{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ONJ55CMNW54QSI6BWVZ72H24G3","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":"9e565e05a683af3b10c7311acd9e85bf486728113eccf0a7640e27baac797124","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-18T16:15:02Z","title_canon_sha256":"71ad5c63439473f88a8b43cf81e79bd470225ab665939a465dea7e6e56ce3fc4"},"schema_version":"1.0","source":{"id":"1212.4406","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4406","created_at":"2026-05-18T03:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4406v1","created_at":"2026-05-18T03:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4406","created_at":"2026-05-18T03:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"ONJ55CMNW54Q","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"ONJ55CMNW54QSI6B","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"ONJ55CMN","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:c88cf6e4fb5edca90a225932b61216248615aebe6df31c86eece817f170bb7c4","target":"graph","created_at":"2026-05-18T03:38:13Z","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":"Some mean value theorems in the style of Bombieri-Vinogradov's theorem are discussed. They concern binary and ternary additive problems with primes in arithmetic progressions and short intervals. Nontrivial estimates for some of these mean values are given. As application inter alia, we show that for large odd n\\not\\equiv 1 (6), Goldbach's ternary problem n=p_1+p_2+p_3 is solvable with primes p_1,p_2 in short intervals p_i \\in [X_i,X_i+Y] with X_{i}^{\\theta_i}=Y, i=1,2, and \\theta_1,\\theta_2\\geq 0.933 such that (p_1+2)(p_2+2) has at most 9 prime factors.","authors_text":"Karin Halupczok","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-18T16:15:02Z","title":"Goldbach's problem with primes in arithmetic progressions and in short intervals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4406","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":"sha256:41b8cff5e6ee8c4285886aff6c3fb829d03d3b465815d3b7318b00f22f8bf6ed","target":"record","created_at":"2026-05-18T03:38:13Z","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":"9e565e05a683af3b10c7311acd9e85bf486728113eccf0a7640e27baac797124","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-18T16:15:02Z","title_canon_sha256":"71ad5c63439473f88a8b43cf81e79bd470225ab665939a465dea7e6e56ce3fc4"},"schema_version":"1.0","source":{"id":"1212.4406","kind":"arxiv","version":1}},"canonical_sha256":"7353de898db7790923c1b573fd1f5c36c3eacc7882bd0a492cac081315d80477","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7353de898db7790923c1b573fd1f5c36c3eacc7882bd0a492cac081315d80477","first_computed_at":"2026-05-18T03:38:13.101516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:13.101516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lTB7My5TgbR6YsqolZlsSA+BUJnzV/H+XRZfcAp4m/XUR01A6kJLpJOKCnV0/cGi4RJBo/3qongrJNWIEdyyAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:13.101980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4406","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41b8cff5e6ee8c4285886aff6c3fb829d03d3b465815d3b7318b00f22f8bf6ed","sha256:c88cf6e4fb5edca90a225932b61216248615aebe6df31c86eece817f170bb7c4"],"state_sha256":"52e894c1e95c1504019e181e8e95ef8c60b2b1c25c70b57bb9c004bd1898632b"}