{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:YNPCU4WV5FZO3IJWUDBYJQ33IH","short_pith_number":"pith:YNPCU4WV","schema_version":"1.0","canonical_sha256":"c35e2a72d5e972eda136a0c384c37b41d0027d5705b7f762ec289dbcbb25fa0d","source":{"kind":"arxiv","id":"1702.03458","version":2},"attestation_state":"computed","paper":{"title":"Macdonald's Theorem for Analytic Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"R. C. McPhedran","submitted_at":"2017-02-11T20:40:19Z","abstract_excerpt":"A proof is reconstructed for a useful theorem on the zeros of derivatives of analytic functions due to H. M. Macdonald, which appears to be now little known. The Theorem states that, if a function $f(z)$ is analytic inside a bounded region bounded by a contour on which the modulus of $f(z)$ is constant, then the number of zeros (counted according to multiplicity) of $f(z)$ and of its derivative in the region differ by unity."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1702.03458","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-02-11T20:40:19Z","cross_cats_sorted":[],"title_canon_sha256":"20d5fa54479fb594e1feaad917ada72d5ee89b656b8a59053bdd71350782ab54","abstract_canon_sha256":"41c6ad63d17843b9d60329630e18ef2db6bd065cdbfa13b14b8a5e376e17001d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:46.313197Z","signature_b64":"5KmPKJMEUIkUpIsZI2+UXl2BqzwJScgoIAYLwk/aWkeGQEebTmDHpw76738LWSVT8uzATdG6+ySr2B8ZQ8eNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c35e2a72d5e972eda136a0c384c37b41d0027d5705b7f762ec289dbcbb25fa0d","last_reissued_at":"2026-05-18T00:46:46.312413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:46.312413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Macdonald's Theorem for Analytic Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"R. C. McPhedran","submitted_at":"2017-02-11T20:40:19Z","abstract_excerpt":"A proof is reconstructed for a useful theorem on the zeros of derivatives of analytic functions due to H. M. Macdonald, which appears to be now little known. The Theorem states that, if a function $f(z)$ is analytic inside a bounded region bounded by a contour on which the modulus of $f(z)$ is constant, then the number of zeros (counted according to multiplicity) of $f(z)$ and of its derivative in the region differ by unity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03458","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1702.03458","created_at":"2026-05-18T00:46:46.312542+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.03458v2","created_at":"2026-05-18T00:46:46.312542+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03458","created_at":"2026-05-18T00:46:46.312542+00:00"},{"alias_kind":"pith_short_12","alias_value":"YNPCU4WV5FZO","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"YNPCU4WV5FZO3IJW","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"YNPCU4WV","created_at":"2026-05-18T12:31:56.362134+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YNPCU4WV5FZO3IJWUDBYJQ33IH","json":"https://pith.science/pith/YNPCU4WV5FZO3IJWUDBYJQ33IH.json","graph_json":"https://pith.science/api/pith-number/YNPCU4WV5FZO3IJWUDBYJQ33IH/graph.json","events_json":"https://pith.science/api/pith-number/YNPCU4WV5FZO3IJWUDBYJQ33IH/events.json","paper":"https://pith.science/paper/YNPCU4WV"},"agent_actions":{"view_html":"https://pith.science/pith/YNPCU4WV5FZO3IJWUDBYJQ33IH","download_json":"https://pith.science/pith/YNPCU4WV5FZO3IJWUDBYJQ33IH.json","view_paper":"https://pith.science/paper/YNPCU4WV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.03458&json=true","fetch_graph":"https://pith.science/api/pith-number/YNPCU4WV5FZO3IJWUDBYJQ33IH/graph.json","fetch_events":"https://pith.science/api/pith-number/YNPCU4WV5FZO3IJWUDBYJQ33IH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YNPCU4WV5FZO3IJWUDBYJQ33IH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YNPCU4WV5FZO3IJWUDBYJQ33IH/action/storage_attestation","attest_author":"https://pith.science/pith/YNPCU4WV5FZO3IJWUDBYJQ33IH/action/author_attestation","sign_citation":"https://pith.science/pith/YNPCU4WV5FZO3IJWUDBYJQ33IH/action/citation_signature","submit_replication":"https://pith.science/pith/YNPCU4WV5FZO3IJWUDBYJQ33IH/action/replication_record"}},"created_at":"2026-05-18T00:46:46.312542+00:00","updated_at":"2026-05-18T00:46:46.312542+00:00"}