{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OJHAB2WBXXVFKOTTRUXKTTGHV6","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":"bf97c16b509b8ddc9c45186e21113fd3ed62208f7356c31ca2bc0641938ab57d","cross_cats_sorted":["math.CO","math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2026-05-04T22:36:00Z","title_canon_sha256":"6b33fabf84711eca23078519518a69436b4eec38e53a66746fe6fe648155d8fd"},"schema_version":"1.0","source":{"id":"2605.03200","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.03200","created_at":"2026-06-19T16:09:58Z"},{"alias_kind":"arxiv_version","alias_value":"2605.03200v3","created_at":"2026-06-19T16:09:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.03200","created_at":"2026-06-19T16:09:58Z"},{"alias_kind":"pith_short_12","alias_value":"OJHAB2WBXXVF","created_at":"2026-06-19T16:09:58Z"},{"alias_kind":"pith_short_16","alias_value":"OJHAB2WBXXVFKOTT","created_at":"2026-06-19T16:09:58Z"},{"alias_kind":"pith_short_8","alias_value":"OJHAB2WB","created_at":"2026-06-19T16:09:58Z"}],"graph_snapshots":[{"event_id":"sha256:dd7e055595078603ee033d239061ac1fa2ee2024575eb40fae8d563e9648be4d","target":"graph","created_at":"2026-06-19T16:09:58Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"Analytic summation determines the rational functions to which these series converge; these functions are expressed in terms of Chebyshev polynomials evaluated at a specific argument, yielding new closed-form formulas for sums at various values and combinatorial identities for Fibonacci, Lucas, and Pell numbers and their convolutions."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the relation between polynomial degree and derivative order, together with the analytic properties of Chebyshev polynomials of the second kind, permits term-by-term differentiation and summation inside the disk of convergence without additional justification for the specific series considered."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Analytic summation yields closed forms for series of higher derivatives of Chebyshev polynomials of the second kind, giving identities for convolved linear recurrent sequences including Fibonacci numbers."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Series of higher-order derivatives of Chebyshev polynomials of the second kind sum analytically to rational functions expressed in the polynomials."}],"snapshot_sha256":"72eb026eda8fe6ba4473c9fc18bbf0ab818f2c92690d03fac4cb8d6308fde703"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"59a8ceb427b44ceaaa3e4844efe0b0ed217534dfff23709f6def4729692b4764"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-20T14:35:39.918143Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-20T01:31:21.940999Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T15:35:07.074118Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.03200/integrity.json","findings":[],"snapshot_sha256":"e7c9816471fa7a12f57f5900878a6996b0bc2d4e97a090f158d58b4a792468fe","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper considers functional series whose terms are higher-order derivatives of Chebyshev polynomials of the second kind, where the degree of the polynomial is related to the order of the derivative. Analytic summation is used to determine the rational functions to which these series converge. These functions are expressed in terms of Chebyshev polynomials evaluated at a specific argument. Connections are established between derivatives of Chebyshev polynomials of the second kind and special numerical sequences generated by linear recurrence relations. New closed-form formulas are obtained ","authors_text":"Alexander Stokolos, Daniel Gray, Dmitriy Dmitrishin, Vitaly Khamitov","cross_cats":["math.CO","math.NT"],"headline":"Series of higher-order derivatives of Chebyshev polynomials of the second kind sum analytically to rational functions expressed in the polynomials.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2026-05-04T22:36:00Z","title":"Analytic summation of series involving higher-order derivatives of Chebyshev polynomials of the second kind and their applications to convolved linear recurrent sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.03200","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-14T21:25:59.261345Z","id":"0d6b5f1d-0c6b-45aa-a062-532277ddbe06","model_set":{"reader":"grok-4.3"},"one_line_summary":"Analytic summation yields closed forms for series of higher derivatives of Chebyshev polynomials of the second kind, giving identities for convolved linear recurrent sequences including Fibonacci numbers.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Series of higher-order derivatives of Chebyshev polynomials of the second kind sum analytically to rational functions expressed in the polynomials.","strongest_claim":"Analytic summation determines the rational functions to which these series converge; these functions are expressed in terms of Chebyshev polynomials evaluated at a specific argument, yielding new closed-form formulas for sums at various values and combinatorial identities for Fibonacci, Lucas, and Pell numbers and their convolutions.","weakest_assumption":"That the relation between polynomial degree and derivative order, together with the analytic properties of Chebyshev polynomials of the second kind, permits term-by-term differentiation and summation inside the disk of convergence without additional justification for the specific series considered."}},"verdict_id":"0d6b5f1d-0c6b-45aa-a062-532277ddbe06"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:20ca4f5beb389196fb8b9921ed236aef48e9624c6cb9f35182143bb89b024b18","target":"record","created_at":"2026-06-19T16:09:58Z","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":"bf97c16b509b8ddc9c45186e21113fd3ed62208f7356c31ca2bc0641938ab57d","cross_cats_sorted":["math.CO","math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2026-05-04T22:36:00Z","title_canon_sha256":"6b33fabf84711eca23078519518a69436b4eec38e53a66746fe6fe648155d8fd"},"schema_version":"1.0","source":{"id":"2605.03200","kind":"arxiv","version":3}},"canonical_sha256":"724e00eac1bdea553a738d2ea9ccc7af89055cc26c19f8c0d14ea9bafcbbbd41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"724e00eac1bdea553a738d2ea9ccc7af89055cc26c19f8c0d14ea9bafcbbbd41","first_computed_at":"2026-06-19T16:09:58.868529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:09:58.868529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VQTh61hSqpHj1eFiL/+/k+Ei9C00C4hDZpd+mLcMaWub1qEpG3PTv+yj5EppzsJDMRPtUhap8SUmpDQsTOzADw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:09:58.868924Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.03200","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20ca4f5beb389196fb8b9921ed236aef48e9624c6cb9f35182143bb89b024b18","sha256:dd7e055595078603ee033d239061ac1fa2ee2024575eb40fae8d563e9648be4d"],"state_sha256":"fe02b8606414b1b8e80c726869bc8d6cef36062f918722c5157c4f53162c64e4"}