{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DJOULEUU4R7GCYMGMQ3FS7KTO7","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":"0a5407783c48bb05842c90f4b23f0cd2fc479b1ad8717a1359b36317c8c5a2f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-22T11:58:54Z","title_canon_sha256":"6ead93511b25ad1d266065855bfe25dbecc61203b38091f7aa439fa01fe1eb46"},"schema_version":"1.0","source":{"id":"1408.5271","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5271","created_at":"2026-05-18T02:44:33Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5271v1","created_at":"2026-05-18T02:44:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5271","created_at":"2026-05-18T02:44:33Z"},{"alias_kind":"pith_short_12","alias_value":"DJOULEUU4R7G","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DJOULEUU4R7GCYMG","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DJOULEUU","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:891283c8b1765aabcbddc2879663526d1c5545e86ba221d5f585245092baee5f","target":"graph","created_at":"2026-05-18T02:44:33Z","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":"In this paper we introduce a general framework for proving lower bounds for various Ramsey type problems within random settings. The main idea is to view the problem from an algorithmic perspective: we aim at providing an algorithm that finds the desired colouring with high probability. Our framework allows to reduce the probabilistic problem of whether the Ramsey property at hand holds for random (hyper)graphs with edge probability $p$ to a deterministic question of whether there exists a finite graph that forms an obstruction.\n  In the second part of the paper we apply this framework to addr","authors_text":"Angelika Steger, Nemanja \\v{S}kori\\'c, Rajko Nenadov, Yury Person","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-22T11:58:54Z","title":"An algorithmic framework for obtaining lower bounds for random Ramsey problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5271","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:c9549e7373b0bbefcaa0f050513576d9fe85f94150986f93ea395cf49be44959","target":"record","created_at":"2026-05-18T02:44:33Z","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":"0a5407783c48bb05842c90f4b23f0cd2fc479b1ad8717a1359b36317c8c5a2f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-22T11:58:54Z","title_canon_sha256":"6ead93511b25ad1d266065855bfe25dbecc61203b38091f7aa439fa01fe1eb46"},"schema_version":"1.0","source":{"id":"1408.5271","kind":"arxiv","version":1}},"canonical_sha256":"1a5d459294e47e6161866436597d5377f4cc8fc11c2dcb8761bc331ac6498298","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a5d459294e47e6161866436597d5377f4cc8fc11c2dcb8761bc331ac6498298","first_computed_at":"2026-05-18T02:44:33.524914Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:33.524914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4XKxxgw9ke12BQ8DBCzSNxOw3U8GueEHGY33HbnKJQBn8Pc9aDa/X1Q5owByITkLWh4jStgKixV8Q1WaHaiRAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:33.525551Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5271","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9549e7373b0bbefcaa0f050513576d9fe85f94150986f93ea395cf49be44959","sha256:891283c8b1765aabcbddc2879663526d1c5545e86ba221d5f585245092baee5f"],"state_sha256":"fe971178439a3aa0400df64e966caac1685433ff6dcd3d5e2a411041ae2ee07e"}