{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KPCV3F7GBFBWHSFXFFBSTGJX3Z","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":"67a4b565c31bad0a2664290f6911667bd61662b6f82ef427f3ab08746d08dd69","cross_cats_sorted":["cs.DM","cs.PF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-16T17:23:32Z","title_canon_sha256":"1b662e6d9781f6c5524d814bb1f14fafe23534087a194bfeee89a7be85239c59"},"schema_version":"1.0","source":{"id":"1904.08283","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.08283","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"arxiv_version","alias_value":"1904.08283v1","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.08283","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"pith_short_12","alias_value":"KPCV3F7GBFBW","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KPCV3F7GBFBWHSFX","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KPCV3F7G","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:9383afbb2269beb71c65515fead649684ea938953a0e0fa41971586b37a75077","target":"graph","created_at":"2026-05-17T23:48:18Z","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":"For any complex parameters $x$ and $\\nu$, we provide a new class of linear inversion formulas $T = A(x,\\nu) \\cdot S \\Leftrightarrow S = B(x,\\nu) \\cdot T$ between sequences $S = (S_n)_{n \\in \\mathbb{N}^*}$ and $T = (T_n)_{n \\in \\mathbb{N}^*}$, where the infinite lower-triangular matrix $A(x,\\nu)$ and its inverse $B(x,\\nu)$ involve Hypergeometric polynomials $F(\\cdot)$, namely $$\n  \\left\\{\n  \\begin{array}{ll}\n  A_{n,k}(x,\\nu) = \\displaystyle (-1)^k\\binom{n}{k}F(k-n,-n\\nu;-n;x),\n  \\\\\n  B_{n,k}(x,\\nu) = \\displaystyle (-1)^k\\binom{n}{k}F(k-n,k\\nu;k;x)\n  \\end{array} \\right. $$ for $1 \\leqslant k \\le","authors_text":"Alain Simonian, Fabrice Guillemin, Ridha Nasri","cross_cats":["cs.DM","cs.PF"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-16T17:23:32Z","title":"Inversion formula with hypergeometric polynomials and its application to an integral equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08283","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":"sha256:30a3a87d6824dbc79fc0351be83d3ab527ad4ef97e5d3694a56eab5308cedd00","target":"record","created_at":"2026-05-17T23:48:18Z","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":"67a4b565c31bad0a2664290f6911667bd61662b6f82ef427f3ab08746d08dd69","cross_cats_sorted":["cs.DM","cs.PF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-16T17:23:32Z","title_canon_sha256":"1b662e6d9781f6c5524d814bb1f14fafe23534087a194bfeee89a7be85239c59"},"schema_version":"1.0","source":{"id":"1904.08283","kind":"arxiv","version":1}},"canonical_sha256":"53c55d97e6094363c8b72943299937de67e11317f8ae70e423a122f36cb3d989","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53c55d97e6094363c8b72943299937de67e11317f8ae70e423a122f36cb3d989","first_computed_at":"2026-05-17T23:48:18.137561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:18.137561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6MvqV0Vba2wbKdjaVIFvYgLQhGKeSKncLjdT5d7kAIpLCSyDtrtpCklsMbOHFptDE2WY1zdGgOueP2WBzY55Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:18.138287Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.08283","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30a3a87d6824dbc79fc0351be83d3ab527ad4ef97e5d3694a56eab5308cedd00","sha256:9383afbb2269beb71c65515fead649684ea938953a0e0fa41971586b37a75077"],"state_sha256":"068cbc8ff0b476693fc85b37541baf41fcee59dfab1d05fa03bbec7dd7b79b09"}