{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SVKWEO22N3PP24F5YYCN37H4LI","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":"6d69caeb843bf6f4febbf8a217cf5b3d8b1efd9f555265c9481bea2980b849f1","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-05-07T08:58:56Z","title_canon_sha256":"c36003463a1887eff954396589352dd75efc6a4877a9927af9c2fa53614d49d0"},"schema_version":"1.0","source":{"id":"1905.02418","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.02418","created_at":"2026-05-17T23:46:51Z"},{"alias_kind":"arxiv_version","alias_value":"1905.02418v1","created_at":"2026-05-17T23:46:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.02418","created_at":"2026-05-17T23:46:51Z"},{"alias_kind":"pith_short_12","alias_value":"SVKWEO22N3PP","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SVKWEO22N3PP24F5","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SVKWEO22","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:f68770f592288b1961bde3417a425fcd1decb50c1653b2e834f36c4f53a26bc9","target":"graph","created_at":"2026-05-17T23:46:51Z","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":"The goal of this paper is to explicitly describe a minimal binomial generating set of a class of lattice ideals, namely the ideal of certain Veronese $3$-fold projections. More precisely, for any integer $d\\ge 4$ and any $d$-th root $e$ of 1 we denote by $X_d$ the toric variety defined as the image of the morphism $\\varphi _{T_d}:\\mathbb{P}^3 \\longrightarrow \\mathbb{P}^{\\mu (T_d)-1}$ where $T_d$ are all monomials of degree $d$ in $k[x,y,z,t]$ invariant under the action of the diagonal matrix $M(1,e,e^2,e^3).$ In this work, we describe a $\\mathbb{Z}$-basis of the lattice $L_{\\eta }$ associated ","authors_text":"Liena Colarte G\\'omez, Rosa Maria Mir\\'o-Roig","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-05-07T08:58:56Z","title":"Minimal set of binomial generators for certain Veronese 3-fold projections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.02418","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":"sha256:8f0bf004a96f95a146a43b741aa9eee89a77253c1ed79947494a35f4e1b3e51b","target":"record","created_at":"2026-05-17T23:46:51Z","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":"6d69caeb843bf6f4febbf8a217cf5b3d8b1efd9f555265c9481bea2980b849f1","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-05-07T08:58:56Z","title_canon_sha256":"c36003463a1887eff954396589352dd75efc6a4877a9927af9c2fa53614d49d0"},"schema_version":"1.0","source":{"id":"1905.02418","kind":"arxiv","version":1}},"canonical_sha256":"9555623b5a6edefd70bdc604ddfcfc5a22072b1a6ebf9697f2658183191baabc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9555623b5a6edefd70bdc604ddfcfc5a22072b1a6ebf9697f2658183191baabc","first_computed_at":"2026-05-17T23:46:51.534842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:51.534842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VyFoGClVAmCua6NCDH/Ny6D/I4YvjN5Dek5TFNaiydNbT6yM12N3JszG2R7pXz8+COnoZOJj0Hi9h7BFB8ESCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:51.535443Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.02418","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f0bf004a96f95a146a43b741aa9eee89a77253c1ed79947494a35f4e1b3e51b","sha256:f68770f592288b1961bde3417a425fcd1decb50c1653b2e834f36c4f53a26bc9"],"state_sha256":"8ecb461e6e30c5ccb10c09b40e2ae451450e098011795599ad758f3a5f103ebd"}