{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:4SHNJYPJ4LHWATBFRCWDE5MQQN","short_pith_number":"pith:4SHNJYPJ","canonical_record":{"source":{"id":"1907.00265","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-06-29T19:31:05Z","cross_cats_sorted":[],"title_canon_sha256":"367e2e4c1b225f728d102034f57069ae1cb0ea0c9324fe608c8b81d6c21898dc","abstract_canon_sha256":"6f5ba9965bd754b877015f1fe2d025547b5428d0bd3449e8e1b3aefbea2936fc"},"schema_version":"1.0"},"canonical_sha256":"e48ed4e1e9e2cf604c2588ac327590835d5c7524f61ced83ed9923293e8458e3","source":{"kind":"arxiv","id":"1907.00265","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.00265","created_at":"2026-05-17T23:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1907.00265v1","created_at":"2026-05-17T23:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00265","created_at":"2026-05-17T23:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"4SHNJYPJ4LHW","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4SHNJYPJ4LHWATBF","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4SHNJYPJ","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:4SHNJYPJ4LHWATBFRCWDE5MQQN","target":"record","payload":{"canonical_record":{"source":{"id":"1907.00265","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-06-29T19:31:05Z","cross_cats_sorted":[],"title_canon_sha256":"367e2e4c1b225f728d102034f57069ae1cb0ea0c9324fe608c8b81d6c21898dc","abstract_canon_sha256":"6f5ba9965bd754b877015f1fe2d025547b5428d0bd3449e8e1b3aefbea2936fc"},"schema_version":"1.0"},"canonical_sha256":"e48ed4e1e9e2cf604c2588ac327590835d5c7524f61ced83ed9923293e8458e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:52.294957Z","signature_b64":"TIExDP5YqeKm3EkCYAaCuNm1TLuFOi7dPsiUvEz3C1x5aysPOt4nD2kkhx0hRWDnOhktCgCeoaIQKB8EVl0mCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e48ed4e1e9e2cf604c2588ac327590835d5c7524f61ced83ed9923293e8458e3","last_reissued_at":"2026-05-17T23:41:52.293270Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:52.293270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.00265","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":"2026-05-17T23:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bPtAzPYpDHkbRcRwNIWpR9T+kOhFGpbteFOIQPV4xO+5iTuznC+w955z1sgK5L+lOM7srFM21drL+jzgQoHEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:45:08.843653Z"},"content_sha256":"b773f3f8adac6a080d0ab34fac37b344f9f7b6febd3a410f689b8c463b20e164","schema_version":"1.0","event_id":"sha256:b773f3f8adac6a080d0ab34fac37b344f9f7b6febd3a410f689b8c463b20e164"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:4SHNJYPJ4LHWATBFRCWDE5MQQN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Generalization of Fourier Series occurring in Atomic Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bernard J. Laurenzi","submitted_at":"2019-06-29T19:31:05Z","abstract_excerpt":"A number of the Fourier Series which occur in the theory of the semi-classical atom due to Englert and Schwinger are generalized and presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00265","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":"2026-05-17T23:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"247Zj/rDUjPOTvHP2Q/J0fi4xfWiMSxr0ws1032Tcjgk5ZqOrWUW8bjHEcPWcgtxmNtp4mX+wE+P2AfVSHTACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:45:08.844197Z"},"content_sha256":"14f1a18f45a8af1ea4ba906016d4839a5f635536e9058ea17a4fcce57b5094fe","schema_version":"1.0","event_id":"sha256:14f1a18f45a8af1ea4ba906016d4839a5f635536e9058ea17a4fcce57b5094fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4SHNJYPJ4LHWATBFRCWDE5MQQN/bundle.json","state_url":"https://pith.science/pith/4SHNJYPJ4LHWATBFRCWDE5MQQN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4SHNJYPJ4LHWATBFRCWDE5MQQN/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":"2026-06-11T03:45:08Z","links":{"resolver":"https://pith.science/pith/4SHNJYPJ4LHWATBFRCWDE5MQQN","bundle":"https://pith.science/pith/4SHNJYPJ4LHWATBFRCWDE5MQQN/bundle.json","state":"https://pith.science/pith/4SHNJYPJ4LHWATBFRCWDE5MQQN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4SHNJYPJ4LHWATBFRCWDE5MQQN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4SHNJYPJ4LHWATBFRCWDE5MQQN","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":"6f5ba9965bd754b877015f1fe2d025547b5428d0bd3449e8e1b3aefbea2936fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-06-29T19:31:05Z","title_canon_sha256":"367e2e4c1b225f728d102034f57069ae1cb0ea0c9324fe608c8b81d6c21898dc"},"schema_version":"1.0","source":{"id":"1907.00265","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.00265","created_at":"2026-05-17T23:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1907.00265v1","created_at":"2026-05-17T23:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00265","created_at":"2026-05-17T23:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"4SHNJYPJ4LHW","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4SHNJYPJ4LHWATBF","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4SHNJYPJ","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:14f1a18f45a8af1ea4ba906016d4839a5f635536e9058ea17a4fcce57b5094fe","target":"graph","created_at":"2026-05-17T23:41:52Z","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":"A number of the Fourier Series which occur in the theory of the semi-classical atom due to Englert and Schwinger are generalized and presented.","authors_text":"Bernard J. Laurenzi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-06-29T19:31:05Z","title":"A Generalization of Fourier Series occurring in Atomic Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00265","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:b773f3f8adac6a080d0ab34fac37b344f9f7b6febd3a410f689b8c463b20e164","target":"record","created_at":"2026-05-17T23:41:52Z","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":"6f5ba9965bd754b877015f1fe2d025547b5428d0bd3449e8e1b3aefbea2936fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-06-29T19:31:05Z","title_canon_sha256":"367e2e4c1b225f728d102034f57069ae1cb0ea0c9324fe608c8b81d6c21898dc"},"schema_version":"1.0","source":{"id":"1907.00265","kind":"arxiv","version":1}},"canonical_sha256":"e48ed4e1e9e2cf604c2588ac327590835d5c7524f61ced83ed9923293e8458e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e48ed4e1e9e2cf604c2588ac327590835d5c7524f61ced83ed9923293e8458e3","first_computed_at":"2026-05-17T23:41:52.293270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:52.293270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TIExDP5YqeKm3EkCYAaCuNm1TLuFOi7dPsiUvEz3C1x5aysPOt4nD2kkhx0hRWDnOhktCgCeoaIQKB8EVl0mCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:52.294957Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.00265","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b773f3f8adac6a080d0ab34fac37b344f9f7b6febd3a410f689b8c463b20e164","sha256:14f1a18f45a8af1ea4ba906016d4839a5f635536e9058ea17a4fcce57b5094fe"],"state_sha256":"9f077e8d6b9822ed4b47a2afa9a7dfe91a5c71ec916c57595019de67ccd840b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JheFdXy3cdjKgXkW+tDjfqjGNm+2kkwqskYpYSUWy3cdQVUnjTCgdQdxEzBCbg93ILGT3UuWpCTeON0+YOyUBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T03:45:08.847027Z","bundle_sha256":"df181a14ff3a10f64a9473ed2e928348286d3161809b599f239440008a62e2e0"}}