{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EOHPOKOH3MQEARK2QPDDUO5CQD","short_pith_number":"pith:EOHPOKOH","canonical_record":{"source":{"id":"1411.2989","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-11T21:33:45Z","cross_cats_sorted":[],"title_canon_sha256":"af2fb0f937eaefe59d19484b77f16df7750461cd1e3ff3df9ad213d236e51226","abstract_canon_sha256":"388034373022422f9358d430ac192b2754e86f542f01724debfb65d59cdd6359"},"schema_version":"1.0"},"canonical_sha256":"238ef729c7db2040455a83c63a3ba280e0afa2182d6ea40bc7938e843330a501","source":{"kind":"arxiv","id":"1411.2989","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2989","created_at":"2026-05-18T01:32:18Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2989v2","created_at":"2026-05-18T01:32:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2989","created_at":"2026-05-18T01:32:18Z"},{"alias_kind":"pith_short_12","alias_value":"EOHPOKOH3MQE","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EOHPOKOH3MQEARK2","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EOHPOKOH","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EOHPOKOH3MQEARK2QPDDUO5CQD","target":"record","payload":{"canonical_record":{"source":{"id":"1411.2989","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-11T21:33:45Z","cross_cats_sorted":[],"title_canon_sha256":"af2fb0f937eaefe59d19484b77f16df7750461cd1e3ff3df9ad213d236e51226","abstract_canon_sha256":"388034373022422f9358d430ac192b2754e86f542f01724debfb65d59cdd6359"},"schema_version":"1.0"},"canonical_sha256":"238ef729c7db2040455a83c63a3ba280e0afa2182d6ea40bc7938e843330a501","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:18.899566Z","signature_b64":"jfBEdg6q+XCbelPFVK5Xy+WWnYNKjHTiDC2kSPvxnLyeo2knKksKz1L9qexGuBQlZMItqdQw+JbVhN3RrhrSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"238ef729c7db2040455a83c63a3ba280e0afa2182d6ea40bc7938e843330a501","last_reissued_at":"2026-05-18T01:32:18.898909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:18.898909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.2989","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":"2026-05-18T01:32:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R0m74Nj4Yl8MACPozz2Kr8jrCJCMuQO83AD6zMwsRqp4BVoBIrdFOzptwqYwLzOrwVaKACR64M1NyY9YbVZ8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:37:22.857397Z"},"content_sha256":"64aa106ccb5dde1b3576e3a5b74978c73ccadd69bfc259baf300570cffcd1ad2","schema_version":"1.0","event_id":"sha256:64aa106ccb5dde1b3576e3a5b74978c73ccadd69bfc259baf300570cffcd1ad2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EOHPOKOH3MQEARK2QPDDUO5CQD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gaps between Primes in Beatty Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Liangyi Zhao, Roger C. Baker","submitted_at":"2014-11-11T21:33:45Z","abstract_excerpt":"In this paper, we study the gaps between primes in Beatty sequences following the methods in the recent breakthrough of J. Maynard."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2989","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":"2026-05-18T01:32:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hsev1QQU5wRFDcFKjch6psKVlEKgLdTdAONzy62jiaXHjeL+AxfB2hQaVKtp3u7a+YtpWiZe7qk2G7bN04MVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:37:22.857754Z"},"content_sha256":"1c1a7205b968629d34f09d127549677db86713a033c664043608c3c9f8dd74ad","schema_version":"1.0","event_id":"sha256:1c1a7205b968629d34f09d127549677db86713a033c664043608c3c9f8dd74ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EOHPOKOH3MQEARK2QPDDUO5CQD/bundle.json","state_url":"https://pith.science/pith/EOHPOKOH3MQEARK2QPDDUO5CQD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EOHPOKOH3MQEARK2QPDDUO5CQD/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":"2026-06-07T02:37:22Z","links":{"resolver":"https://pith.science/pith/EOHPOKOH3MQEARK2QPDDUO5CQD","bundle":"https://pith.science/pith/EOHPOKOH3MQEARK2QPDDUO5CQD/bundle.json","state":"https://pith.science/pith/EOHPOKOH3MQEARK2QPDDUO5CQD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EOHPOKOH3MQEARK2QPDDUO5CQD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EOHPOKOH3MQEARK2QPDDUO5CQD","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":"388034373022422f9358d430ac192b2754e86f542f01724debfb65d59cdd6359","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-11T21:33:45Z","title_canon_sha256":"af2fb0f937eaefe59d19484b77f16df7750461cd1e3ff3df9ad213d236e51226"},"schema_version":"1.0","source":{"id":"1411.2989","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2989","created_at":"2026-05-18T01:32:18Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2989v2","created_at":"2026-05-18T01:32:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2989","created_at":"2026-05-18T01:32:18Z"},{"alias_kind":"pith_short_12","alias_value":"EOHPOKOH3MQE","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EOHPOKOH3MQEARK2","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EOHPOKOH","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:1c1a7205b968629d34f09d127549677db86713a033c664043608c3c9f8dd74ad","target":"graph","created_at":"2026-05-18T01:32:18Z","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 study the gaps between primes in Beatty sequences following the methods in the recent breakthrough of J. Maynard.","authors_text":"Liangyi Zhao, Roger C. Baker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-11T21:33:45Z","title":"Gaps between Primes in Beatty Sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2989","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":"sha256:64aa106ccb5dde1b3576e3a5b74978c73ccadd69bfc259baf300570cffcd1ad2","target":"record","created_at":"2026-05-18T01:32:18Z","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":"388034373022422f9358d430ac192b2754e86f542f01724debfb65d59cdd6359","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-11T21:33:45Z","title_canon_sha256":"af2fb0f937eaefe59d19484b77f16df7750461cd1e3ff3df9ad213d236e51226"},"schema_version":"1.0","source":{"id":"1411.2989","kind":"arxiv","version":2}},"canonical_sha256":"238ef729c7db2040455a83c63a3ba280e0afa2182d6ea40bc7938e843330a501","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"238ef729c7db2040455a83c63a3ba280e0afa2182d6ea40bc7938e843330a501","first_computed_at":"2026-05-18T01:32:18.898909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:18.898909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jfBEdg6q+XCbelPFVK5Xy+WWnYNKjHTiDC2kSPvxnLyeo2knKksKz1L9qexGuBQlZMItqdQw+JbVhN3RrhrSBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:18.899566Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2989","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64aa106ccb5dde1b3576e3a5b74978c73ccadd69bfc259baf300570cffcd1ad2","sha256:1c1a7205b968629d34f09d127549677db86713a033c664043608c3c9f8dd74ad"],"state_sha256":"34a63cba990784ed5b3d7304fe77e2a96de8094726e2b6c41e18a790ea96d3fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KMgnIP3c8zcvZuwF2NX6MvYyhOSSP+kJepb6LYYPFL7Qy1kIbHBP2NljNAnnw6ggstUmj/vxHD3gy2fzujJbDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T02:37:22.860269Z","bundle_sha256":"82e4434f60f0aa10cf6359ce44047b4a9b48393b6db8058e089cbd0a902a601a"}}