{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:U56YBOKT655OCOVGCCR52DYCMP","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":"fd905781ff31f65439a9f42f592a84166ac801a75b96bdc2b1a04d2938a2d498","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-06-12T09:28:09Z","title_canon_sha256":"6909f041eb2a2a933d063b8ed43820f42dd7564a2298e61061b56b9fe47aa685"},"schema_version":"1.0","source":{"id":"1206.2473","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2473","created_at":"2026-05-18T03:30:28Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2473v3","created_at":"2026-05-18T03:30:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2473","created_at":"2026-05-18T03:30:28Z"},{"alias_kind":"pith_short_12","alias_value":"U56YBOKT655O","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"U56YBOKT655OCOVG","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"U56YBOKT","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:27f2a35b55ad04db9613511283ad7a3e6e598f3b49a7ef22054c9719e7e6d911","target":"graph","created_at":"2026-05-18T03:30:28Z","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":"For arbitrary $c_0>0$, if $A$ is a subset of the primes less than $x$ with cardinality $\\delta x (\\log x)^{-1}$ with $\\delta\\geq (\\log x)^{-c_0}$, then there exists a positive constant $c$ such that the cardinality of $A+A$ is larger than $c\\, \\delta x (\\log\\log x)^{-1}$.","authors_text":"Boqing Xue, Hongze Li, Zhen Cui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-06-12T09:28:09Z","title":"On sums of sparse prime subsets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2473","kind":"arxiv","version":3},"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:f15b77d6d246bd6af11c53f7646ecef26fbfe2302ca55c19e4afa54a31128d11","target":"record","created_at":"2026-05-18T03:30:28Z","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":"fd905781ff31f65439a9f42f592a84166ac801a75b96bdc2b1a04d2938a2d498","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-06-12T09:28:09Z","title_canon_sha256":"6909f041eb2a2a933d063b8ed43820f42dd7564a2298e61061b56b9fe47aa685"},"schema_version":"1.0","source":{"id":"1206.2473","kind":"arxiv","version":3}},"canonical_sha256":"a77d80b953f77ae13aa610a3dd0f0263ed2215b4a15a0643972e9d92b399d2f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a77d80b953f77ae13aa610a3dd0f0263ed2215b4a15a0643972e9d92b399d2f7","first_computed_at":"2026-05-18T03:30:28.045015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:28.045015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pnIGhqB1UT0OrF5+KHpUCy3QAmBs9kXs/RoHP5lziBiZsAzZ1Mwf3G9HZPUXyGwAkNQUFLKPvZpyAZxHQIBICQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:28.045571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.2473","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f15b77d6d246bd6af11c53f7646ecef26fbfe2302ca55c19e4afa54a31128d11","sha256:27f2a35b55ad04db9613511283ad7a3e6e598f3b49a7ef22054c9719e7e6d911"],"state_sha256":"95026ec900a4550ddd95ce27484b5c6fbb0ff0d517451ff97c448115d96fe345"}