{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:M4ACT4XJGGOTNRPCJKYYQKS7QP","short_pith_number":"pith:M4ACT4XJ","schema_version":"1.0","canonical_sha256":"670029f2e9319d36c5e24ab1882a5f83d470e916d7a8ce3f3765c9b40c1f17ca","source":{"kind":"arxiv","id":"2306.06729","version":1},"attestation_state":"computed","paper":{"title":"A new proximity function estimate on the quotient of the difference and the derivative of a meromorphic function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Juha-Matti Huusko, Lasse Asikainen, Risto Korhonen","submitted_at":"2023-06-11T17:33:07Z","abstract_excerpt":"It is shown that, under certain assumptions on the growth and value distribution of a meromorphic function $f(z)$, \\begin{equation*} m\\left(r,\\frac{\\Delta_cf - ac}{f' - a}\\right)=S(r,f'), \\end{equation*} where $\\Delta_c f=f(z+c)-f(z)$ and $a,c\\in\\mathbb{C}$. This estimate implies a lower bound for the Nevanlinna ramification term in terms of the difference operator with an arbitrary shift. As a consequence it follows, for instance, that if $f$ is an entire function of hyper-order $<1$ whose derivative does not attain a value $a\\in\\mathbb{C}$ often $$N\\left(r,\\frac{1}{f'-a}\\right)=S(r,f),$$ the"},"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":"2306.06729","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2023-06-11T17:33:07Z","cross_cats_sorted":[],"title_canon_sha256":"12e324ed9c6c6935e41f916e61f593edf08675c25c37796c8430313d08f61ed4","abstract_canon_sha256":"a42a52725597f5b00915188edd34470862751d8cdadbf2799cb835f5aeeca5dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:19:43.384593Z","signature_b64":"K4cMzemeqUiYOaLq4CENoaOsNLmznNjZ5Y0W2KBFqjWjHi1oq5UQT440YxM6+VmvSlqGfHYToQth5s6LNx1jCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"670029f2e9319d36c5e24ab1882a5f83d470e916d7a8ce3f3765c9b40c1f17ca","last_reissued_at":"2026-07-05T06:19:43.384173Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:19:43.384173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new proximity function estimate on the quotient of the difference and the derivative of a meromorphic function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Juha-Matti Huusko, Lasse Asikainen, Risto Korhonen","submitted_at":"2023-06-11T17:33:07Z","abstract_excerpt":"It is shown that, under certain assumptions on the growth and value distribution of a meromorphic function $f(z)$, \\begin{equation*} m\\left(r,\\frac{\\Delta_cf - ac}{f' - a}\\right)=S(r,f'), \\end{equation*} where $\\Delta_c f=f(z+c)-f(z)$ and $a,c\\in\\mathbb{C}$. This estimate implies a lower bound for the Nevanlinna ramification term in terms of the difference operator with an arbitrary shift. As a consequence it follows, for instance, that if $f$ is an entire function of hyper-order $<1$ whose derivative does not attain a value $a\\in\\mathbb{C}$ often $$N\\left(r,\\frac{1}{f'-a}\\right)=S(r,f),$$ the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.06729","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.06729/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2306.06729","created_at":"2026-07-05T06:19:43.384227+00:00"},{"alias_kind":"arxiv_version","alias_value":"2306.06729v1","created_at":"2026-07-05T06:19:43.384227+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.06729","created_at":"2026-07-05T06:19:43.384227+00:00"},{"alias_kind":"pith_short_12","alias_value":"M4ACT4XJGGOT","created_at":"2026-07-05T06:19:43.384227+00:00"},{"alias_kind":"pith_short_16","alias_value":"M4ACT4XJGGOTNRPC","created_at":"2026-07-05T06:19:43.384227+00:00"},{"alias_kind":"pith_short_8","alias_value":"M4ACT4XJ","created_at":"2026-07-05T06:19:43.384227+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.21150","citing_title":"Vanishing, Unbounded and Angular Shifts on the Quotient of the Difference and the Derivative of a Meromorphic Function","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M4ACT4XJGGOTNRPCJKYYQKS7QP","json":"https://pith.science/pith/M4ACT4XJGGOTNRPCJKYYQKS7QP.json","graph_json":"https://pith.science/api/pith-number/M4ACT4XJGGOTNRPCJKYYQKS7QP/graph.json","events_json":"https://pith.science/api/pith-number/M4ACT4XJGGOTNRPCJKYYQKS7QP/events.json","paper":"https://pith.science/paper/M4ACT4XJ"},"agent_actions":{"view_html":"https://pith.science/pith/M4ACT4XJGGOTNRPCJKYYQKS7QP","download_json":"https://pith.science/pith/M4ACT4XJGGOTNRPCJKYYQKS7QP.json","view_paper":"https://pith.science/paper/M4ACT4XJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2306.06729&json=true","fetch_graph":"https://pith.science/api/pith-number/M4ACT4XJGGOTNRPCJKYYQKS7QP/graph.json","fetch_events":"https://pith.science/api/pith-number/M4ACT4XJGGOTNRPCJKYYQKS7QP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M4ACT4XJGGOTNRPCJKYYQKS7QP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M4ACT4XJGGOTNRPCJKYYQKS7QP/action/storage_attestation","attest_author":"https://pith.science/pith/M4ACT4XJGGOTNRPCJKYYQKS7QP/action/author_attestation","sign_citation":"https://pith.science/pith/M4ACT4XJGGOTNRPCJKYYQKS7QP/action/citation_signature","submit_replication":"https://pith.science/pith/M4ACT4XJGGOTNRPCJKYYQKS7QP/action/replication_record"}},"created_at":"2026-07-05T06:19:43.384227+00:00","updated_at":"2026-07-05T06:19:43.384227+00:00"}