{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MWUQXSWYGDI77ATVVNQYQ4F4D6","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":"029caf026694f0f02034cd5c66e25b319d201b5df073182f98486171680504cc","cross_cats_sorted":["hep-th","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-08-13T07:19:59Z","title_canon_sha256":"6d2684e7c845b01f5351ddd4e18686570774966ed0dd57aade6e6173b8a8a766"},"schema_version":"1.0","source":{"id":"1308.2774","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2774","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2774v2","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2774","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"pith_short_12","alias_value":"MWUQXSWYGDI7","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MWUQXSWYGDI77ATV","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MWUQXSWY","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:2f268b7b5df5714519def995e7db40cb8f76a1ab18e6e2b4dfb8cd92fc248575","target":"graph","created_at":"2026-05-18T03:07:42Z","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":"In this note we introduce a new family of non-commutative spaces that we call non-commutative toric varieties and we describe some of their main properties. The main technical tool in this investigation is a natural extension of LVM-theory for the irrational case. In order to introduce the moduli space of (non-commutative) toric varieties we use variations on the notion of diffeology as models for non-commutative spaces.","authors_text":"Alberto Verjovsky, Ernesto Lupercio, Laurent Meersseman, Ludmil Katzarkov","cross_cats":["hep-th","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-08-13T07:19:59Z","title":"Non-commutative Toric Varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2774","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:fd36e1207fd6dd2eee498f75fbbeb4bb2f3a3704f40f2d57fbcedbe620ceeb20","target":"record","created_at":"2026-05-18T03:07:42Z","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":"029caf026694f0f02034cd5c66e25b319d201b5df073182f98486171680504cc","cross_cats_sorted":["hep-th","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-08-13T07:19:59Z","title_canon_sha256":"6d2684e7c845b01f5351ddd4e18686570774966ed0dd57aade6e6173b8a8a766"},"schema_version":"1.0","source":{"id":"1308.2774","kind":"arxiv","version":2}},"canonical_sha256":"65a90bcad830d1ff8275ab618870bc1fa5188dfeb24541337466c27800d03799","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65a90bcad830d1ff8275ab618870bc1fa5188dfeb24541337466c27800d03799","first_computed_at":"2026-05-18T03:07:42.201679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:42.201679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ggTc7Xn8cRft/TU7sXRfk6Uz22TsLox0wpyvgXHj1MxAP+c2btwbfki6hIWspDvERzws1hZ+8qlsg4j6DkUcCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:42.202290Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.2774","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd36e1207fd6dd2eee498f75fbbeb4bb2f3a3704f40f2d57fbcedbe620ceeb20","sha256:2f268b7b5df5714519def995e7db40cb8f76a1ab18e6e2b4dfb8cd92fc248575"],"state_sha256":"538c19b462222ebe3498e2220ec123b6240b5e8ce2a224ae707035d7a663d7a7"}