{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UQGFMBXCCNACM3TGQYEKU6PITT","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":"b36ab8a137db2a32fd673366101544c6e02be67479a532c7eaaadb7035bd33f2","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-07T20:19:24Z","title_canon_sha256":"09398007123f3f70807b38b796399de63e1593b56c4c8a018682cd143bc4ade4"},"schema_version":"1.0","source":{"id":"1805.02727","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.02727","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"arxiv_version","alias_value":"1805.02727v4","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02727","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"pith_short_12","alias_value":"UQGFMBXCCNAC","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UQGFMBXCCNACM3TG","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UQGFMBXC","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:2e64af778115554e59a36990292586857ff35b731df83926c7edccbfacc7962e","target":"graph","created_at":"2026-05-17T23:50:38Z","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 an integer matrix, and assume that its semigroup ring $\\mathbb{C}[\\mathbb{N}A]$ is normal. Fix a face $F$ of the cone of $A$. We show that the projection and restriction of an $A$-hypergeometric system to the coordinate subspace corresponding to $F$ are essentially $F$-hypergeometric; moreover, at most one of them is nonzero.\n  We also show that, if $A$ is in addition homogeneous, the holonomic dual of an $A$-hypergeometric system is itself $A$-hypergeometric. This extends a result of Uli Walther, proving a conjecture of Nobuki Takayama in the normal homogeneous case.","authors_text":"Avi Steiner","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-07T20:19:24Z","title":"Dualizing, projecting, and restricting GKZ systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02727","kind":"arxiv","version":4},"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":"sha256:8483f8d41730ea7c3a17bf54dfb967afd76c15367c535ef6ec10d2912bcc036c","target":"record","created_at":"2026-05-17T23:50:38Z","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":"b36ab8a137db2a32fd673366101544c6e02be67479a532c7eaaadb7035bd33f2","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-07T20:19:24Z","title_canon_sha256":"09398007123f3f70807b38b796399de63e1593b56c4c8a018682cd143bc4ade4"},"schema_version":"1.0","source":{"id":"1805.02727","kind":"arxiv","version":4}},"canonical_sha256":"a40c5606e21340266e668608aa79e89ccf042eb84c104a18c4bbfa1b33426d97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a40c5606e21340266e668608aa79e89ccf042eb84c104a18c4bbfa1b33426d97","first_computed_at":"2026-05-17T23:50:38.646573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:38.646573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JcVH5XsTwUUhOi8mh4gAe6iuoyiq157RZbgW92Fn7dwEgPvtsHLDRIKlNsIvl6ZBR9XJKlRsvPu3SL1+XeL2Ag==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:38.647067Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.02727","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8483f8d41730ea7c3a17bf54dfb967afd76c15367c535ef6ec10d2912bcc036c","sha256:2e64af778115554e59a36990292586857ff35b731df83926c7edccbfacc7962e"],"state_sha256":"1eb831074cb24ad5a6b75cc44d90a6087a44f6a7baa3367665fe807c5b217643"}