{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:OVUHSQL542YQFSUWNSGVHOVQEU","short_pith_number":"pith:OVUHSQL5","schema_version":"1.0","canonical_sha256":"756879417de6b102ca966c8d53bab02506b9110470f6d854c44dd8c91fe0457e","source":{"kind":"arxiv","id":"1401.2436","version":1},"attestation_state":"computed","paper":{"title":"Hardness of robust graph isomorphism, Lasserre gaps, and asymmetry of random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Chenggang Wu, John Wright, Ryan O'Donnell, Yuan Zhou","submitted_at":"2014-01-10T19:50:15Z","abstract_excerpt":"Building on work of Cai, F\\\"urer, and Immerman \\cite{CFI92}, we show two hardness results for the Graph Isomorphism problem. First, we show that there are pairs of nonisomorphic $n$-vertex graphs $G$ and $H$ such that any sum-of-squares (SOS) proof of nonisomorphism requires degree $\\Omega(n)$. In other words, we show an $\\Omega(n)$-round integrality gap for the Lasserre SDP relaxation. In fact, we show this for pairs $G$ and $H$ which are not even $(1-10^{-14})$-isomorphic. (Here we say that two $n$-vertex, $m$-edge graphs $G$ and $H$ are $\\alpha$-isomorphic if there is a bijection between th"},"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":"1401.2436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-01-10T19:50:15Z","cross_cats_sorted":[],"title_canon_sha256":"fd5d259e0045a1e42c3a476d8f10202e6e26ac83a0b3d409265e8634d7132e6b","abstract_canon_sha256":"a32d63d230d40deebda4b280b5cf2fa50ef48c4e2db3e279cb2f8fcb3033d88d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:45.279171Z","signature_b64":"PpePyrFXVT80glpa1BEfnH95atS0+eY62JVx0rSYlKJHX+Yol+QcbBOkOXQKH30RJtbjD9jMLNYMzyIX+2VDBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"756879417de6b102ca966c8d53bab02506b9110470f6d854c44dd8c91fe0457e","last_reissued_at":"2026-05-18T03:02:45.278468Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:45.278468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hardness of robust graph isomorphism, Lasserre gaps, and asymmetry of random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Chenggang Wu, John Wright, Ryan O'Donnell, Yuan Zhou","submitted_at":"2014-01-10T19:50:15Z","abstract_excerpt":"Building on work of Cai, F\\\"urer, and Immerman \\cite{CFI92}, we show two hardness results for the Graph Isomorphism problem. First, we show that there are pairs of nonisomorphic $n$-vertex graphs $G$ and $H$ such that any sum-of-squares (SOS) proof of nonisomorphism requires degree $\\Omega(n)$. In other words, we show an $\\Omega(n)$-round integrality gap for the Lasserre SDP relaxation. In fact, we show this for pairs $G$ and $H$ which are not even $(1-10^{-14})$-isomorphic. (Here we say that two $n$-vertex, $m$-edge graphs $G$ and $H$ are $\\alpha$-isomorphic if there is a bijection between th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2436","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":""},"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":"1401.2436","created_at":"2026-05-18T03:02:45.278574+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.2436v1","created_at":"2026-05-18T03:02:45.278574+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2436","created_at":"2026-05-18T03:02:45.278574+00:00"},{"alias_kind":"pith_short_12","alias_value":"OVUHSQL542YQ","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OVUHSQL542YQFSUW","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OVUHSQL5","created_at":"2026-05-18T12:28:43.426989+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OVUHSQL542YQFSUWNSGVHOVQEU","json":"https://pith.science/pith/OVUHSQL542YQFSUWNSGVHOVQEU.json","graph_json":"https://pith.science/api/pith-number/OVUHSQL542YQFSUWNSGVHOVQEU/graph.json","events_json":"https://pith.science/api/pith-number/OVUHSQL542YQFSUWNSGVHOVQEU/events.json","paper":"https://pith.science/paper/OVUHSQL5"},"agent_actions":{"view_html":"https://pith.science/pith/OVUHSQL542YQFSUWNSGVHOVQEU","download_json":"https://pith.science/pith/OVUHSQL542YQFSUWNSGVHOVQEU.json","view_paper":"https://pith.science/paper/OVUHSQL5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.2436&json=true","fetch_graph":"https://pith.science/api/pith-number/OVUHSQL542YQFSUWNSGVHOVQEU/graph.json","fetch_events":"https://pith.science/api/pith-number/OVUHSQL542YQFSUWNSGVHOVQEU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OVUHSQL542YQFSUWNSGVHOVQEU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OVUHSQL542YQFSUWNSGVHOVQEU/action/storage_attestation","attest_author":"https://pith.science/pith/OVUHSQL542YQFSUWNSGVHOVQEU/action/author_attestation","sign_citation":"https://pith.science/pith/OVUHSQL542YQFSUWNSGVHOVQEU/action/citation_signature","submit_replication":"https://pith.science/pith/OVUHSQL542YQFSUWNSGVHOVQEU/action/replication_record"}},"created_at":"2026-05-18T03:02:45.278574+00:00","updated_at":"2026-05-18T03:02:45.278574+00:00"}