{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4HJYUOWIGRRJGFC6FZOSKATTIL","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":"b4eb642780ef3edb47a24372d18153765fe1d1dd335f0d3e966a5dba7ee6c599","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-03-27T06:43:55Z","title_canon_sha256":"8a221f3fae7af69423de66f60a21dd56e3cfe17aeaed3aeb80eacc01d11d8180"},"schema_version":"1.0","source":{"id":"1403.6927","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6927","created_at":"2026-05-18T02:55:20Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6927v2","created_at":"2026-05-18T02:55:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6927","created_at":"2026-05-18T02:55:20Z"},{"alias_kind":"pith_short_12","alias_value":"4HJYUOWIGRRJ","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4HJYUOWIGRRJGFC6","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4HJYUOWI","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:de4fe1f4a2d48ffb98d97c8cd91824462aeef38c8696d5a6aaddc69240c77e11","target":"graph","created_at":"2026-05-18T02:55:20Z","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 $\\{Q^{(\\alpha)}_{n,\\lambda}\\}_{n\\geq 0}$ be the sequence of monic orthogonal polynomials with respect the Gegenbauer-Sobolev inner product $$\\langle f,g\\rangle_{S}:=\\int_{-1}^{1}f(x)g(x)(1-x^{2})^{\\alpha-\\frac{1}{2}}dx+\\lambda \\int_{-1}^{1}f'(x)g'(x)(1-x^{2})^{\\alpha-\\frac{1}{2}} dx,$$ where $\\alpha>-\\frac{1}{2}$ and $\\lambda\\geq 0$. In this paper we use a recent result due to B.D. Bojanov and N.\n  Naidenov \\cite{BN2010}, in order to study the maximization of a local extremum of the $k$th derivative $\\frac{d^k}{dx^k}Q^{(\\alpha)}_{n,\\lambda}$ in $[-M_{n,\\lambda}, M_{n,\\lambda}]$, where\n  $M","authors_text":"Dilcia P\\'erez, Vanessa G. Paschoa, Yamilet Quintana","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-03-27T06:43:55Z","title":"On a Theorem by Bojanov and Naidenov applied to families of Gegenbauer-Sobolev polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6927","kind":"arxiv","version":2},"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:bc3cbebfd44d91cfd8dd66aa269cfd05af831b3dccc274e5c69580b2fc88eaa4","target":"record","created_at":"2026-05-18T02:55:20Z","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":"b4eb642780ef3edb47a24372d18153765fe1d1dd335f0d3e966a5dba7ee6c599","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-03-27T06:43:55Z","title_canon_sha256":"8a221f3fae7af69423de66f60a21dd56e3cfe17aeaed3aeb80eacc01d11d8180"},"schema_version":"1.0","source":{"id":"1403.6927","kind":"arxiv","version":2}},"canonical_sha256":"e1d38a3ac8346293145e2e5d25027342f4816c14b7b860830c6684848110f185","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1d38a3ac8346293145e2e5d25027342f4816c14b7b860830c6684848110f185","first_computed_at":"2026-05-18T02:55:20.191375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:20.191375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JnKUWIwo09EgyNdqpSQgQlbfcu0AF6CB9QwaF4lr86t1RjTfn4qeKp3j/RK410VuADRZw1+LcA3bbI0lKA6NAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:20.191743Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6927","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc3cbebfd44d91cfd8dd66aa269cfd05af831b3dccc274e5c69580b2fc88eaa4","sha256:de4fe1f4a2d48ffb98d97c8cd91824462aeef38c8696d5a6aaddc69240c77e11"],"state_sha256":"1c5d383166446f22b4807e36a5a7662488d2fd770aa183ce3d9702a4557137b8"}