{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KBASI7AA7UGCV7OQQ6T3TOF7W7","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":"c48c5fe892802e93ff8f61e9f4c566ae8be7f7b5cff3e760cf34a4cf63c7bde2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"hep-th","submitted_at":"2013-05-31T16:26:15Z","title_canon_sha256":"dd50d266a478c015273b9934ca4e959e59c8299cc356684ef14ca22cb6f74efb"},"schema_version":"1.0","source":{"id":"1305.7479","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.7479","created_at":"2026-05-18T03:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"1305.7479v3","created_at":"2026-05-18T03:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.7479","created_at":"2026-05-18T03:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"KBASI7AA7UGC","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KBASI7AA7UGCV7OQ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KBASI7AA","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:c5cd2e20633b09968f73fca8fbd073cefbd931565b9f74ce3a52c14766c32825","target":"graph","created_at":"2026-05-18T03:10:14Z","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 consider a generalization of the basic fuzzy torus to a fuzzy torus with non-trivial modular parameter, based on a finite matrix algebra. We discuss the modular properties of this fuzzy torus, and compute the matrix Laplacian for a scalar field. In the semi-classical limit, the generalized fuzzy torus can be used to approximate a generic commutative torus represented by two generic vectors in the complex plane, with generic modular parameter $\\tau$. The effective classical geometry and the spectrum of the Laplacian are correctly reproduced in the limit. The spectrum of a matrix Dirac operat","authors_text":"Harold Steinacker, Paul Schreivogl","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"hep-th","submitted_at":"2013-05-31T16:26:15Z","title":"Generalized Fuzzy Torus and its Modular Properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7479","kind":"arxiv","version":3},"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:ee9fd1f9effa0c40615219fd419401a68f2d5385e9a1dd3703cd1942d3700069","target":"record","created_at":"2026-05-18T03:10:14Z","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":"c48c5fe892802e93ff8f61e9f4c566ae8be7f7b5cff3e760cf34a4cf63c7bde2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"hep-th","submitted_at":"2013-05-31T16:26:15Z","title_canon_sha256":"dd50d266a478c015273b9934ca4e959e59c8299cc356684ef14ca22cb6f74efb"},"schema_version":"1.0","source":{"id":"1305.7479","kind":"arxiv","version":3}},"canonical_sha256":"5041247c00fd0c2afdd087a7b9b8bfb7dda8a9acf9270484f3b8c1f3a0a66c43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5041247c00fd0c2afdd087a7b9b8bfb7dda8a9acf9270484f3b8c1f3a0a66c43","first_computed_at":"2026-05-18T03:10:14.250657Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:14.250657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6ICufzE3KTERG6bv8TX4aqA18s0EhNoMShuurIbOFOBXE2g6cP5r9Gjbi7daNEi6Ng4nn6a0ckDMG/VOVrjxBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:14.251171Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.7479","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee9fd1f9effa0c40615219fd419401a68f2d5385e9a1dd3703cd1942d3700069","sha256:c5cd2e20633b09968f73fca8fbd073cefbd931565b9f74ce3a52c14766c32825"],"state_sha256":"6a883266281acf8c83cdf43b517b31cde7a2566f6616eedc0b55a7b19d6d1850"}