{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:STFSFNU3X6J762UF4XU65XJPVG","short_pith_number":"pith:STFSFNU3","canonical_record":{"source":{"id":"1309.6259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-24T17:24:26Z","cross_cats_sorted":[],"title_canon_sha256":"0f0ebaa7e0a520bfac7b88b8ea2c4bbd70a636cca0092ed09488ddf1619e1fbb","abstract_canon_sha256":"e7f4e344e450545bb9e2f2e5b79fa5fef2e71f5d497bb780d6af720eb2ee07d5"},"schema_version":"1.0"},"canonical_sha256":"94cb22b69bbf93ff6a85e5e9eedd2fa9b6ad147a46e3c8785296660289a3115f","source":{"kind":"arxiv","id":"1309.6259","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6259","created_at":"2026-05-18T03:12:23Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6259v1","created_at":"2026-05-18T03:12:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6259","created_at":"2026-05-18T03:12:23Z"},{"alias_kind":"pith_short_12","alias_value":"STFSFNU3X6J7","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"STFSFNU3X6J762UF","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"STFSFNU3","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:STFSFNU3X6J762UF4XU65XJPVG","target":"record","payload":{"canonical_record":{"source":{"id":"1309.6259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-24T17:24:26Z","cross_cats_sorted":[],"title_canon_sha256":"0f0ebaa7e0a520bfac7b88b8ea2c4bbd70a636cca0092ed09488ddf1619e1fbb","abstract_canon_sha256":"e7f4e344e450545bb9e2f2e5b79fa5fef2e71f5d497bb780d6af720eb2ee07d5"},"schema_version":"1.0"},"canonical_sha256":"94cb22b69bbf93ff6a85e5e9eedd2fa9b6ad147a46e3c8785296660289a3115f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:23.337033Z","signature_b64":"Wci5Sztb9Ud+9HU7BHML/JTb/acVaHOZPCPqDQjMfLf5JuHKtebQ2eaNRsezBIaRerTtZhyFmdTdXbds19Q2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94cb22b69bbf93ff6a85e5e9eedd2fa9b6ad147a46e3c8785296660289a3115f","last_reissued_at":"2026-05-18T03:12:23.336062Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:23.336062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.6259","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":"2026-05-18T03:12:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/zFLWsmGtfN5w96VRwaWMQXVbHGmIflm5MrX25pHI17VlPG1yhmO8DuPo/Ns9fgvYCQrzK94FuYHoFC3OOVuCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:15:15.230506Z"},"content_sha256":"bb513ebb2145318aeb58ad5a1b4a0509f45823857d0eca35367c129c93a01a6b","schema_version":"1.0","event_id":"sha256:bb513ebb2145318aeb58ad5a1b4a0509f45823857d0eca35367c129c93a01a6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:STFSFNU3X6J762UF4XU65XJPVG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differential equations for discrete Laguerre-Sobolev orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Antonio J. Dur\\'an, Manuel D. de la Iglesia","submitted_at":"2013-09-24T17:24:26Z","abstract_excerpt":"The aim of this paper is to study differential properties of orthogonal polynomials with respect to a discrete Laguerre-Sobolev bilinear form with mass point at zero. In particular we construct the orthogonal polynomials using certain Casorati determinants. Using this construction, we prove that they are eigenfunctions of a differential operator (which will be explicitly constructed). Moreover, the order of this differential operator is explicitly computed in terms of the matrix which defines the discrete Laguerre-Sobolev bilinear form."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6259","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":"2026-05-18T03:12:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bjqC5vs4wNnLwGcLgd2+GCrTptl4hSdeoCwfazFSlx7Iz4HmGZ8VpQ1aclZ71N2sKrg6waHVQ1iNeA1fvmfqCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:15:15.230852Z"},"content_sha256":"33a0cfeccc9045ed6a9f37c171266584245a63d00f7a2402c29f18d035b89762","schema_version":"1.0","event_id":"sha256:33a0cfeccc9045ed6a9f37c171266584245a63d00f7a2402c29f18d035b89762"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/STFSFNU3X6J762UF4XU65XJPVG/bundle.json","state_url":"https://pith.science/pith/STFSFNU3X6J762UF4XU65XJPVG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/STFSFNU3X6J762UF4XU65XJPVG/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":"2026-06-22T11:15:15Z","links":{"resolver":"https://pith.science/pith/STFSFNU3X6J762UF4XU65XJPVG","bundle":"https://pith.science/pith/STFSFNU3X6J762UF4XU65XJPVG/bundle.json","state":"https://pith.science/pith/STFSFNU3X6J762UF4XU65XJPVG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/STFSFNU3X6J762UF4XU65XJPVG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:STFSFNU3X6J762UF4XU65XJPVG","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":"e7f4e344e450545bb9e2f2e5b79fa5fef2e71f5d497bb780d6af720eb2ee07d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-24T17:24:26Z","title_canon_sha256":"0f0ebaa7e0a520bfac7b88b8ea2c4bbd70a636cca0092ed09488ddf1619e1fbb"},"schema_version":"1.0","source":{"id":"1309.6259","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6259","created_at":"2026-05-18T03:12:23Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6259v1","created_at":"2026-05-18T03:12:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6259","created_at":"2026-05-18T03:12:23Z"},{"alias_kind":"pith_short_12","alias_value":"STFSFNU3X6J7","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"STFSFNU3X6J762UF","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"STFSFNU3","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:33a0cfeccc9045ed6a9f37c171266584245a63d00f7a2402c29f18d035b89762","target":"graph","created_at":"2026-05-18T03:12:23Z","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":"The aim of this paper is to study differential properties of orthogonal polynomials with respect to a discrete Laguerre-Sobolev bilinear form with mass point at zero. In particular we construct the orthogonal polynomials using certain Casorati determinants. Using this construction, we prove that they are eigenfunctions of a differential operator (which will be explicitly constructed). Moreover, the order of this differential operator is explicitly computed in terms of the matrix which defines the discrete Laguerre-Sobolev bilinear form.","authors_text":"Antonio J. Dur\\'an, Manuel D. de la Iglesia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-24T17:24:26Z","title":"Differential equations for discrete Laguerre-Sobolev orthogonal polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6259","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:bb513ebb2145318aeb58ad5a1b4a0509f45823857d0eca35367c129c93a01a6b","target":"record","created_at":"2026-05-18T03:12:23Z","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":"e7f4e344e450545bb9e2f2e5b79fa5fef2e71f5d497bb780d6af720eb2ee07d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-24T17:24:26Z","title_canon_sha256":"0f0ebaa7e0a520bfac7b88b8ea2c4bbd70a636cca0092ed09488ddf1619e1fbb"},"schema_version":"1.0","source":{"id":"1309.6259","kind":"arxiv","version":1}},"canonical_sha256":"94cb22b69bbf93ff6a85e5e9eedd2fa9b6ad147a46e3c8785296660289a3115f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94cb22b69bbf93ff6a85e5e9eedd2fa9b6ad147a46e3c8785296660289a3115f","first_computed_at":"2026-05-18T03:12:23.336062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:23.336062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wci5Sztb9Ud+9HU7BHML/JTb/acVaHOZPCPqDQjMfLf5JuHKtebQ2eaNRsezBIaRerTtZhyFmdTdXbds19Q2Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:23.337033Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.6259","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb513ebb2145318aeb58ad5a1b4a0509f45823857d0eca35367c129c93a01a6b","sha256:33a0cfeccc9045ed6a9f37c171266584245a63d00f7a2402c29f18d035b89762"],"state_sha256":"b0a68ba9bb506aabe86227ec409d4384f385584dc76cf6e71907c8b822a598b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jKtYIIKCEtCBiydpZZ/xmOwtgqAYd/KhHStx2VlcPFw+b3MTbxUkANwM7O5EcEm+rgDVKXB9fCkA2AjuVK8MCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T11:15:15.232793Z","bundle_sha256":"cb38f624caccf4008796b3fa0ba426980d8961c24562183015948255d8fcbf4f"}}