{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:GQIGKLXGPAQTOOXRWBNGYPN3RU","short_pith_number":"pith:GQIGKLXG","canonical_record":{"source":{"id":"2309.00567","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-09-01T16:22:26Z","cross_cats_sorted":[],"title_canon_sha256":"79de23fafc95d9aef2b6514a81ffc728de7278391a8118619f4b2ce9c9b95e92","abstract_canon_sha256":"ce4aaff5c68634bee6e90d862e664511694ac35532137273770442916c1fdfc3"},"schema_version":"1.0"},"canonical_sha256":"3410652ee67821373af1b05a6c3dbb8d080d48de330503de789d3a19a7f17ffb","source":{"kind":"arxiv","id":"2309.00567","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.00567","created_at":"2026-07-05T07:27:50Z"},{"alias_kind":"arxiv_version","alias_value":"2309.00567v2","created_at":"2026-07-05T07:27:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.00567","created_at":"2026-07-05T07:27:50Z"},{"alias_kind":"pith_short_12","alias_value":"GQIGKLXGPAQT","created_at":"2026-07-05T07:27:50Z"},{"alias_kind":"pith_short_16","alias_value":"GQIGKLXGPAQTOOXR","created_at":"2026-07-05T07:27:50Z"},{"alias_kind":"pith_short_8","alias_value":"GQIGKLXG","created_at":"2026-07-05T07:27:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:GQIGKLXGPAQTOOXRWBNGYPN3RU","target":"record","payload":{"canonical_record":{"source":{"id":"2309.00567","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-09-01T16:22:26Z","cross_cats_sorted":[],"title_canon_sha256":"79de23fafc95d9aef2b6514a81ffc728de7278391a8118619f4b2ce9c9b95e92","abstract_canon_sha256":"ce4aaff5c68634bee6e90d862e664511694ac35532137273770442916c1fdfc3"},"schema_version":"1.0"},"canonical_sha256":"3410652ee67821373af1b05a6c3dbb8d080d48de330503de789d3a19a7f17ffb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:27:50.049644Z","signature_b64":"zgn/5m7S1sfbQgTlPiLpLibM3zCgYhN0/RJqqB68psp7Z78UMMh5k9bySDkC6Yi3oWARvtgOtUHZOSYoSDk2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3410652ee67821373af1b05a6c3dbb8d080d48de330503de789d3a19a7f17ffb","last_reissued_at":"2026-07-05T07:27:50.049109Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:27:50.049109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.00567","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":"2026-07-05T07:27:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qwU5i7H9SUiCOkfFa9Uz1Rsr28RYBunFCbv1qBvKuaodrOJQf/FAMPQix8NR8sRL86fo9aXvLCyD2shcrzSTBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T15:39:50.474854Z"},"content_sha256":"698127b96a6eb7b5f1701ba25753e2b6392fd0e11354f3ac9ee0ffca7428aa05","schema_version":"1.0","event_id":"sha256:698127b96a6eb7b5f1701ba25753e2b6392fd0e11354f3ac9ee0ffca7428aa05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:GQIGKLXGPAQTOOXRWBNGYPN3RU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Remarks on a Formula of Ramanujan","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andr\\'es Chirre, Steven M. Gonek","submitted_at":"2023-09-01T16:22:26Z","abstract_excerpt":"Assuming an averaged form of Mertens' conjecture and that the ordinates of the non-trivial zeros of the Riemann zeta function are linearly independent over the rationals, we analyze the finer structure of the terms in a well-known formula of Ramanujan."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.00567","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.00567/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:27:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2UagWUlP7AHGxVlhY4AhjwC48SixCJDRHbS8h4hqbLEOXKjed8tJSSqI1ZN6GwI+miKL7ooe9U5PLdgUyId4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T15:39:50.475826Z"},"content_sha256":"88e866bd67563328b2914ee6b27060a233780685dcd283b8f0f1e27aa5185ad0","schema_version":"1.0","event_id":"sha256:88e866bd67563328b2914ee6b27060a233780685dcd283b8f0f1e27aa5185ad0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GQIGKLXGPAQTOOXRWBNGYPN3RU/bundle.json","state_url":"https://pith.science/pith/GQIGKLXGPAQTOOXRWBNGYPN3RU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GQIGKLXGPAQTOOXRWBNGYPN3RU/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":"2026-08-12T15:39:50Z","links":{"resolver":"https://pith.science/pith/GQIGKLXGPAQTOOXRWBNGYPN3RU","bundle":"https://pith.science/pith/GQIGKLXGPAQTOOXRWBNGYPN3RU/bundle.json","state":"https://pith.science/pith/GQIGKLXGPAQTOOXRWBNGYPN3RU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GQIGKLXGPAQTOOXRWBNGYPN3RU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:GQIGKLXGPAQTOOXRWBNGYPN3RU","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":"ce4aaff5c68634bee6e90d862e664511694ac35532137273770442916c1fdfc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-09-01T16:22:26Z","title_canon_sha256":"79de23fafc95d9aef2b6514a81ffc728de7278391a8118619f4b2ce9c9b95e92"},"schema_version":"1.0","source":{"id":"2309.00567","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.00567","created_at":"2026-07-05T07:27:50Z"},{"alias_kind":"arxiv_version","alias_value":"2309.00567v2","created_at":"2026-07-05T07:27:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.00567","created_at":"2026-07-05T07:27:50Z"},{"alias_kind":"pith_short_12","alias_value":"GQIGKLXGPAQT","created_at":"2026-07-05T07:27:50Z"},{"alias_kind":"pith_short_16","alias_value":"GQIGKLXGPAQTOOXR","created_at":"2026-07-05T07:27:50Z"},{"alias_kind":"pith_short_8","alias_value":"GQIGKLXG","created_at":"2026-07-05T07:27:50Z"}],"graph_snapshots":[{"event_id":"sha256:88e866bd67563328b2914ee6b27060a233780685dcd283b8f0f1e27aa5185ad0","target":"graph","created_at":"2026-07-05T07:27:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.00567/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Assuming an averaged form of Mertens' conjecture and that the ordinates of the non-trivial zeros of the Riemann zeta function are linearly independent over the rationals, we analyze the finer structure of the terms in a well-known formula of Ramanujan.","authors_text":"Andr\\'es Chirre, Steven M. Gonek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-09-01T16:22:26Z","title":"Remarks on a Formula of Ramanujan"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.00567","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":"sha256:698127b96a6eb7b5f1701ba25753e2b6392fd0e11354f3ac9ee0ffca7428aa05","target":"record","created_at":"2026-07-05T07:27:50Z","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":"ce4aaff5c68634bee6e90d862e664511694ac35532137273770442916c1fdfc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-09-01T16:22:26Z","title_canon_sha256":"79de23fafc95d9aef2b6514a81ffc728de7278391a8118619f4b2ce9c9b95e92"},"schema_version":"1.0","source":{"id":"2309.00567","kind":"arxiv","version":2}},"canonical_sha256":"3410652ee67821373af1b05a6c3dbb8d080d48de330503de789d3a19a7f17ffb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3410652ee67821373af1b05a6c3dbb8d080d48de330503de789d3a19a7f17ffb","first_computed_at":"2026-07-05T07:27:50.049109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:27:50.049109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zgn/5m7S1sfbQgTlPiLpLibM3zCgYhN0/RJqqB68psp7Z78UMMh5k9bySDkC6Yi3oWARvtgOtUHZOSYoSDk2Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:27:50.049644Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.00567","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:698127b96a6eb7b5f1701ba25753e2b6392fd0e11354f3ac9ee0ffca7428aa05","sha256:88e866bd67563328b2914ee6b27060a233780685dcd283b8f0f1e27aa5185ad0"],"state_sha256":"d1e46353ac5ffba167637875cd6c245d69c0f323999b4598c8e34417466e6496"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XbRREIOnSIntrT/mLrN2cbuiucz6GcUcdqF6TP5P9N13EjbXB1bOBYN+3uarf8qLUjkOjTH7nGFGOodsE7t6DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T15:39:50.481199Z","bundle_sha256":"b3a452ed6a1ba5654c8ab307d84280cc0e63b0dee1eaab6f4242a6edefed720d"}}