{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3QAFGHRCP5UGCQIG2BSGRLU54A","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":"9bfa2bf6273508172796b342c4dacf32e0605a109a4c54946028235dd9a87b3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-21T20:14:47Z","title_canon_sha256":"aaaebe2df1fa62039016d279ebf3912e6ef094042c348ed1d3c54aa22cde4c6e"},"schema_version":"1.0","source":{"id":"1611.06991","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06991","created_at":"2026-05-18T00:57:00Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06991v2","created_at":"2026-05-18T00:57:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06991","created_at":"2026-05-18T00:57:00Z"},{"alias_kind":"pith_short_12","alias_value":"3QAFGHRCP5UG","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3QAFGHRCP5UGCQIG","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3QAFGHRC","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:e57bd140979eb3d21dac2ddb9947bb4031c2d44c92a2fe840f0045641137e5a7","target":"graph","created_at":"2026-05-18T00:57:00Z","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 call Krawtchouk-Griffiths systems, or KG-systems, systems of multivariate polynomials orthogonal with respect to corresponding multinomial distributions. The original Krawtchouk polynomials are orthogonal with respect to a binomial distribution. Our approach is to work directly with matrices comprising the values of the polynomials at points of a discrete grid based on the possible counting values of the underlying multinomial distribution. The starting point for the construction of a KG-system is a generating matrix satisfying the K-condition, orthogonality with respect to the basic probab","authors_text":"Philip Feinsilver","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-21T20:14:47Z","title":"Krawtchouk-Griffiths Systems I: Matrix Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06991","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":"sha256:6f386d66522621bf815e197edc0896a8f4958902177b7e00b390f9505ea8e83e","target":"record","created_at":"2026-05-18T00:57:00Z","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":"9bfa2bf6273508172796b342c4dacf32e0605a109a4c54946028235dd9a87b3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-21T20:14:47Z","title_canon_sha256":"aaaebe2df1fa62039016d279ebf3912e6ef094042c348ed1d3c54aa22cde4c6e"},"schema_version":"1.0","source":{"id":"1611.06991","kind":"arxiv","version":2}},"canonical_sha256":"dc00531e227f68614106d06468ae9de000185bba3e65edcb1aa6441b2a9507f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc00531e227f68614106d06468ae9de000185bba3e65edcb1aa6441b2a9507f2","first_computed_at":"2026-05-18T00:57:00.605943Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:00.605943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eSflLqy8Qb8CsltVxrdBU9bl18o358aVDGRI9nayhlI/oXTzx39J7yvYkX6TR77KyLGJmRP78Xy88ZHnvnDACw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:00.606410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.06991","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f386d66522621bf815e197edc0896a8f4958902177b7e00b390f9505ea8e83e","sha256:e57bd140979eb3d21dac2ddb9947bb4031c2d44c92a2fe840f0045641137e5a7"],"state_sha256":"2e803e8a4c16b5eab885a10ef01aee548e2324a38057e6848abd9db8aa464920"}