{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UDFBTVTJQFT33WP55L5P4SEPYR","short_pith_number":"pith:UDFBTVTJ","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"},"canonical_sha256":"a0ca19d6698167bdd9fdeafafe488fc4538ab296e190ab0d05f4ac46418cfc2a","source":{"kind":"arxiv","id":"1504.04767","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04767","created_at":"2026-05-18T02:18:03Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04767v2","created_at":"2026-05-18T02:18:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04767","created_at":"2026-05-18T02:18:03Z"},{"alias_kind":"pith_short_12","alias_value":"UDFBTVTJQFT3","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UDFBTVTJQFT33WP5","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UDFBTVTJ","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UDFBTVTJQFT33WP55L5P4SEPYR","target":"record","payload":{"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"},"canonical_sha256":"a0ca19d6698167bdd9fdeafafe488fc4538ab296e190ab0d05f4ac46418cfc2a","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"},"source_kind":"arxiv","source_id":"1504.04767","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:18:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LMS+mUfHl/auVx+Yz/EJbwyKFs5adMEepRF9HakkvH0oA25UesEx2Epij3lYHuQP5BeGNsksxB+f4S5a2bH3AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:13:13.520983Z"},"content_sha256":"918e35c4298843b8bf23a98f8e55666f1f53cf9aefbfb57c7908fd51d91f2f23","schema_version":"1.0","event_id":"sha256:918e35c4298843b8bf23a98f8e55666f1f53cf9aefbfb57c7908fd51d91f2f23"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UDFBTVTJQFT33WP55L5P4SEPYR","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:18:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ggvC7Fk4LTzDufduymFw0EkzI7IObQxLSQsNZw/9bXGxWJwRUR851NKN57z3lxTIhf3E4QOdbGIrPc+zMpDEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:13:13.521666Z"},"content_sha256":"9098cb05f022904b30e36625da975a1109b3878d708090db9353c6e62147e5f0","schema_version":"1.0","event_id":"sha256:9098cb05f022904b30e36625da975a1109b3878d708090db9353c6e62147e5f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UDFBTVTJQFT33WP55L5P4SEPYR/bundle.json","state_url":"https://pith.science/pith/UDFBTVTJQFT33WP55L5P4SEPYR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UDFBTVTJQFT33WP55L5P4SEPYR/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":"2026-05-31T04:13:13Z","links":{"resolver":"https://pith.science/pith/UDFBTVTJQFT33WP55L5P4SEPYR","bundle":"https://pith.science/pith/UDFBTVTJQFT33WP55L5P4SEPYR/bundle.json","state":"https://pith.science/pith/UDFBTVTJQFT33WP55L5P4SEPYR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UDFBTVTJQFT33WP55L5P4SEPYR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UDFBTVTJQFT33WP55L5P4SEPYR","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":"946f30a332f83d3d05c6b33d2a364c34dfaf6fe607b10bf92e63944ad91fc01b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-04-18T21:55:07Z","title_canon_sha256":"011a75d187d0b979ac446b2e8bacb3e06048dbd27a7ff3c2cbd0f0e8fdd81e8e"},"schema_version":"1.0","source":{"id":"1504.04767","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04767","created_at":"2026-05-18T02:18:03Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04767v2","created_at":"2026-05-18T02:18:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04767","created_at":"2026-05-18T02:18:03Z"},{"alias_kind":"pith_short_12","alias_value":"UDFBTVTJQFT3","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UDFBTVTJQFT33WP5","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UDFBTVTJ","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:9098cb05f022904b30e36625da975a1109b3878d708090db9353c6e62147e5f0","target":"graph","created_at":"2026-05-18T02:18:03Z","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 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","authors_text":"Anupam Gupta, Guru Guruganesh, Nikhil Bansal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-04-18T21:55:07Z","title":"On the Lov\\'asz Theta function for Independent Sets in Sparse Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04767","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":"sha256:918e35c4298843b8bf23a98f8e55666f1f53cf9aefbfb57c7908fd51d91f2f23","target":"record","created_at":"2026-05-18T02:18:03Z","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":"946f30a332f83d3d05c6b33d2a364c34dfaf6fe607b10bf92e63944ad91fc01b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-04-18T21:55:07Z","title_canon_sha256":"011a75d187d0b979ac446b2e8bacb3e06048dbd27a7ff3c2cbd0f0e8fdd81e8e"},"schema_version":"1.0","source":{"id":"1504.04767","kind":"arxiv","version":2}},"canonical_sha256":"a0ca19d6698167bdd9fdeafafe488fc4538ab296e190ab0d05f4ac46418cfc2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0ca19d6698167bdd9fdeafafe488fc4538ab296e190ab0d05f4ac46418cfc2a","first_computed_at":"2026-05-18T02:18:03.269894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:03.269894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HxwHoCDBZzWQ4dqm9g6riiaA1fMmFCdZQ+ocxuW4Vd/3q1IHyXQFUcWyVBdmNcPVPewIv7Kuts2ntnXnbbCBCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:03.270623Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.04767","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:918e35c4298843b8bf23a98f8e55666f1f53cf9aefbfb57c7908fd51d91f2f23","sha256:9098cb05f022904b30e36625da975a1109b3878d708090db9353c6e62147e5f0"],"state_sha256":"397d30f81d639f4b324169dd95123222db8da1c2b3624f98b335f19f534357c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iZvMx9O5Via+NRSCQf6hMJ0/FX3r+CtSXfpM2C3aKwlUYNeHEfjmw8sPvHvVfH4vzNjLGaLx9trKVAbDt3BvDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:13:13.525289Z","bundle_sha256":"d1d1ee6d74d5c69bbbf1436297b8208a63abb2ed6ff8a9bae63ac4255540b467"}}