{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:F6WCR6VT4I7BPRDYMIAQC3HW5W","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":"99ab5477f5957e7d5a86857b544dfdc00622f4780460c69865e2f7b25435c74c","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-07T03:31:47Z","title_canon_sha256":"de1f9d84d63dd9ca543d4f39b983fd4545fbda0c6c80b4c809db160b3e70c939"},"schema_version":"1.0","source":{"id":"1708.01978","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01978","created_at":"2026-05-18T00:38:32Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01978v1","created_at":"2026-05-18T00:38:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01978","created_at":"2026-05-18T00:38:32Z"},{"alias_kind":"pith_short_12","alias_value":"F6WCR6VT4I7B","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"F6WCR6VT4I7BPRDY","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"F6WCR6VT","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:e12b33ec210bd3b901011a9242f4662dfbaa535b35fab4285ff8cbee02b2919c","target":"graph","created_at":"2026-05-18T00:38:32Z","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":"Studying the isotropy orbits of compact symmetric spaces Reiswich introduced a family of explicit polynomials in one variable in order to describe the unique minimal isotropy orbit of compact symmetric spaces with Dynkin diagram of type $D_m$. Based on this geometric interpretation he conjectured that these polynomials all have pairwise different real roots in the interval $[\\,0,1\\,]$. In this article the polynomials constructed by Reiswich will be identified as special cases of Jacobi polynomials thus proving the conjecture about minimal isotropy orbits of compact symmetric spaces with Dynkin","authors_text":"Gregor Weingart","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-07T03:31:47Z","title":"Sequences of Orthogonal Polynomials related to Isotropy Orbits of Symmetric Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01978","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":"sha256:2742e471e2725b1316d2c34816ac261534fd2c86cd595fd4a477a4a13bb88f8c","target":"record","created_at":"2026-05-18T00:38:32Z","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":"99ab5477f5957e7d5a86857b544dfdc00622f4780460c69865e2f7b25435c74c","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-07T03:31:47Z","title_canon_sha256":"de1f9d84d63dd9ca543d4f39b983fd4545fbda0c6c80b4c809db160b3e70c939"},"schema_version":"1.0","source":{"id":"1708.01978","kind":"arxiv","version":1}},"canonical_sha256":"2fac28fab3e23e17c4786201016cf6ed980c0416b33330238cf4bcd774af1066","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fac28fab3e23e17c4786201016cf6ed980c0416b33330238cf4bcd774af1066","first_computed_at":"2026-05-18T00:38:32.651569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:32.651569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yN7n7choxXh5Xg+AZlKrGdt8Hmj5BxGcGPAy22kltDUaIL2tHqtk+k5C35n4Yl33wQEdoLSjon3Tc4kZG/vBDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:32.652015Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.01978","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2742e471e2725b1316d2c34816ac261534fd2c86cd595fd4a477a4a13bb88f8c","sha256:e12b33ec210bd3b901011a9242f4662dfbaa535b35fab4285ff8cbee02b2919c"],"state_sha256":"05a3d98c29db2755eab165f7a94fc18236841b17d77f60545abce85666fe3993"}