{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:RFBWJDBBECNWR4R2CYONCI6DON","short_pith_number":"pith:RFBWJDBB","canonical_record":{"source":{"id":"1211.6997","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-11-29T17:30:38Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"db5899deb6c76fbc2b3b87deba2629a45b29ace115337d76d9667681e0723999","abstract_canon_sha256":"dcb882b0b64d161c144fd2f31b92b3f97850860bb05f591733e3c426a09f140c"},"schema_version":"1.0"},"canonical_sha256":"8943648c21209b68f23a161cd123c3735b4a67bac94ce8cce094b1a9e29156d1","source":{"kind":"arxiv","id":"1211.6997","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6997","created_at":"2026-05-18T03:39:41Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6997v2","created_at":"2026-05-18T03:39:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6997","created_at":"2026-05-18T03:39:41Z"},{"alias_kind":"pith_short_12","alias_value":"RFBWJDBBECNW","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RFBWJDBBECNWR4R2","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RFBWJDBB","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:RFBWJDBBECNWR4R2CYONCI6DON","target":"record","payload":{"canonical_record":{"source":{"id":"1211.6997","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-11-29T17:30:38Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"db5899deb6c76fbc2b3b87deba2629a45b29ace115337d76d9667681e0723999","abstract_canon_sha256":"dcb882b0b64d161c144fd2f31b92b3f97850860bb05f591733e3c426a09f140c"},"schema_version":"1.0"},"canonical_sha256":"8943648c21209b68f23a161cd123c3735b4a67bac94ce8cce094b1a9e29156d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:41.153927Z","signature_b64":"8aHDh9127WQcLDcpSeH1h1mzI9fiLCoZs6QLGfNDDKMeTcH1lk0YrQGRu2q0phxwomlvnlJJh0aRphtWhyMmDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8943648c21209b68f23a161cd123c3735b4a67bac94ce8cce094b1a9e29156d1","last_reissued_at":"2026-05-18T03:39:41.153305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:41.153305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.6997","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":"2026-05-18T03:39:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cT5fZ1FneO9C0kWpIonpF+Cg1Qwqua/5yaryVbZtAK9XCUgdnBosT1PcZNixKCV6CYQswaCTUydT8PmprdgeCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:23:22.870218Z"},"content_sha256":"89bf712d1ac955d261def6a43df3c8f456fb0748f2ae4eee93877a5991e6079f","schema_version":"1.0","event_id":"sha256:89bf712d1ac955d261def6a43df3c8f456fb0748f2ae4eee93877a5991e6079f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:RFBWJDBBECNWR4R2CYONCI6DON","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Power of Choice for Random Satisfiability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CC","authors_text":"Cristopher Moore, Josep Diaz, Thomas Hayes, Varsha Dani","submitted_at":"2012-11-29T17:30:38Z","abstract_excerpt":"We consider Achlioptas processes for k-SAT formulas. We create a semi-random formula with n variables and m clauses, where each clause is a choice, made on-line, between two or more uniformly random clauses. Our goal is to delay the satisfiability/unsatisfiability transition, keeping the formula satisfiable up to densities m/n beyond the satisfiability threshold alpha_k for random k-SAT. We show that three choices suffice to raise the threshold for any k >= 3, and that two choices suffice for all 3 <= k <= 25. We also show that two choices suffice to lower the threshold for all k >= 3, making "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6997","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":"2026-05-18T03:39:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ozXTNjU5TcitVMVipxq0P7CX43lLUpjdmCRo7fJ0PL+ayrXmnM7K49TWGCRLybPqZCFdO8Rbf+Eyyj10Dw28Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:23:22.870577Z"},"content_sha256":"307dc6425662faa7dd7fff20be668205ce5396373f7a4253ddff85a8eed762ef","schema_version":"1.0","event_id":"sha256:307dc6425662faa7dd7fff20be668205ce5396373f7a4253ddff85a8eed762ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RFBWJDBBECNWR4R2CYONCI6DON/bundle.json","state_url":"https://pith.science/pith/RFBWJDBBECNWR4R2CYONCI6DON/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RFBWJDBBECNWR4R2CYONCI6DON/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":"2026-06-01T11:23:22Z","links":{"resolver":"https://pith.science/pith/RFBWJDBBECNWR4R2CYONCI6DON","bundle":"https://pith.science/pith/RFBWJDBBECNWR4R2CYONCI6DON/bundle.json","state":"https://pith.science/pith/RFBWJDBBECNWR4R2CYONCI6DON/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RFBWJDBBECNWR4R2CYONCI6DON/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RFBWJDBBECNWR4R2CYONCI6DON","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":"dcb882b0b64d161c144fd2f31b92b3f97850860bb05f591733e3c426a09f140c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-11-29T17:30:38Z","title_canon_sha256":"db5899deb6c76fbc2b3b87deba2629a45b29ace115337d76d9667681e0723999"},"schema_version":"1.0","source":{"id":"1211.6997","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6997","created_at":"2026-05-18T03:39:41Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6997v2","created_at":"2026-05-18T03:39:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6997","created_at":"2026-05-18T03:39:41Z"},{"alias_kind":"pith_short_12","alias_value":"RFBWJDBBECNW","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RFBWJDBBECNWR4R2","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RFBWJDBB","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:307dc6425662faa7dd7fff20be668205ce5396373f7a4253ddff85a8eed762ef","target":"graph","created_at":"2026-05-18T03:39:41Z","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 Achlioptas processes for k-SAT formulas. We create a semi-random formula with n variables and m clauses, where each clause is a choice, made on-line, between two or more uniformly random clauses. Our goal is to delay the satisfiability/unsatisfiability transition, keeping the formula satisfiable up to densities m/n beyond the satisfiability threshold alpha_k for random k-SAT. We show that three choices suffice to raise the threshold for any k >= 3, and that two choices suffice for all 3 <= k <= 25. We also show that two choices suffice to lower the threshold for all k >= 3, making ","authors_text":"Cristopher Moore, Josep Diaz, Thomas Hayes, Varsha Dani","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-11-29T17:30:38Z","title":"The Power of Choice for Random Satisfiability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6997","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":"sha256:89bf712d1ac955d261def6a43df3c8f456fb0748f2ae4eee93877a5991e6079f","target":"record","created_at":"2026-05-18T03:39:41Z","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":"dcb882b0b64d161c144fd2f31b92b3f97850860bb05f591733e3c426a09f140c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-11-29T17:30:38Z","title_canon_sha256":"db5899deb6c76fbc2b3b87deba2629a45b29ace115337d76d9667681e0723999"},"schema_version":"1.0","source":{"id":"1211.6997","kind":"arxiv","version":2}},"canonical_sha256":"8943648c21209b68f23a161cd123c3735b4a67bac94ce8cce094b1a9e29156d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8943648c21209b68f23a161cd123c3735b4a67bac94ce8cce094b1a9e29156d1","first_computed_at":"2026-05-18T03:39:41.153305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:41.153305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8aHDh9127WQcLDcpSeH1h1mzI9fiLCoZs6QLGfNDDKMeTcH1lk0YrQGRu2q0phxwomlvnlJJh0aRphtWhyMmDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:41.153927Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.6997","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89bf712d1ac955d261def6a43df3c8f456fb0748f2ae4eee93877a5991e6079f","sha256:307dc6425662faa7dd7fff20be668205ce5396373f7a4253ddff85a8eed762ef"],"state_sha256":"5f3b97201930bb76dadf085473de47031da2f47c681de382290ce752a9a305b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vr8KCnqdw27ZzFHn0YXE4lEd++A1Fz1kahvBCugnFh5+Ai5Mhs8D2q3FjgyqjwiSFWZxg2NNJnnufqhlY474Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T11:23:22.872460Z","bundle_sha256":"3d049ac614a2a56a24d72f7c1095c360dd2b2b5af8ad5f207caef25af3d3a7a7"}}