{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5VFRWNKEJGTWFSTBGWTBC4PBUI","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":"92b38ca65d9c796c65b1049c3ae58c6140776d1bf93abcc4bd3ab69516149848","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-10-16T13:48:53Z","title_canon_sha256":"a5f3e5d18e21058cb929d73b56348cf07040e2d20b192bb4b986fcc0ab16c927"},"schema_version":"1.0","source":{"id":"1210.4408","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4408","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4408v1","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4408","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"pith_short_12","alias_value":"5VFRWNKEJGTW","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5VFRWNKEJGTWFSTB","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5VFRWNKE","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:07ebad5684af9c38bf3ef59eaa36d558926a82aced152b4802851c197e0d89a8","target":"graph","created_at":"2026-05-18T03:43:06Z","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":"One of the earliest and best-known application of the probabilistic method is the proof of existence of a 2 log n$-Ramsey graph, i.e., a graph with n nodes that contains no clique or independent set of size 2 log n. The explicit construction of such a graph is a major open problem. We show that a reasonable hardness assumption implies that in polynomial time one can construct a list containing polylog(n) graphs such that most of them are 2 log n-Ramsey.","authors_text":"Marius Zimand","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-10-16T13:48:53Z","title":"On efficient constructions of short lists containing mostly Ramsey graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4408","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":"sha256:86009d9100d31b2c7f19748e122b8602e7ce52dd42264d73c85cc1f9c57ba9fc","target":"record","created_at":"2026-05-18T03:43:06Z","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":"92b38ca65d9c796c65b1049c3ae58c6140776d1bf93abcc4bd3ab69516149848","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-10-16T13:48:53Z","title_canon_sha256":"a5f3e5d18e21058cb929d73b56348cf07040e2d20b192bb4b986fcc0ab16c927"},"schema_version":"1.0","source":{"id":"1210.4408","kind":"arxiv","version":1}},"canonical_sha256":"ed4b1b354449a762ca6135a61171e1a233a145f91a549b3949c7fce786e9ac95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed4b1b354449a762ca6135a61171e1a233a145f91a549b3949c7fce786e9ac95","first_computed_at":"2026-05-18T03:43:06.061281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:06.061281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3QXq/7hQqP+dKLNh8Cegtrrm6TcUgezVfFNr1sfTwm2LshfmQxSSq+iuuFVTcN8OLC2JXUHZsDJzusB8LoZHCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:06.062042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4408","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86009d9100d31b2c7f19748e122b8602e7ce52dd42264d73c85cc1f9c57ba9fc","sha256:07ebad5684af9c38bf3ef59eaa36d558926a82aced152b4802851c197e0d89a8"],"state_sha256":"6a6871ab8486081f54497944597d78eaa1446634c3c148c7de043854ea452be9"}