{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UDFBTVTJQFT33WP55L5P4SEPYR","short_pith_number":"pith:UDFBTVTJ","schema_version":"1.0","canonical_sha256":"a0ca19d6698167bdd9fdeafafe488fc4538ab296e190ab0d05f4ac46418cfc2a","source":{"kind":"arxiv","id":"1504.04767","version":2},"attestation_state":"computed","paper":{"title":"On the Lov\\'asz Theta function for Independent Sets in Sparse Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anupam Gupta, Guru Guruganesh, Nikhil Bansal","submitted_at":"2015-04-18T21:55:07Z","abstract_excerpt":"We consider the maximum independent set problem on graphs with maximum degree~$d$. We show that the integrality gap of the Lov\\'asz $\\vartheta$-function based SDP is $\\widetilde{O}(d/\\log^{3/2} d)$. This improves on the previous best result of $\\widetilde{O}(d/\\log d)$, and almost matches the integrality gap of $\\widetilde{O}(d/\\log^2 d)$ recently shown for stronger SDPs, namely those obtained using poly-$(\\log(d))$ levels of the $SA^+$ semidefinite hierarchy. The improvement comes from an improved Ramsey-theoretic bound on the independence number of $K_r$-free graphs for large values of $r$.\n"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1504.04767","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-04-18T21:55:07Z","cross_cats_sorted":[],"title_canon_sha256":"011a75d187d0b979ac446b2e8bacb3e06048dbd27a7ff3c2cbd0f0e8fdd81e8e","abstract_canon_sha256":"946f30a332f83d3d05c6b33d2a364c34dfaf6fe607b10bf92e63944ad91fc01b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:03.270623Z","signature_b64":"HxwHoCDBZzWQ4dqm9g6riiaA1fMmFCdZQ+ocxuW4Vd/3q1IHyXQFUcWyVBdmNcPVPewIv7Kuts2ntnXnbbCBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0ca19d6698167bdd9fdeafafe488fc4538ab296e190ab0d05f4ac46418cfc2a","last_reissued_at":"2026-05-18T02:18:03.269894Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:03.269894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Lov\\'asz Theta function for Independent Sets in Sparse Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anupam Gupta, Guru Guruganesh, Nikhil Bansal","submitted_at":"2015-04-18T21:55:07Z","abstract_excerpt":"We consider the maximum independent set problem on graphs with maximum degree~$d$. We show that the integrality gap of the Lov\\'asz $\\vartheta$-function based SDP is $\\widetilde{O}(d/\\log^{3/2} d)$. This improves on the previous best result of $\\widetilde{O}(d/\\log d)$, and almost matches the integrality gap of $\\widetilde{O}(d/\\log^2 d)$ recently shown for stronger SDPs, namely those obtained using poly-$(\\log(d))$ levels of the $SA^+$ semidefinite hierarchy. The improvement comes from an improved Ramsey-theoretic bound on the independence number of $K_r$-free graphs for large values of $r$.\n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04767","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1504.04767","created_at":"2026-05-18T02:18:03.270001+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.04767v2","created_at":"2026-05-18T02:18:03.270001+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04767","created_at":"2026-05-18T02:18:03.270001+00:00"},{"alias_kind":"pith_short_12","alias_value":"UDFBTVTJQFT3","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UDFBTVTJQFT33WP5","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UDFBTVTJ","created_at":"2026-05-18T12:29:44.643036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2603.17730","citing_title":"Fractional coloring via entropy","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UDFBTVTJQFT33WP55L5P4SEPYR","json":"https://pith.science/pith/UDFBTVTJQFT33WP55L5P4SEPYR.json","graph_json":"https://pith.science/api/pith-number/UDFBTVTJQFT33WP55L5P4SEPYR/graph.json","events_json":"https://pith.science/api/pith-number/UDFBTVTJQFT33WP55L5P4SEPYR/events.json","paper":"https://pith.science/paper/UDFBTVTJ"},"agent_actions":{"view_html":"https://pith.science/pith/UDFBTVTJQFT33WP55L5P4SEPYR","download_json":"https://pith.science/pith/UDFBTVTJQFT33WP55L5P4SEPYR.json","view_paper":"https://pith.science/paper/UDFBTVTJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.04767&json=true","fetch_graph":"https://pith.science/api/pith-number/UDFBTVTJQFT33WP55L5P4SEPYR/graph.json","fetch_events":"https://pith.science/api/pith-number/UDFBTVTJQFT33WP55L5P4SEPYR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UDFBTVTJQFT33WP55L5P4SEPYR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UDFBTVTJQFT33WP55L5P4SEPYR/action/storage_attestation","attest_author":"https://pith.science/pith/UDFBTVTJQFT33WP55L5P4SEPYR/action/author_attestation","sign_citation":"https://pith.science/pith/UDFBTVTJQFT33WP55L5P4SEPYR/action/citation_signature","submit_replication":"https://pith.science/pith/UDFBTVTJQFT33WP55L5P4SEPYR/action/replication_record"}},"created_at":"2026-05-18T02:18:03.270001+00:00","updated_at":"2026-05-18T02:18:03.270001+00:00"}