{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:EREFWCZPMWXWPHWHWEVMSLQHWG","short_pith_number":"pith:EREFWCZP","schema_version":"1.0","canonical_sha256":"24485b0b2f65af679ec7b12ac92e07b1a3ee6c1ba39180cbf344865ea234b9ee","source":{"kind":"arxiv","id":"2108.01136","version":3},"attestation_state":"computed","paper":{"title":"Dirac operators for matrix algebras converging to coadjoint orbits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","quant-ph"],"primary_cat":"math.OA","authors_text":"Marc A. Rieffel","submitted_at":"2021-08-02T19:35:22Z","abstract_excerpt":"In the high-energy physics literature one finds statements such as ``matrix algebras converge to the sphere''. Earlier I provided a general precise setting for understanding such statements, in which the matrix algebras are viewed as quantum metric spaces, and convergence is with respect to a quantum Gromov-Hausdorff-type distance.\n  But physicists want even more to treat structures on spheres (and other spaces), such as vector bundles, Yang-Mills functionals, Dirac operators, etc., and they want to approximate these by corresponding structures on matrix algebras. In the present paper we provi"},"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":"2108.01136","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2021-08-02T19:35:22Z","cross_cats_sorted":["hep-th","math-ph","math.MP","quant-ph"],"title_canon_sha256":"a38faa0ba39af2be762cf16ab2aa58c160bdca1fd59ba1ea7e4a164ae2f786f5","abstract_canon_sha256":"c9ee6e0153e3e43c491d55f806b5bd4c0f08797ba7f712985aead1122ff237dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:34:16.224660Z","signature_b64":"lvxNFG0YsRJMJlu0JWHDjrtfo6zxU2pyBBTEQYY/tvtvrKJGeLWJYymsJBm9WbB/gxuqEHdNIHk29OuIts63Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24485b0b2f65af679ec7b12ac92e07b1a3ee6c1ba39180cbf344865ea234b9ee","last_reissued_at":"2026-07-05T06:34:16.224263Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:34:16.224263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dirac operators for matrix algebras converging to coadjoint orbits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","quant-ph"],"primary_cat":"math.OA","authors_text":"Marc A. Rieffel","submitted_at":"2021-08-02T19:35:22Z","abstract_excerpt":"In the high-energy physics literature one finds statements such as ``matrix algebras converge to the sphere''. Earlier I provided a general precise setting for understanding such statements, in which the matrix algebras are viewed as quantum metric spaces, and convergence is with respect to a quantum Gromov-Hausdorff-type distance.\n  But physicists want even more to treat structures on spheres (and other spaces), such as vector bundles, Yang-Mills functionals, Dirac operators, etc., and they want to approximate these by corresponding structures on matrix algebras. In the present paper we provi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.01136","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.01136/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2108.01136","created_at":"2026-07-05T06:34:16.224327+00:00"},{"alias_kind":"arxiv_version","alias_value":"2108.01136v3","created_at":"2026-07-05T06:34:16.224327+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.01136","created_at":"2026-07-05T06:34:16.224327+00:00"},{"alias_kind":"pith_short_12","alias_value":"EREFWCZPMWXW","created_at":"2026-07-05T06:34:16.224327+00:00"},{"alias_kind":"pith_short_16","alias_value":"EREFWCZPMWXWPHWH","created_at":"2026-07-05T06:34:16.224327+00:00"},{"alias_kind":"pith_short_8","alias_value":"EREFWCZP","created_at":"2026-07-05T06:34:16.224327+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.04717","citing_title":"Quantization of Algebraic Varieties Defined by Casimir Polynomials via Matrix Regularization: Fuzzy $S^7$ and Beyond","ref_index":67,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EREFWCZPMWXWPHWHWEVMSLQHWG","json":"https://pith.science/pith/EREFWCZPMWXWPHWHWEVMSLQHWG.json","graph_json":"https://pith.science/api/pith-number/EREFWCZPMWXWPHWHWEVMSLQHWG/graph.json","events_json":"https://pith.science/api/pith-number/EREFWCZPMWXWPHWHWEVMSLQHWG/events.json","paper":"https://pith.science/paper/EREFWCZP"},"agent_actions":{"view_html":"https://pith.science/pith/EREFWCZPMWXWPHWHWEVMSLQHWG","download_json":"https://pith.science/pith/EREFWCZPMWXWPHWHWEVMSLQHWG.json","view_paper":"https://pith.science/paper/EREFWCZP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2108.01136&json=true","fetch_graph":"https://pith.science/api/pith-number/EREFWCZPMWXWPHWHWEVMSLQHWG/graph.json","fetch_events":"https://pith.science/api/pith-number/EREFWCZPMWXWPHWHWEVMSLQHWG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EREFWCZPMWXWPHWHWEVMSLQHWG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EREFWCZPMWXWPHWHWEVMSLQHWG/action/storage_attestation","attest_author":"https://pith.science/pith/EREFWCZPMWXWPHWHWEVMSLQHWG/action/author_attestation","sign_citation":"https://pith.science/pith/EREFWCZPMWXWPHWHWEVMSLQHWG/action/citation_signature","submit_replication":"https://pith.science/pith/EREFWCZPMWXWPHWHWEVMSLQHWG/action/replication_record"}},"created_at":"2026-07-05T06:34:16.224327+00:00","updated_at":"2026-07-05T06:34:16.224327+00:00"}