{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:44OQP2STIRWKQTW3KZ3JKYE6WZ","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":"b9508ad3302710c9138a37c552a0ef94d86d929fd0af7b910ef17625b2144e7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-08T17:46:41Z","title_canon_sha256":"242b542fd1ae0a2e18178f463f057d3970bc43581f7c86f0020ad4a351a51e20"},"schema_version":"1.0","source":{"id":"1905.03235","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.03235","created_at":"2026-05-17T23:46:42Z"},{"alias_kind":"arxiv_version","alias_value":"1905.03235v1","created_at":"2026-05-17T23:46:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03235","created_at":"2026-05-17T23:46:42Z"},{"alias_kind":"pith_short_12","alias_value":"44OQP2STIRWK","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"44OQP2STIRWKQTW3","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"44OQP2ST","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:4d80732ab37975d1301bdfbc143a6823ec14c6cdb7a437eee9aa453bcf123eab","target":"graph","created_at":"2026-05-17T23:46:42Z","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":"Let $A$ be a set of $N$ vectors in ${\\mathbb Z}^n$ and let $v$ be a vector in ${\\mathbb C}^N$ that has minimal negative support for $A$. Such a vector $v$ gives rise to a formal series solution of the $A$-hypergeometric system with parameter $\\beta=Av$. If $v$ lies in ${\\mathbb Q}^n$, then this series has rational coefficients. Let $p$ be a prime number. We characterize those $v$ whose coordinates are rational, $p$-integral, and lie in the closed interval $[-1,0]$ for which the corresponding normalized series solution has $p$-integral coefficients. From this we deduce further integrality resul","authors_text":"Alan Adolphson, Steven Sperber","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-08T17:46:41Z","title":"On integrality properties of hypergeometric series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03235","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":"sha256:3db2194ec98b064587802b6906e30b1e25f3a2337d5dc44a5cd8f77665fbb7e8","target":"record","created_at":"2026-05-17T23:46:42Z","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":"b9508ad3302710c9138a37c552a0ef94d86d929fd0af7b910ef17625b2144e7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-08T17:46:41Z","title_canon_sha256":"242b542fd1ae0a2e18178f463f057d3970bc43581f7c86f0020ad4a351a51e20"},"schema_version":"1.0","source":{"id":"1905.03235","kind":"arxiv","version":1}},"canonical_sha256":"e71d07ea53446ca84edb567695609eb65c3e9e4a5fa5921ae80f2c2d62be82bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e71d07ea53446ca84edb567695609eb65c3e9e4a5fa5921ae80f2c2d62be82bd","first_computed_at":"2026-05-17T23:46:42.479259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:42.479259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4a8sIwoNhwm/W40UhDbd3EE715+fLid7TnPRjGLUkvK5Wx12f3lwzSjTtCM57zfDZoNb0gGaFtTnGkRsLbt3Ag==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:42.479781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.03235","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3db2194ec98b064587802b6906e30b1e25f3a2337d5dc44a5cd8f77665fbb7e8","sha256:4d80732ab37975d1301bdfbc143a6823ec14c6cdb7a437eee9aa453bcf123eab"],"state_sha256":"65f75b03a27428346b969c89b68eb3356e9ce235bb5c2bac2bfed7ba070a3db4"}