{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:MWUQXSWYGDI77ATVVNQYQ4F4D6","short_pith_number":"pith:MWUQXSWY","schema_version":"1.0","canonical_sha256":"65a90bcad830d1ff8275ab618870bc1fa5188dfeb24541337466c27800d03799","source":{"kind":"arxiv","id":"1308.2774","version":2},"attestation_state":"computed","paper":{"title":"Non-commutative Toric Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG"],"primary_cat":"math.SG","authors_text":"Alberto Verjovsky, Ernesto Lupercio, Laurent Meersseman, Ludmil Katzarkov","submitted_at":"2013-08-13T07:19:59Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1308.2774","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-08-13T07:19:59Z","cross_cats_sorted":["hep-th","math.AG"],"title_canon_sha256":"6d2684e7c845b01f5351ddd4e18686570774966ed0dd57aade6e6173b8a8a766","abstract_canon_sha256":"029caf026694f0f02034cd5c66e25b319d201b5df073182f98486171680504cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:42.202290Z","signature_b64":"ggTc7Xn8cRft/TU7sXRfk6Uz22TsLox0wpyvgXHj1MxAP+c2btwbfki6hIWspDvERzws1hZ+8qlsg4j6DkUcCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65a90bcad830d1ff8275ab618870bc1fa5188dfeb24541337466c27800d03799","last_reissued_at":"2026-05-18T03:07:42.201679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:42.201679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-commutative Toric Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG"],"primary_cat":"math.SG","authors_text":"Alberto Verjovsky, Ernesto Lupercio, Laurent Meersseman, Ludmil Katzarkov","submitted_at":"2013-08-13T07:19:59Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2774","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1308.2774","created_at":"2026-05-18T03:07:42.201768+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.2774v2","created_at":"2026-05-18T03:07:42.201768+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2774","created_at":"2026-05-18T03:07:42.201768+00:00"},{"alias_kind":"pith_short_12","alias_value":"MWUQXSWYGDI7","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"MWUQXSWYGDI77ATV","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"MWUQXSWY","created_at":"2026-05-18T12:27:52.871228+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MWUQXSWYGDI77ATVVNQYQ4F4D6","json":"https://pith.science/pith/MWUQXSWYGDI77ATVVNQYQ4F4D6.json","graph_json":"https://pith.science/api/pith-number/MWUQXSWYGDI77ATVVNQYQ4F4D6/graph.json","events_json":"https://pith.science/api/pith-number/MWUQXSWYGDI77ATVVNQYQ4F4D6/events.json","paper":"https://pith.science/paper/MWUQXSWY"},"agent_actions":{"view_html":"https://pith.science/pith/MWUQXSWYGDI77ATVVNQYQ4F4D6","download_json":"https://pith.science/pith/MWUQXSWYGDI77ATVVNQYQ4F4D6.json","view_paper":"https://pith.science/paper/MWUQXSWY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.2774&json=true","fetch_graph":"https://pith.science/api/pith-number/MWUQXSWYGDI77ATVVNQYQ4F4D6/graph.json","fetch_events":"https://pith.science/api/pith-number/MWUQXSWYGDI77ATVVNQYQ4F4D6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MWUQXSWYGDI77ATVVNQYQ4F4D6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MWUQXSWYGDI77ATVVNQYQ4F4D6/action/storage_attestation","attest_author":"https://pith.science/pith/MWUQXSWYGDI77ATVVNQYQ4F4D6/action/author_attestation","sign_citation":"https://pith.science/pith/MWUQXSWYGDI77ATVVNQYQ4F4D6/action/citation_signature","submit_replication":"https://pith.science/pith/MWUQXSWYGDI77ATVVNQYQ4F4D6/action/replication_record"}},"created_at":"2026-05-18T03:07:42.201768+00:00","updated_at":"2026-05-18T03:07:42.201768+00:00"}