{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:TFKCRA7RQ645GYNIIGYFJ3VZFF","short_pith_number":"pith:TFKCRA7R","schema_version":"1.0","canonical_sha256":"99542883f187b9d361a841b054eeb929609c4e27eb5f2b43b6a204ffaf1335e2","source":{"kind":"arxiv","id":"1505.00964","version":2},"attestation_state":"computed","paper":{"title":"Modular curvature and Morita equivalence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.OA"],"primary_cat":"math.QA","authors_text":"Henri Moscovici, Matthias Lesch","submitted_at":"2015-05-05T11:39:10Z","abstract_excerpt":"The curvature of the noncommutative torus $T^2_\\theta$ ($\\theta$ irrational) endowed with a noncommutative conformal metric has been the focus of attention of several recent works. Continuing the approach taken in the paper [A. Connes and H. Moscovici, http://arxiv.org/abs/1110.3500] we extend the study of the curvature to twisted Dirac spectral triples constructed out of Heisenberg bimodules that implement the Morita equivalence of the $C^*$-algebra $A_\\theta = C(T^2_\\theta)$ with other toric algebras $A_{\\theta'}$. In the enlarged context the conformal metric on $T^2_\\theta$ is exchanged wit"},"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":"1505.00964","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-05-05T11:39:10Z","cross_cats_sorted":["math.DG","math.OA"],"title_canon_sha256":"f2a597cbe5af854b1ebca35bd79671929985075d0d235373f141cafc5b576bc0","abstract_canon_sha256":"3f704faa2d7a60ae1950ce057b588bf290c532c9c0ee06ce3a6ac7db294d86bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:04.901539Z","signature_b64":"coH+d/GOBtKxiODjvt4+hhRI/acObzJtHpDMMh1dovAgmbLv8KpivOBEma8sa25mFdzajKzeH0q8+279nsDlCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99542883f187b9d361a841b054eeb929609c4e27eb5f2b43b6a204ffaf1335e2","last_reissued_at":"2026-05-18T00:49:04.901086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:04.901086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modular curvature and Morita equivalence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.OA"],"primary_cat":"math.QA","authors_text":"Henri Moscovici, Matthias Lesch","submitted_at":"2015-05-05T11:39:10Z","abstract_excerpt":"The curvature of the noncommutative torus $T^2_\\theta$ ($\\theta$ irrational) endowed with a noncommutative conformal metric has been the focus of attention of several recent works. Continuing the approach taken in the paper [A. Connes and H. Moscovici, http://arxiv.org/abs/1110.3500] we extend the study of the curvature to twisted Dirac spectral triples constructed out of Heisenberg bimodules that implement the Morita equivalence of the $C^*$-algebra $A_\\theta = C(T^2_\\theta)$ with other toric algebras $A_{\\theta'}$. In the enlarged context the conformal metric on $T^2_\\theta$ is exchanged wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00964","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":"1505.00964","created_at":"2026-05-18T00:49:04.901147+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.00964v2","created_at":"2026-05-18T00:49:04.901147+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00964","created_at":"2026-05-18T00:49:04.901147+00:00"},{"alias_kind":"pith_short_12","alias_value":"TFKCRA7RQ645","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"TFKCRA7RQ645GYNI","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"TFKCRA7R","created_at":"2026-05-18T12:29:42.218222+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/TFKCRA7RQ645GYNIIGYFJ3VZFF","json":"https://pith.science/pith/TFKCRA7RQ645GYNIIGYFJ3VZFF.json","graph_json":"https://pith.science/api/pith-number/TFKCRA7RQ645GYNIIGYFJ3VZFF/graph.json","events_json":"https://pith.science/api/pith-number/TFKCRA7RQ645GYNIIGYFJ3VZFF/events.json","paper":"https://pith.science/paper/TFKCRA7R"},"agent_actions":{"view_html":"https://pith.science/pith/TFKCRA7RQ645GYNIIGYFJ3VZFF","download_json":"https://pith.science/pith/TFKCRA7RQ645GYNIIGYFJ3VZFF.json","view_paper":"https://pith.science/paper/TFKCRA7R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.00964&json=true","fetch_graph":"https://pith.science/api/pith-number/TFKCRA7RQ645GYNIIGYFJ3VZFF/graph.json","fetch_events":"https://pith.science/api/pith-number/TFKCRA7RQ645GYNIIGYFJ3VZFF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TFKCRA7RQ645GYNIIGYFJ3VZFF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TFKCRA7RQ645GYNIIGYFJ3VZFF/action/storage_attestation","attest_author":"https://pith.science/pith/TFKCRA7RQ645GYNIIGYFJ3VZFF/action/author_attestation","sign_citation":"https://pith.science/pith/TFKCRA7RQ645GYNIIGYFJ3VZFF/action/citation_signature","submit_replication":"https://pith.science/pith/TFKCRA7RQ645GYNIIGYFJ3VZFF/action/replication_record"}},"created_at":"2026-05-18T00:49:04.901147+00:00","updated_at":"2026-05-18T00:49:04.901147+00:00"}