{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EBES6WNMSU5EEMXIY5HCQJ5MC5","short_pith_number":"pith:EBES6WNM","canonical_record":{"source":{"id":"1606.00869","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-02T20:42:45Z","cross_cats_sorted":[],"title_canon_sha256":"231965c00cd75b85d7d6edef4f1529cc769c06bd27777a596ef96e92fe6d4f42","abstract_canon_sha256":"adfb3a56effeefca2c493c86c8cb610913f14d18877e7f60761ab17b7b9e1375"},"schema_version":"1.0"},"canonical_sha256":"20492f59ac953a4232e8c74e2827ac1752059249a143df22036fd0f794789b97","source":{"kind":"arxiv","id":"1606.00869","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00869","created_at":"2026-05-18T00:39:23Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00869v2","created_at":"2026-05-18T00:39:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00869","created_at":"2026-05-18T00:39:23Z"},{"alias_kind":"pith_short_12","alias_value":"EBES6WNMSU5E","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EBES6WNMSU5EEMXI","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EBES6WNM","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EBES6WNMSU5EEMXIY5HCQJ5MC5","target":"record","payload":{"canonical_record":{"source":{"id":"1606.00869","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-02T20:42:45Z","cross_cats_sorted":[],"title_canon_sha256":"231965c00cd75b85d7d6edef4f1529cc769c06bd27777a596ef96e92fe6d4f42","abstract_canon_sha256":"adfb3a56effeefca2c493c86c8cb610913f14d18877e7f60761ab17b7b9e1375"},"schema_version":"1.0"},"canonical_sha256":"20492f59ac953a4232e8c74e2827ac1752059249a143df22036fd0f794789b97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:23.154282Z","signature_b64":"C7OVpLx0D3KfDh2cG7D74HprvBQRb4FXyCGzPSSYK2c3RW9QvqfVfce+xhNYlB/FxC4j32Xs+mpJxwlT0acNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20492f59ac953a4232e8c74e2827ac1752059249a143df22036fd0f794789b97","last_reissued_at":"2026-05-18T00:39:23.153720Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:23.153720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.00869","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":"2026-05-18T00:39:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FXoCugQE+30UzYRRHGriAQ5l2Tp/6tcvK3AV5HpqkwIpFS817DpH0pF0UfVJ39y3YfWY+Mf5mKzPuRtBc60qDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:31:22.717480Z"},"content_sha256":"b03c7bc9e2c32d3ad52512070becf385ecc092c4a8ca2f23ba084fb61a9acbb3","schema_version":"1.0","event_id":"sha256:b03c7bc9e2c32d3ad52512070becf385ecc092c4a8ca2f23ba084fb61a9acbb3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EBES6WNMSU5EEMXIY5HCQJ5MC5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ces\\`aro average in short intervals for Goldbach numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alessandro Languasco, Alessandro Zaccagnini","submitted_at":"2016-06-02T20:42:45Z","abstract_excerpt":"We prove that a suitable explicit formula for the Cesaro-averaged number of representations of an integer as a sum of two primes holds in short intervals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00869","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":"2026-05-18T00:39:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iqBc1eO0qV8ouxODDSueaCLKKDJNJ2gySQLSJqp1QfyX+GjC9HMFaQi1+6BCqoZem4wvwVXiQUFVO3TSLfLFAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:31:22.717817Z"},"content_sha256":"c1b50fb95ad39a7864efe5680a64a78436b241ba5e33650fcde562161cf2b166","schema_version":"1.0","event_id":"sha256:c1b50fb95ad39a7864efe5680a64a78436b241ba5e33650fcde562161cf2b166"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EBES6WNMSU5EEMXIY5HCQJ5MC5/bundle.json","state_url":"https://pith.science/pith/EBES6WNMSU5EEMXIY5HCQJ5MC5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EBES6WNMSU5EEMXIY5HCQJ5MC5/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":"2026-06-07T07:31:22Z","links":{"resolver":"https://pith.science/pith/EBES6WNMSU5EEMXIY5HCQJ5MC5","bundle":"https://pith.science/pith/EBES6WNMSU5EEMXIY5HCQJ5MC5/bundle.json","state":"https://pith.science/pith/EBES6WNMSU5EEMXIY5HCQJ5MC5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EBES6WNMSU5EEMXIY5HCQJ5MC5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EBES6WNMSU5EEMXIY5HCQJ5MC5","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":"adfb3a56effeefca2c493c86c8cb610913f14d18877e7f60761ab17b7b9e1375","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-02T20:42:45Z","title_canon_sha256":"231965c00cd75b85d7d6edef4f1529cc769c06bd27777a596ef96e92fe6d4f42"},"schema_version":"1.0","source":{"id":"1606.00869","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00869","created_at":"2026-05-18T00:39:23Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00869v2","created_at":"2026-05-18T00:39:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00869","created_at":"2026-05-18T00:39:23Z"},{"alias_kind":"pith_short_12","alias_value":"EBES6WNMSU5E","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EBES6WNMSU5EEMXI","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EBES6WNM","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:c1b50fb95ad39a7864efe5680a64a78436b241ba5e33650fcde562161cf2b166","target":"graph","created_at":"2026-05-18T00:39:23Z","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":"We prove that a suitable explicit formula for the Cesaro-averaged number of representations of an integer as a sum of two primes holds in short intervals.","authors_text":"Alessandro Languasco, Alessandro Zaccagnini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-02T20:42:45Z","title":"Ces\\`aro average in short intervals for Goldbach numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00869","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:b03c7bc9e2c32d3ad52512070becf385ecc092c4a8ca2f23ba084fb61a9acbb3","target":"record","created_at":"2026-05-18T00:39:23Z","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":"adfb3a56effeefca2c493c86c8cb610913f14d18877e7f60761ab17b7b9e1375","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-02T20:42:45Z","title_canon_sha256":"231965c00cd75b85d7d6edef4f1529cc769c06bd27777a596ef96e92fe6d4f42"},"schema_version":"1.0","source":{"id":"1606.00869","kind":"arxiv","version":2}},"canonical_sha256":"20492f59ac953a4232e8c74e2827ac1752059249a143df22036fd0f794789b97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20492f59ac953a4232e8c74e2827ac1752059249a143df22036fd0f794789b97","first_computed_at":"2026-05-18T00:39:23.153720Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:23.153720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C7OVpLx0D3KfDh2cG7D74HprvBQRb4FXyCGzPSSYK2c3RW9QvqfVfce+xhNYlB/FxC4j32Xs+mpJxwlT0acNCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:23.154282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.00869","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b03c7bc9e2c32d3ad52512070becf385ecc092c4a8ca2f23ba084fb61a9acbb3","sha256:c1b50fb95ad39a7864efe5680a64a78436b241ba5e33650fcde562161cf2b166"],"state_sha256":"4fdaffcc6f5c827f86bd527d57713f3c60b6713f0e6baa8f28e63e315dcee93f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nt/RCYK2Yyz8n2XDSRAI2G0NCCkyxMaHjBqBaflDNE1+EI4avRoc4IT9xwuMypcO4n7TRdUNHKb5GQ78a5isCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T07:31:22.719560Z","bundle_sha256":"44936f78c223182158c68d06f91bee4a6c41735c213dcb37199fb2cf470244e8"}}