{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PZD3I427HUMUEDCGBTYVX33PX6","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":"d980b0ec68d5449aac69f381841b9580708a0e1ea8b0075a2a145f5161bc84d3","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-11-20T22:34:03Z","title_canon_sha256":"337927bf9b2d01f61d51484b5c7740aced819bd198b84fd68b2176185a812236"},"schema_version":"1.0","source":{"id":"1311.5252","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.5252","created_at":"2026-05-18T01:35:52Z"},{"alias_kind":"arxiv_version","alias_value":"1311.5252v2","created_at":"2026-05-18T01:35:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.5252","created_at":"2026-05-18T01:35:52Z"},{"alias_kind":"pith_short_12","alias_value":"PZD3I427HUMU","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"PZD3I427HUMUEDCG","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"PZD3I427","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:9ccf8206e4a056b4be7980b2f36ffef5e591e62100917ecf1ffc77b08adf7119","target":"graph","created_at":"2026-05-18T01:35:52Z","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.","authors_text":"Alan Adolphson, Steven Sperber","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-11-20T22:34:03Z","title":"On the $p$-integrality of $A$-hypergeometric series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5252","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":"sha256:005663979f79196d55d92d76cc1e80e690ad92bc54cc109bd17da88005740b87","target":"record","created_at":"2026-05-18T01:35:52Z","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":"d980b0ec68d5449aac69f381841b9580708a0e1ea8b0075a2a145f5161bc84d3","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-11-20T22:34:03Z","title_canon_sha256":"337927bf9b2d01f61d51484b5c7740aced819bd198b84fd68b2176185a812236"},"schema_version":"1.0","source":{"id":"1311.5252","kind":"arxiv","version":2}},"canonical_sha256":"7e47b4735f3d19420c460cf15bef6fbfba237d31c79deb8d9afa937bdb5acf74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e47b4735f3d19420c460cf15bef6fbfba237d31c79deb8d9afa937bdb5acf74","first_computed_at":"2026-05-18T01:35:52.952672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:52.952672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gcXkGtNGUiAFLD4KVItk0sZPEN2lV5fEw2Lz5Y/0CuyKW3phwigUTnMM1CFLRkz1cXr9+g6Y780p2vUxdT11Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:52.953334Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.5252","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:005663979f79196d55d92d76cc1e80e690ad92bc54cc109bd17da88005740b87","sha256:9ccf8206e4a056b4be7980b2f36ffef5e591e62100917ecf1ffc77b08adf7119"],"state_sha256":"20b56c617aad832a660a0006eb0df89c5a22ef14e9547a135e0428d11a5d3909"}