{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5NUXAUVZESMZF7NHSWDAZ4J4N6","short_pith_number":"pith:5NUXAUVZ","canonical_record":{"source":{"id":"1610.03693","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-12T12:48:31Z","cross_cats_sorted":[],"title_canon_sha256":"1550238610c3f0eabb8237c3f85974e9eac2686b9772a8a0154ba56a09ad82cb","abstract_canon_sha256":"404a741e91565caf2a4e53c9fa256814224dfed7dd6e04bc6e9a6127f04e4800"},"schema_version":"1.0"},"canonical_sha256":"eb697052b9249992fda795860cf13c6fab573d8b9138ac499de733447cb64353","source":{"kind":"arxiv","id":"1610.03693","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03693","created_at":"2026-05-18T01:02:29Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03693v1","created_at":"2026-05-18T01:02:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03693","created_at":"2026-05-18T01:02:29Z"},{"alias_kind":"pith_short_12","alias_value":"5NUXAUVZESMZ","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5NUXAUVZESMZF7NH","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5NUXAUVZ","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5NUXAUVZESMZF7NHSWDAZ4J4N6","target":"record","payload":{"canonical_record":{"source":{"id":"1610.03693","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-12T12:48:31Z","cross_cats_sorted":[],"title_canon_sha256":"1550238610c3f0eabb8237c3f85974e9eac2686b9772a8a0154ba56a09ad82cb","abstract_canon_sha256":"404a741e91565caf2a4e53c9fa256814224dfed7dd6e04bc6e9a6127f04e4800"},"schema_version":"1.0"},"canonical_sha256":"eb697052b9249992fda795860cf13c6fab573d8b9138ac499de733447cb64353","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:29.572976Z","signature_b64":"99xfXH03cDtnnmL7SVh9eYRlK722YpLjDWK78pEfH0lvwctXKltyBDRYZtmhS1ppQHpaU1xyqzvvP6b3Xq1bBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb697052b9249992fda795860cf13c6fab573d8b9138ac499de733447cb64353","last_reissued_at":"2026-05-18T01:02:29.572305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:29.572305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.03693","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V2oeq2FmGcaNrHRl7R1nnUGhSIDRp0J80KjMBzxgDYcELrJKPZ1cO1AYjUDXMpfVR3Dycz5npYBYPKU2syzZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:38:21.846874Z"},"content_sha256":"607cd79d2a1f1454334bca2d19e16e1348c0cc22b79982c15f644eb358523ba8","schema_version":"1.0","event_id":"sha256:607cd79d2a1f1454334bca2d19e16e1348c0cc22b79982c15f644eb358523ba8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5NUXAUVZESMZF7NHSWDAZ4J4N6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The series that Ramanujan misunderstood","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aleksander Zujev, Geoffrey B Campbell","submitted_at":"2016-10-12T12:48:31Z","abstract_excerpt":"We give a new appraisal of a famous oscillating power series considered by Hardy and Ramanujan related to the erroneous theory of distribution of primes by Ramanujan."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03693","kind":"arxiv","version":1},"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":"2026-05-18T01:02:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8lPVFGbPLX/1M3rOjb3rvjr9piuQA0e4QlEAfjsI+13YlT5OKlCYVVl3xsrxHO4IG1FvyavKribAeOGQuMkkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:38:21.847223Z"},"content_sha256":"5908d4f21fa2f6a9a3cc3cc95114fe22ccd649a850d1506752baff5bd600d598","schema_version":"1.0","event_id":"sha256:5908d4f21fa2f6a9a3cc3cc95114fe22ccd649a850d1506752baff5bd600d598"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5NUXAUVZESMZF7NHSWDAZ4J4N6/bundle.json","state_url":"https://pith.science/pith/5NUXAUVZESMZF7NHSWDAZ4J4N6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5NUXAUVZESMZF7NHSWDAZ4J4N6/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":"2026-06-11T12:38:21Z","links":{"resolver":"https://pith.science/pith/5NUXAUVZESMZF7NHSWDAZ4J4N6","bundle":"https://pith.science/pith/5NUXAUVZESMZF7NHSWDAZ4J4N6/bundle.json","state":"https://pith.science/pith/5NUXAUVZESMZF7NHSWDAZ4J4N6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5NUXAUVZESMZF7NHSWDAZ4J4N6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5NUXAUVZESMZF7NHSWDAZ4J4N6","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":"404a741e91565caf2a4e53c9fa256814224dfed7dd6e04bc6e9a6127f04e4800","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-12T12:48:31Z","title_canon_sha256":"1550238610c3f0eabb8237c3f85974e9eac2686b9772a8a0154ba56a09ad82cb"},"schema_version":"1.0","source":{"id":"1610.03693","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03693","created_at":"2026-05-18T01:02:29Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03693v1","created_at":"2026-05-18T01:02:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03693","created_at":"2026-05-18T01:02:29Z"},{"alias_kind":"pith_short_12","alias_value":"5NUXAUVZESMZ","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5NUXAUVZESMZF7NH","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5NUXAUVZ","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:5908d4f21fa2f6a9a3cc3cc95114fe22ccd649a850d1506752baff5bd600d598","target":"graph","created_at":"2026-05-18T01:02:29Z","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 give a new appraisal of a famous oscillating power series considered by Hardy and Ramanujan related to the erroneous theory of distribution of primes by Ramanujan.","authors_text":"Aleksander Zujev, Geoffrey B Campbell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-12T12:48:31Z","title":"The series that Ramanujan misunderstood"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03693","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":"sha256:607cd79d2a1f1454334bca2d19e16e1348c0cc22b79982c15f644eb358523ba8","target":"record","created_at":"2026-05-18T01:02:29Z","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":"404a741e91565caf2a4e53c9fa256814224dfed7dd6e04bc6e9a6127f04e4800","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-12T12:48:31Z","title_canon_sha256":"1550238610c3f0eabb8237c3f85974e9eac2686b9772a8a0154ba56a09ad82cb"},"schema_version":"1.0","source":{"id":"1610.03693","kind":"arxiv","version":1}},"canonical_sha256":"eb697052b9249992fda795860cf13c6fab573d8b9138ac499de733447cb64353","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb697052b9249992fda795860cf13c6fab573d8b9138ac499de733447cb64353","first_computed_at":"2026-05-18T01:02:29.572305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:29.572305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"99xfXH03cDtnnmL7SVh9eYRlK722YpLjDWK78pEfH0lvwctXKltyBDRYZtmhS1ppQHpaU1xyqzvvP6b3Xq1bBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:29.572976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03693","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:607cd79d2a1f1454334bca2d19e16e1348c0cc22b79982c15f644eb358523ba8","sha256:5908d4f21fa2f6a9a3cc3cc95114fe22ccd649a850d1506752baff5bd600d598"],"state_sha256":"f34a41156f69c3bf2c00e3950eb1ff0a153ab1d2ec378fd05ca4c44dcdc3345e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BnHjQm0OGV63A7gak5ZQrWPd3EBpOJ9HPE/C7wHbfQEEncZreI5MLT9qMa8j3A35dVBwI7dCKEIhcjtfHreWDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T12:38:21.849336Z","bundle_sha256":"5bff777d46317e0c3f16ab90fe28be736ad240f2721d0a1236e2acc3f6f8531b"}}