{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UQGFMBXCCNACM3TGQYEKU6PITT","short_pith_number":"pith:UQGFMBXC","canonical_record":{"source":{"id":"1805.02727","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-07T20:19:24Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"09398007123f3f70807b38b796399de63e1593b56c4c8a018682cd143bc4ade4","abstract_canon_sha256":"b36ab8a137db2a32fd673366101544c6e02be67479a532c7eaaadb7035bd33f2"},"schema_version":"1.0"},"canonical_sha256":"a40c5606e21340266e668608aa79e89ccf042eb84c104a18c4bbfa1b33426d97","source":{"kind":"arxiv","id":"1805.02727","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UQGFMBXCCNACM3TGQYEKU6PITT","target":"record","payload":{"canonical_record":{"source":{"id":"1805.02727","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-07T20:19:24Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"09398007123f3f70807b38b796399de63e1593b56c4c8a018682cd143bc4ade4","abstract_canon_sha256":"b36ab8a137db2a32fd673366101544c6e02be67479a532c7eaaadb7035bd33f2"},"schema_version":"1.0"},"canonical_sha256":"a40c5606e21340266e668608aa79e89ccf042eb84c104a18c4bbfa1b33426d97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:38.647067Z","signature_b64":"JcVH5XsTwUUhOi8mh4gAe6iuoyiq157RZbgW92Fn7dwEgPvtsHLDRIKlNsIvl6ZBR9XJKlRsvPu3SL1+XeL2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a40c5606e21340266e668608aa79e89ccf042eb84c104a18c4bbfa1b33426d97","last_reissued_at":"2026-05-17T23:50:38.646573Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:38.646573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.02727","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NGPAL5uRrsZMQszMdonOWKNb/iBbGiLHzGJIpzcgeYHnT8321Xe9XzlQl+FgW+hW9YW9xo2nYiUvSkwa2ZSmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T04:58:09.422170Z"},"content_sha256":"8483f8d41730ea7c3a17bf54dfb967afd76c15367c535ef6ec10d2912bcc036c","schema_version":"1.0","event_id":"sha256:8483f8d41730ea7c3a17bf54dfb967afd76c15367c535ef6ec10d2912bcc036c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UQGFMBXCCNACM3TGQYEKU6PITT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dualizing, projecting, and restricting GKZ systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Avi Steiner","submitted_at":"2018-05-07T20:19:24Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02727","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qi23v5+lGlvPZaHKewbD9LXlbK4ImFa6VWIP2eu11WJ3hZVJmSrRXt8wUh9eeNhWcbXsFEOXatwg+iZn04KyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T04:58:09.422905Z"},"content_sha256":"2e64af778115554e59a36990292586857ff35b731df83926c7edccbfacc7962e","schema_version":"1.0","event_id":"sha256:2e64af778115554e59a36990292586857ff35b731df83926c7edccbfacc7962e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UQGFMBXCCNACM3TGQYEKU6PITT/bundle.json","state_url":"https://pith.science/pith/UQGFMBXCCNACM3TGQYEKU6PITT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UQGFMBXCCNACM3TGQYEKU6PITT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T04:58:09Z","links":{"resolver":"https://pith.science/pith/UQGFMBXCCNACM3TGQYEKU6PITT","bundle":"https://pith.science/pith/UQGFMBXCCNACM3TGQYEKU6PITT/bundle.json","state":"https://pith.science/pith/UQGFMBXCCNACM3TGQYEKU6PITT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UQGFMBXCCNACM3TGQYEKU6PITT/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KY7x4ne8y2d8aDzlbDOahX8IergokNfZoQYjlseMbSd/MMku+1jYKuN31s67b4FhJ+3+Ak1TrkHOLzwWk4umCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T04:58:09.427097Z","bundle_sha256":"c82a8dba407868c13efbd124a61d84748fa8ae3928b77ac598e7cfeda044dcee"}}