtain a ","authors_text":"Guy Kortsarz, Magn\\'us M. Halld\\'orsson, Marek Cygan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-08-12T15:14:57Z","title":"Tight Bounds on Subexponential Time Approximation of Set Cover and Related Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.05374","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:fb47dfc12c62763c3fcd9b0249227a4e21742ea18b835e347a684b0894f9e108","target":"record","created_at":"2026-07-05T01:26:46Z","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":"f686e24d3549eb47a952df56218a1d564aa808c9a393cf992d2d9f1ed6552234","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-08-12T15:14:57Z","title_canon_sha256":"6cb3e8392c1766c5008b3ec697e34b3010c9d816db4316172bacaefee84f096c"},"schema_version":"1.0","source":{"id":"2008.05374","kind":"arxiv","version":1}},"canonical_sha256":"02344957265a837b5ded5301ecb00297ebe627d5b12cfcada8833fa97fb6f41b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02344957265a837b5ded5301ecb00297ebe627d5b12cfcada8833fa97fb6f41b","first_computed_at":"2026-07-05T01:26:46.107581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:26:46.107581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PT09aabHgTAVe59+lWvLYC8TNxGeAZXKSrP2eUnuAk2dOpLTOxIPPZ/DxG1NDcoBpu636d3q38LMSKisKWW1BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:26:46.107980Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.05374","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb47dfc12c62763c3fcd9b0249227a4e21742ea18b835e347a684b0894f9e108","sha256:54e687754d5c4f42ceeabb31e37988cbd6cee17c8dc188469fe4ba2ee913ba76"],"state_sha256":"6be8132a162d47059543ed9efd22c7e8b55c23552969f8b099734da98a2a068f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JEdYAwFqbjf5ykcjYJNZahubO8D8+XlHZfO7LLeoA6m2lasTnXPa82SjN1Uy5FkN1YNUPIoSFBYgSG+xdnGxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T23:10:25.657268Z","bundle_sha256":"0cdd36e50f7d18ef1e8a1917ac51d96234be00a50872d3dfb0fda8ff2957620d"}}