{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CH6ER4AY2I5SMOVLYZQ7KAVA7D","short_pith_number":"pith:CH6ER4AY","canonical_record":{"source":{"id":"1607.03251","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-12T07:44:03Z","cross_cats_sorted":[],"title_canon_sha256":"acb752f62768bf7cba2ecdcb39f7c1534481f71efd6c6417a556f690d9e913f1","abstract_canon_sha256":"2cb0faad76c74094f66d1d212acdc825b12206b31d459b3c99a03c18e55f0bab"},"schema_version":"1.0"},"canonical_sha256":"11fc48f018d23b263aabc661f502a0f8db9a1a4da3d057344af36e3589e5b89d","source":{"kind":"arxiv","id":"1607.03251","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03251","created_at":"2026-05-18T00:39:13Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03251v1","created_at":"2026-05-18T00:39:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03251","created_at":"2026-05-18T00:39:13Z"},{"alias_kind":"pith_short_12","alias_value":"CH6ER4AY2I5S","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CH6ER4AY2I5SMOVL","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CH6ER4AY","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CH6ER4AY2I5SMOVLYZQ7KAVA7D","target":"record","payload":{"canonical_record":{"source":{"id":"1607.03251","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-12T07:44:03Z","cross_cats_sorted":[],"title_canon_sha256":"acb752f62768bf7cba2ecdcb39f7c1534481f71efd6c6417a556f690d9e913f1","abstract_canon_sha256":"2cb0faad76c74094f66d1d212acdc825b12206b31d459b3c99a03c18e55f0bab"},"schema_version":"1.0"},"canonical_sha256":"11fc48f018d23b263aabc661f502a0f8db9a1a4da3d057344af36e3589e5b89d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:13.382903Z","signature_b64":"zIDWKjwT0cLoab7ywFszSHalIAKSL+CBCdiideCupFJBrJsmfgogO6QSAVKt2+p5mhRTfjtg7Q2xcbAchxbkDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11fc48f018d23b263aabc661f502a0f8db9a1a4da3d057344af36e3589e5b89d","last_reissued_at":"2026-05-18T00:39:13.382277Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:13.382277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.03251","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:39:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4cMFNjhdAM9vDJb0w3yw2wGoyBBfJ16wGRu5OhUHbi+f79XUixXdvZVnNp6f21/krUSO7tVqq1IGmZv/KYM+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:45:34.823882Z"},"content_sha256":"142375a5633e5812c57033a814db23244762f79b265331dbffc8c841dda3d8f5","schema_version":"1.0","event_id":"sha256:142375a5633e5812c57033a814db23244762f79b265331dbffc8c841dda3d8f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CH6ER4AY2I5SMOVLYZQ7KAVA7D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Majorization results for zeros of orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Walter Van Assche","submitted_at":"2016-07-12T07:44:03Z","abstract_excerpt":"We show that the zeros of consecutive orthogonal polynomials $p_n$ and $p_{n-1}$ are linearly connected by a doubly stochastic matrix for which the entries are explicitly computed in terms of Christoffel numbers. We give similar results for the zeros of $p_n$ and the associated polynomial $p_{n-1}^{(1)}$ and for the zeros of the polynomial obtained by deleting the $k$th row and column $(1 \\leq k \\leq n)$ in the corresponding Jacobi matrix."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03251","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:39:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ul4YS7Pb7yJql1hySv918TyscKOMZKDKO5eZsj1XmpFW6AV2qEPLR0bE559gbMwDicHiRhIbKQXTCf3rKcTgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:45:34.824585Z"},"content_sha256":"f8e94918abee0b42cec86f3c506dee5ccf4131d1bd0e38b0fa618937c64713bb","schema_version":"1.0","event_id":"sha256:f8e94918abee0b42cec86f3c506dee5ccf4131d1bd0e38b0fa618937c64713bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CH6ER4AY2I5SMOVLYZQ7KAVA7D/bundle.json","state_url":"https://pith.science/pith/CH6ER4AY2I5SMOVLYZQ7KAVA7D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CH6ER4AY2I5SMOVLYZQ7KAVA7D/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T09:45:34Z","links":{"resolver":"https://pith.science/pith/CH6ER4AY2I5SMOVLYZQ7KAVA7D","bundle":"https://pith.science/pith/CH6ER4AY2I5SMOVLYZQ7KAVA7D/bundle.json","state":"https://pith.science/pith/CH6ER4AY2I5SMOVLYZQ7KAVA7D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CH6ER4AY2I5SMOVLYZQ7KAVA7D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CH6ER4AY2I5SMOVLYZQ7KAVA7D","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":"2cb0faad76c74094f66d1d212acdc825b12206b31d459b3c99a03c18e55f0bab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-12T07:44:03Z","title_canon_sha256":"acb752f62768bf7cba2ecdcb39f7c1534481f71efd6c6417a556f690d9e913f1"},"schema_version":"1.0","source":{"id":"1607.03251","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03251","created_at":"2026-05-18T00:39:13Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03251v1","created_at":"2026-05-18T00:39:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03251","created_at":"2026-05-18T00:39:13Z"},{"alias_kind":"pith_short_12","alias_value":"CH6ER4AY2I5S","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CH6ER4AY2I5SMOVL","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CH6ER4AY","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:f8e94918abee0b42cec86f3c506dee5ccf4131d1bd0e38b0fa618937c64713bb","target":"graph","created_at":"2026-05-18T00:39:13Z","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 the zeros of consecutive orthogonal polynomials $p_n$ and $p_{n-1}$ are linearly connected by a doubly stochastic matrix for which the entries are explicitly computed in terms of Christoffel numbers. We give similar results for the zeros of $p_n$ and the associated polynomial $p_{n-1}^{(1)}$ and for the zeros of the polynomial obtained by deleting the $k$th row and column $(1 \\leq k \\leq n)$ in the corresponding Jacobi matrix.","authors_text":"Walter Van Assche","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-12T07:44:03Z","title":"Majorization results for zeros of orthogonal polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03251","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":"sha256:142375a5633e5812c57033a814db23244762f79b265331dbffc8c841dda3d8f5","target":"record","created_at":"2026-05-18T00:39:13Z","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":"2cb0faad76c74094f66d1d212acdc825b12206b31d459b3c99a03c18e55f0bab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-12T07:44:03Z","title_canon_sha256":"acb752f62768bf7cba2ecdcb39f7c1534481f71efd6c6417a556f690d9e913f1"},"schema_version":"1.0","source":{"id":"1607.03251","kind":"arxiv","version":1}},"canonical_sha256":"11fc48f018d23b263aabc661f502a0f8db9a1a4da3d057344af36e3589e5b89d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11fc48f018d23b263aabc661f502a0f8db9a1a4da3d057344af36e3589e5b89d","first_computed_at":"2026-05-18T00:39:13.382277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:13.382277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zIDWKjwT0cLoab7ywFszSHalIAKSL+CBCdiideCupFJBrJsmfgogO6QSAVKt2+p5mhRTfjtg7Q2xcbAchxbkDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:13.382903Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.03251","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:142375a5633e5812c57033a814db23244762f79b265331dbffc8c841dda3d8f5","sha256:f8e94918abee0b42cec86f3c506dee5ccf4131d1bd0e38b0fa618937c64713bb"],"state_sha256":"7c291da33251adf06635588db0d2cbae319dcf17cccb6003151c71954d3286d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MKPo73RsCTkRX9nKLuPQSgdoloq11ETOprW9pSRpOdav6WqljeEOfh1OjpuVCIYDIS/vSnEkM6SQmAg5WgBIDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:45:34.827974Z","bundle_sha256":"93c9f3a84bcd1e1af7aaa53b56cdc57eed6d6a2735920b09d6c8407e2d499d5d"}}