{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:X7F5DTPEEOOPRUAIEVZU6X4GWL","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":"b00b197291ebf11732c4997ee9055e8f01397b3dc73ad1fb363ea68b9fff8a70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-02-08T11:52:42Z","title_canon_sha256":"91de75400025b0670a1565beaaa9133aa0dbb7168993c155f1eab86b40e5184f"},"schema_version":"1.0","source":{"id":"1102.1578","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1578","created_at":"2026-05-18T04:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1578v1","created_at":"2026-05-18T04:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1578","created_at":"2026-05-18T04:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"X7F5DTPEEOOP","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"X7F5DTPEEOOPRUAI","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"X7F5DTPE","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:3adfcb0d2190eac5dfaa10ff45676ad83f656729685aeef4bc0975744c119a6a","target":"graph","created_at":"2026-05-18T04:29:52Z","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":"We introduce a family of weight matrices $W$ of the form $T(t)T^*(t)$, $T(t)=e^{\\mathscr{A}t}e^{\\mathscr{D}t^2}$, where $\\mathscr{A}$ is certain nilpotent matrix and $\\mathscr{D}$ is a diagonal matrix with negative real entries. The weight matrices $W$ have arbitrary size $N\\times N$ and depend on $N$ parameters.\n  The orthogonal polynomials with respect to this family of weight matrices satisfy a second order differential equation with differential coefficients that are matrix polynomials $F_2$, $F_1$ and $F_0$ (independent of $n$) of degrees not bigger than 2, 1 and 0 respectively.\n  For siz","authors_text":"Antonio J. Dur\\'an, Jorge Borrego, Mirta Castro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-02-08T11:52:42Z","title":"Orthogonal matrix polynomials satisfying differential equations with recurrence coefficients having non-scalar limits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1578","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":"sha256:1fe94214e44b13873cb670504d28180cb11fb44641c5aa5e9b622df20ddd03a6","target":"record","created_at":"2026-05-18T04:29:52Z","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":"b00b197291ebf11732c4997ee9055e8f01397b3dc73ad1fb363ea68b9fff8a70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-02-08T11:52:42Z","title_canon_sha256":"91de75400025b0670a1565beaaa9133aa0dbb7168993c155f1eab86b40e5184f"},"schema_version":"1.0","source":{"id":"1102.1578","kind":"arxiv","version":1}},"canonical_sha256":"bfcbd1cde4239cf8d00825734f5f86b2fc162b12893d60d1bb10563b7fcc6c29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfcbd1cde4239cf8d00825734f5f86b2fc162b12893d60d1bb10563b7fcc6c29","first_computed_at":"2026-05-18T04:29:52.938419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:29:52.938419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TTGPof+b+ZuGaVkeNliSlxPTou+vcClcF3pps4+QjD2WP+83JzuAkpGIfrXk5yeO9wScagYUJ4swHz1m8s5cAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:29:52.938826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.1578","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fe94214e44b13873cb670504d28180cb11fb44641c5aa5e9b622df20ddd03a6","sha256:3adfcb0d2190eac5dfaa10ff45676ad83f656729685aeef4bc0975744c119a6a"],"state_sha256":"cac4f445cdf9a7588ca32d7e884f88c529108486d901d80d23a3421de5f8e901"}