{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:E6C4J7HVDLB6KYUK3X2ZE4BQI3","short_pith_number":"pith:E6C4J7HV","canonical_record":{"source":{"id":"1610.05344","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-17T20:31:52Z","cross_cats_sorted":[],"title_canon_sha256":"a090c1effdd75e499ee1ff464f10781fcd97ca36d2f8792b02945d9767ceb6a4","abstract_canon_sha256":"283dbd377b1d1edef277c0526438981a72d4542ddc9f58d85186746152f0cb87"},"schema_version":"1.0"},"canonical_sha256":"2785c4fcf51ac3e5628addf592703046ddd867a75b7df643866092c0c375698e","source":{"kind":"arxiv","id":"1610.05344","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05344","created_at":"2026-05-18T01:00:18Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05344v2","created_at":"2026-05-18T01:00:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05344","created_at":"2026-05-18T01:00:18Z"},{"alias_kind":"pith_short_12","alias_value":"E6C4J7HVDLB6","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"E6C4J7HVDLB6KYUK","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"E6C4J7HV","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:E6C4J7HVDLB6KYUK3X2ZE4BQI3","target":"record","payload":{"canonical_record":{"source":{"id":"1610.05344","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-17T20:31:52Z","cross_cats_sorted":[],"title_canon_sha256":"a090c1effdd75e499ee1ff464f10781fcd97ca36d2f8792b02945d9767ceb6a4","abstract_canon_sha256":"283dbd377b1d1edef277c0526438981a72d4542ddc9f58d85186746152f0cb87"},"schema_version":"1.0"},"canonical_sha256":"2785c4fcf51ac3e5628addf592703046ddd867a75b7df643866092c0c375698e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:18.926095Z","signature_b64":"gqyKWOl6UHDPXi+1Az7gWTMJFmFjcLJXBR+GofMdOj2LJVs6/MuEcLGWRsYApHt1gGQZFUMzLCbCFZW2D/2/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2785c4fcf51ac3e5628addf592703046ddd867a75b7df643866092c0c375698e","last_reissued_at":"2026-05-18T01:00:18.925587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:18.925587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.05344","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":"2026-05-18T01:00:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L6OHKHK+mH9fjSusdhD4b/SSpmhiV/ahaeJyfS8r0QXxMQkdlug7snbpMTpvhuSteVoJP+PZ7AN0Aw+4C1rgBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T06:29:40.842784Z"},"content_sha256":"2fa47163093cc397ba4b41b78a31747f37160b55179bac63cb61dcb638657f74","schema_version":"1.0","event_id":"sha256:2fa47163093cc397ba4b41b78a31747f37160b55179bac63cb61dcb638657f74"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:E6C4J7HVDLB6KYUK3X2ZE4BQI3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A variant of Bombieri-Vinogradov theorem with explicit constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alisa Sedunova","submitted_at":"2016-10-17T20:31:52Z","abstract_excerpt":"In this paper we improve the result of Akbary and Hambrook by a factor of log x by obtaining a better version of Vaughan's inequality and using the explicit variant of an inequality connected to the M\\\"obius function, derived by Helfgott in his work on ternary Goldbach conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05344","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":"2026-05-18T01:00:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CADY1/2p/+1B3sjXjoep00ee6CI2VXzPmNlkPjRk6UBla7v4BoXvrj9Ljm9EQBxL1RQhnWQJMFvX6tmQr+S6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T06:29:40.843480Z"},"content_sha256":"1c2a56ec0dcb5c353b1ba4a2e42d361846a6b8514cb162d2345d3361f05dd145","schema_version":"1.0","event_id":"sha256:1c2a56ec0dcb5c353b1ba4a2e42d361846a6b8514cb162d2345d3361f05dd145"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E6C4J7HVDLB6KYUK3X2ZE4BQI3/bundle.json","state_url":"https://pith.science/pith/E6C4J7HVDLB6KYUK3X2ZE4BQI3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E6C4J7HVDLB6KYUK3X2ZE4BQI3/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":"2026-06-08T06:29:40Z","links":{"resolver":"https://pith.science/pith/E6C4J7HVDLB6KYUK3X2ZE4BQI3","bundle":"https://pith.science/pith/E6C4J7HVDLB6KYUK3X2ZE4BQI3/bundle.json","state":"https://pith.science/pith/E6C4J7HVDLB6KYUK3X2ZE4BQI3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E6C4J7HVDLB6KYUK3X2ZE4BQI3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:E6C4J7HVDLB6KYUK3X2ZE4BQI3","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":"283dbd377b1d1edef277c0526438981a72d4542ddc9f58d85186746152f0cb87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-17T20:31:52Z","title_canon_sha256":"a090c1effdd75e499ee1ff464f10781fcd97ca36d2f8792b02945d9767ceb6a4"},"schema_version":"1.0","source":{"id":"1610.05344","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05344","created_at":"2026-05-18T01:00:18Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05344v2","created_at":"2026-05-18T01:00:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05344","created_at":"2026-05-18T01:00:18Z"},{"alias_kind":"pith_short_12","alias_value":"E6C4J7HVDLB6","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"E6C4J7HVDLB6KYUK","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"E6C4J7HV","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:1c2a56ec0dcb5c353b1ba4a2e42d361846a6b8514cb162d2345d3361f05dd145","target":"graph","created_at":"2026-05-18T01:00:18Z","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 improve the result of Akbary and Hambrook by a factor of log x by obtaining a better version of Vaughan's inequality and using the explicit variant of an inequality connected to the M\\\"obius function, derived by Helfgott in his work on ternary Goldbach conjecture.","authors_text":"Alisa Sedunova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-17T20:31:52Z","title":"A variant of Bombieri-Vinogradov theorem with explicit constants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05344","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":"sha256:2fa47163093cc397ba4b41b78a31747f37160b55179bac63cb61dcb638657f74","target":"record","created_at":"2026-05-18T01:00:18Z","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":"283dbd377b1d1edef277c0526438981a72d4542ddc9f58d85186746152f0cb87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-17T20:31:52Z","title_canon_sha256":"a090c1effdd75e499ee1ff464f10781fcd97ca36d2f8792b02945d9767ceb6a4"},"schema_version":"1.0","source":{"id":"1610.05344","kind":"arxiv","version":2}},"canonical_sha256":"2785c4fcf51ac3e5628addf592703046ddd867a75b7df643866092c0c375698e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2785c4fcf51ac3e5628addf592703046ddd867a75b7df643866092c0c375698e","first_computed_at":"2026-05-18T01:00:18.925587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:18.925587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gqyKWOl6UHDPXi+1Az7gWTMJFmFjcLJXBR+GofMdOj2LJVs6/MuEcLGWRsYApHt1gGQZFUMzLCbCFZW2D/2/Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:18.926095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.05344","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fa47163093cc397ba4b41b78a31747f37160b55179bac63cb61dcb638657f74","sha256:1c2a56ec0dcb5c353b1ba4a2e42d361846a6b8514cb162d2345d3361f05dd145"],"state_sha256":"b869f80fa09011bd11a8d37c8bc096d07fa307b679add2ce573576800a037a7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X4B6Gbg3Tl1HQzur4Qy1n8mW+1Zs1Y+6SwAjApf80NJ/5+Z8fLfre9nlfmf5SRtCGpE6mqEmcEoGk7+9LetvBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T06:29:40.847855Z","bundle_sha256":"f28fefc4e340d7e7693463f369b6304e818ed95f15ac16b4cdc22ee0291fb163"}}