{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LVMUGRUMD5ILV23QTCSGEYSYZH","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":"046479d584226790ae61ee1c9cf93d3fe580fe5a158b7771476c8fea3033cdc6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2013-02-28T03:22:19Z","title_canon_sha256":"c3de4d697760dcde9f0399dd26cf7a7de3259c91f5fb6918f6c82c999a9d252c"},"schema_version":"1.0","source":{"id":"1302.7066","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.7066","created_at":"2026-05-18T03:29:15Z"},{"alias_kind":"arxiv_version","alias_value":"1302.7066v1","created_at":"2026-05-18T03:29:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.7066","created_at":"2026-05-18T03:29:15Z"},{"alias_kind":"pith_short_12","alias_value":"LVMUGRUMD5IL","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LVMUGRUMD5ILV23Q","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LVMUGRUM","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:27da040ef14e63b13f20c9fd7af3a3a30fc6d0c9657715c1cfb6712688262483","target":"graph","created_at":"2026-05-18T03:29:15Z","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":"Let $ P(z) $ be a polynomial of degree $ n $ having all zeros in $|z|\\leq k$ where $k\\leq 1,$ then it was proved by Dewan \\textit{et al} that for every real or complex number $\\alpha$ with $|\\alpha|\\geq k$ and each $r\\geq 0$\n  $$ n(|\\alpha|-k)\\left\\{\\int\\limits_{0}^{2\\pi}\\left|P\\left(e^{i\\theta}\\right)\\right|^r d\\theta\\right\\}^{\\frac{1}{r}}\\leq\\left\\{\\int\\limits_{0}^{2\\pi}\\left|1+ke^{i\\theta}\\right|^r d\\theta\\right\\}^{\\frac{1}{r}}\\underset{|z|=1}{Max}|D_\\alpha P(z)|. $$\n  \\indent In this paper, we shall present a refinement and generalization of above result and also extend it to the class of ","authors_text":"N. A. Rather, Suhail Gulzar","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2013-02-28T03:22:19Z","title":"Integral mean estimates for the polar derivative of a polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.7066","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":"sha256:2399a6e346a1e8abafe1781d8fe12a49c9f828fdbcffcc317a7d90b9b30cfa4f","target":"record","created_at":"2026-05-18T03:29:15Z","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":"046479d584226790ae61ee1c9cf93d3fe580fe5a158b7771476c8fea3033cdc6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2013-02-28T03:22:19Z","title_canon_sha256":"c3de4d697760dcde9f0399dd26cf7a7de3259c91f5fb6918f6c82c999a9d252c"},"schema_version":"1.0","source":{"id":"1302.7066","kind":"arxiv","version":1}},"canonical_sha256":"5d5943468c1f50baeb7098a4626258c9f80630aa01148b2b36858831c0a0fc78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d5943468c1f50baeb7098a4626258c9f80630aa01148b2b36858831c0a0fc78","first_computed_at":"2026-05-18T03:29:15.493402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:15.493402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dHUipLgvIyLay/6BRP/pbWf0CvshDqoUbEop9NRE1l462kgEf4WwUeNHvvy1U1gQiTG2V08SCEx05JE4gcwQAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:15.493880Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.7066","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2399a6e346a1e8abafe1781d8fe12a49c9f828fdbcffcc317a7d90b9b30cfa4f","sha256:27da040ef14e63b13f20c9fd7af3a3a30fc6d0c9657715c1cfb6712688262483"],"state_sha256":"84b742493edd3836e3924ebf2513331a8fc700499913778b61db04ec71d870d5"}