{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OESNAO2A57O5EWTACAUQ7HTMPL","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":"5c3b652b08605e68fdd1a55a1871ee7c470f2ec930c07274b1a9523d0c64558e","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-10T14:18:58Z","title_canon_sha256":"9f3e13e321b193a6e08136e7a41b4608fbd0d76746e0ec1e78f50e56620c8e6b"},"schema_version":"1.0","source":{"id":"1403.2662","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2662","created_at":"2026-05-18T01:06:29Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2662v2","created_at":"2026-05-18T01:06:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2662","created_at":"2026-05-18T01:06:29Z"},{"alias_kind":"pith_short_12","alias_value":"OESNAO2A57O5","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OESNAO2A57O5EWTA","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OESNAO2A","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:d21c2cc56528819919bc3f3a2fd324f0c9186b47095526367c95cc9115e027c3","target":"graph","created_at":"2026-05-18T01:06:29Z","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 identification mentioned in the title allows a formulation of the multidi mensional Favard Lemma different from the ones currently used in the literature and which exactly parallels the original one dimensional formulation in the sense that the positive Jacobi sequence is replaced by a sequence of positive Hermitean (square) matrices and the real Jacobi sequence by a sequence of Hermitean matri ces of the same dimension. Moreover, in this identification, the multidimensional extension of the compatibility condition for the positive Jacobi sequence becomes the condition which guarantees the","authors_text":"Abdessatar Barhoumi, Ameur Dhahri, Luigi Accardi","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-10T14:18:58Z","title":"Identification of the theory of multidimensional orthogonal polynomials with the theory of symmetric interacting Fock spaces with finite dimensional one particle space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2662","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":"sha256:3f9e94014b63e0b564c95104f20c2c5fe115e7094b8fa1051e4bdc7394e712f8","target":"record","created_at":"2026-05-18T01:06:29Z","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":"5c3b652b08605e68fdd1a55a1871ee7c470f2ec930c07274b1a9523d0c64558e","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-10T14:18:58Z","title_canon_sha256":"9f3e13e321b193a6e08136e7a41b4608fbd0d76746e0ec1e78f50e56620c8e6b"},"schema_version":"1.0","source":{"id":"1403.2662","kind":"arxiv","version":2}},"canonical_sha256":"7124d03b40efddd25a6010290f9e6c7accd736b630e2756ea920ca106cbf5f66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7124d03b40efddd25a6010290f9e6c7accd736b630e2756ea920ca106cbf5f66","first_computed_at":"2026-05-18T01:06:29.400543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:29.400543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mTWr2w3W4vGbDk+idyDItLjnbx59H85BIbBiFnMonk74pwz61KLcwKQ+ZHg3hMjvtO7qSfgTSnP7rqtMca2OCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:29.401176Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.2662","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f9e94014b63e0b564c95104f20c2c5fe115e7094b8fa1051e4bdc7394e712f8","sha256:d21c2cc56528819919bc3f3a2fd324f0c9186b47095526367c95cc9115e027c3"],"state_sha256":"584917ee87a7dd07d1b0cc1aa107bcffdeed2d00610c1f293fd937ed3bbb8fa9"}