{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YRMMIRG6RO3HINLC6FQYEUQSHA","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":"d989652cecdb3a18a7fd1c5432a4f70e687986083de188adabf33d22d3543a73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-09T14:05:43Z","title_canon_sha256":"0717029e7751fb545a7afab724b2c2a7a5e7ad2422e4198606f69df83fe82a5d"},"schema_version":"1.0","source":{"id":"1110.1840","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1840","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1840v2","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1840","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"pith_short_12","alias_value":"YRMMIRG6RO3H","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YRMMIRG6RO3HINLC","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YRMMIRG6","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:da1bf1133965e38eefb0cffddf97c74321b8d58f5534cffb0c1898304c5aa216","target":"graph","created_at":"2026-05-18T03:35:26Z","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":"We discuss an experimental approach to open problems in toric geometry: are smooth projective toric varieties (i) projectively normal and (ii) defined by degree 2 equations? We discuss the creation of lattice polytopes defining smooth toric varieties as well as algorithms checking properties (i) and (ii) and further potential properties, in Particular a weaker version of (ii) asking for scheme-theoretic definition in degree 2.","authors_text":"Winfried Bruns","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-09T14:05:43Z","title":"The quest for counterexamples in toric geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1840","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":"sha256:809077dcf9a40e309ae634dacd58b145f0899ea82172d9aea1c39876be6ca8bc","target":"record","created_at":"2026-05-18T03:35:26Z","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":"d989652cecdb3a18a7fd1c5432a4f70e687986083de188adabf33d22d3543a73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-09T14:05:43Z","title_canon_sha256":"0717029e7751fb545a7afab724b2c2a7a5e7ad2422e4198606f69df83fe82a5d"},"schema_version":"1.0","source":{"id":"1110.1840","kind":"arxiv","version":2}},"canonical_sha256":"c458c444de8bb6743562f161825212381567878499e0f4b91d5583dba01905d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c458c444de8bb6743562f161825212381567878499e0f4b91d5583dba01905d9","first_computed_at":"2026-05-18T03:35:26.289676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:26.289676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0HPiIYd1vhan0HUPAU4ay0mcT2oTZMEcdKvTuiVAWTQKa5aEw1HYAcZ4mdls632u0cbvicHJDqhDTf6jpIZuCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:26.290414Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1840","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:809077dcf9a40e309ae634dacd58b145f0899ea82172d9aea1c39876be6ca8bc","sha256:da1bf1133965e38eefb0cffddf97c74321b8d58f5534cffb0c1898304c5aa216"],"state_sha256":"b5b92bcf18f8072a7164456c87e6f7c5b7a27bdfb53b9efffffc9a401f795dd2"}