{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:SFOS7V27UXXTY4HDGVP3RCOMGA","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":"f452a4307a6f511e422e3492e127176cacf0c7ba11c3148d4c1d7139ac4deeff","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2007-08-19T11:12:15Z","title_canon_sha256":"0d04a055888525dc58bce742671650c38846484796fa25c3a4aa9aec4454a61e"},"schema_version":"1.0","source":{"id":"0708.2539","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.2539","created_at":"2026-05-18T02:16:28Z"},{"alias_kind":"arxiv_version","alias_value":"0708.2539v2","created_at":"2026-05-18T02:16:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.2539","created_at":"2026-05-18T02:16:28Z"},{"alias_kind":"pith_short_12","alias_value":"SFOS7V27UXXT","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"SFOS7V27UXXTY4HD","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"SFOS7V27","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:6e99e6e8c8a3f277ec398bcbb5a9c6eb1740003d6a0754298a7a067ead034f7e","target":"graph","created_at":"2026-05-18T02:16:28Z","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":"Let P be the set of all primes and P_2=P\\cup{p_1p_2: p_1,p_2\\in P}$. We prove that the sumset 2^P+P_2={2^p+q: p\\in P, q\\in P_2} has a positive lower density.","authors_text":"Hao Pan, Hongze Li","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2007-08-19T11:12:15Z","title":"The Romanov theorem revised"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.2539","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:db38b819dbabdc07ccbef2ce562c2694a20593cf7f1163afe404d63ef8bbf822","target":"record","created_at":"2026-05-18T02:16:28Z","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":"f452a4307a6f511e422e3492e127176cacf0c7ba11c3148d4c1d7139ac4deeff","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2007-08-19T11:12:15Z","title_canon_sha256":"0d04a055888525dc58bce742671650c38846484796fa25c3a4aa9aec4454a61e"},"schema_version":"1.0","source":{"id":"0708.2539","kind":"arxiv","version":2}},"canonical_sha256":"915d2fd75fa5ef3c70e3355fb889cc30041589b8f9c55f7b31ffc0bb54d283c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"915d2fd75fa5ef3c70e3355fb889cc30041589b8f9c55f7b31ffc0bb54d283c8","first_computed_at":"2026-05-18T02:16:28.574110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:28.574110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dbLesU8ccHE7z6DjaaDOJGTPk+H9sqmVmmX6TRuLGBLShx3COHro65AqAk6OE7/gAvGH9+Z+xTresQDTESS6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:28.574790Z","signed_message":"canonical_sha256_bytes"},"source_id":"0708.2539","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db38b819dbabdc07ccbef2ce562c2694a20593cf7f1163afe404d63ef8bbf822","sha256:6e99e6e8c8a3f277ec398bcbb5a9c6eb1740003d6a0754298a7a067ead034f7e"],"state_sha256":"9f350e370d28e85bb92b89ccd75265e8a0baa29c1aa544ed70a2263099cafa5d"}