{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FQMUS4GIOYBPRN6OQXO77IAM7A","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":"ac351022150bdb992b6144ffef8d283614b47e9b2985ab1cec53bf8e7e59102c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-04-19T15:33:59Z","title_canon_sha256":"6372268025f9ff2343da32fdcf72bbdad29d6430a93503e0b025dc4f413c364e"},"schema_version":"1.0","source":{"id":"1104.3778","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3778","created_at":"2026-05-18T03:10:27Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3778v1","created_at":"2026-05-18T03:10:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3778","created_at":"2026-05-18T03:10:27Z"},{"alias_kind":"pith_short_12","alias_value":"FQMUS4GIOYBP","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FQMUS4GIOYBPRN6O","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FQMUS4GI","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:4cc4f63ceda5b4bd94d3c53cbda0699b0b20b50358be9f33fef76f72d4ab55ae","target":"graph","created_at":"2026-05-18T03:10:27Z","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 show that multiple orthogonal polynomials for r measures $(\\mu_1,...,\\mu_r)$ satisfy a system of linear recurrence relations only involving nearest neighbor multi-indices $\\vec{n}\\pm \\vec{e}_j$, where $\\vec{e}_j$ are the standard unit vectors. The recurrence coefficients are not arbitrary but satisfy a system of partial difference equations with boundary values given by the recurrence coefficients of the orthogonal polynomials with each of measures $\\mu_j$. We show how the Christoffel-Darboux formula for multiple orthogonal polynomials can be obtained easily using this information. We give ","authors_text":"Walter Van Assche","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-04-19T15:33:59Z","title":"The nearest neighbor recurrence coefficients for multiple orthogonal polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3778","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":"sha256:54fbd9478097ed5c8da11f330acf951e967d924e38213c25c0f902db37d1243b","target":"record","created_at":"2026-05-18T03:10:27Z","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":"ac351022150bdb992b6144ffef8d283614b47e9b2985ab1cec53bf8e7e59102c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-04-19T15:33:59Z","title_canon_sha256":"6372268025f9ff2343da32fdcf72bbdad29d6430a93503e0b025dc4f413c364e"},"schema_version":"1.0","source":{"id":"1104.3778","kind":"arxiv","version":1}},"canonical_sha256":"2c194970c87602f8b7ce85ddffa00cf81cb5624529baca257b63e25a5b27d82a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c194970c87602f8b7ce85ddffa00cf81cb5624529baca257b63e25a5b27d82a","first_computed_at":"2026-05-18T03:10:27.047682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:27.047682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QGS+yvBhhxquQKKuiKOMiHjGHov2/dHl9HZAW7bWc7FlvRWyTDQ9qSPsqwmTyuWMbs0T062i/jRe8Wy/88dcCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:27.048381Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3778","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54fbd9478097ed5c8da11f330acf951e967d924e38213c25c0f902db37d1243b","sha256:4cc4f63ceda5b4bd94d3c53cbda0699b0b20b50358be9f33fef76f72d4ab55ae"],"state_sha256":"005197683e9f05bd86c4480ad411796f22b54bb3249d8ccf239ce7e1f1c19aa9"}