{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JOTHQDGYIN273PLXJHNFNXU4DJ","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":"7338f3fc920201b341b270b3b7dcabe8dc7d11dc509579296e7b18fa9f4f79b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-22T23:51:40Z","title_canon_sha256":"a2b1527c8fe0cf14b002b1f84e648731e2b811286ac96a432730022483b0ebba"},"schema_version":"1.0","source":{"id":"1412.7214","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7214","created_at":"2026-05-18T02:30:40Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7214v1","created_at":"2026-05-18T02:30:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7214","created_at":"2026-05-18T02:30:40Z"},{"alias_kind":"pith_short_12","alias_value":"JOTHQDGYIN27","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JOTHQDGYIN273PLX","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JOTHQDGY","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:cf26eeefb83de2ef5c4e22e88d6ba56c138993dbfbd412cbf685941299a69453","target":"graph","created_at":"2026-05-18T02:30:40Z","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":"In this 1997 Ph.D. dissertation we prove a piecewise form of the discrete part of Wilf and Zeilberger's 1992 conjecture that a hypergeometric term is proper if and only if it is holonomic. We show that a holonomic hypergeometric term on $Z^n$ is piecewise proper and we show that without such a qualification the conjecture is false. We call a term piecewise proper if $Z^n$ can be expressed as the union of a finite number of polyhedral regions (the \"pieces\") and a set of measure zero (which we define to be a finite union of hyperplanes) such that the restriction of the term to each polyhedral re","authors_text":"Garth Payne","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-22T23:51:40Z","title":"Multivariate Hypergeometric Terms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7214","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":"sha256:72b53059cb3222c62da6d401bb11eeaa048908fe9822bd2b5238383dbeb5510f","target":"record","created_at":"2026-05-18T02:30:40Z","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":"7338f3fc920201b341b270b3b7dcabe8dc7d11dc509579296e7b18fa9f4f79b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-22T23:51:40Z","title_canon_sha256":"a2b1527c8fe0cf14b002b1f84e648731e2b811286ac96a432730022483b0ebba"},"schema_version":"1.0","source":{"id":"1412.7214","kind":"arxiv","version":1}},"canonical_sha256":"4ba6780cd84375fdbd7749da56de9c1a5a89c8a7dafeb839b7a7d8c8d60ee9b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ba6780cd84375fdbd7749da56de9c1a5a89c8a7dafeb839b7a7d8c8d60ee9b5","first_computed_at":"2026-05-18T02:30:40.774816Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:40.774816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yEuGTiv8I4vgPupsfit1hGfrt6iWnc3ZGGcqMvZ5xnja7S5MCAFlX8ksqGUfu7oJPscWIJbKUnnrs6w7dV0hAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:40.775420Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7214","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72b53059cb3222c62da6d401bb11eeaa048908fe9822bd2b5238383dbeb5510f","sha256:cf26eeefb83de2ef5c4e22e88d6ba56c138993dbfbd412cbf685941299a69453"],"state_sha256":"c104a7abd7230cab83b37b58b24b7812e585f770db2cb7365719005ae4133db4"}