{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:WKXIVAZXARK46SVISBAMP36F2F","short_pith_number":"pith:WKXIVAZX","canonical_record":{"source":{"id":"hep-th/9912130","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1999-12-15T15:13:13Z","cross_cats_sorted":["cond-mat","gr-qc","hep-lat","math-ph","math.MP","math.QA"],"title_canon_sha256":"7da0c9b563b23bc82acb311392f1aec07ffd8eea578d2f5e156a24c7acb9ba02","abstract_canon_sha256":"bbdd49cec793d9b31f66d8a1830077af31a99d71f033c80f256e582ec79085a6"},"schema_version":"1.0"},"canonical_sha256":"b2ae8a83370455cf4aa89040c7efc5d15db04a4f96e35d57dfc7afb73160c99b","source":{"kind":"arxiv","id":"hep-th/9912130","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9912130","created_at":"2026-07-04T16:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9912130v1","created_at":"2026-07-04T16:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9912130","created_at":"2026-07-04T16:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"WKXIVAZXARK4","created_at":"2026-07-04T16:15:05Z"},{"alias_kind":"pith_short_16","alias_value":"WKXIVAZXARK46SVI","created_at":"2026-07-04T16:15:05Z"},{"alias_kind":"pith_short_8","alias_value":"WKXIVAZX","created_at":"2026-07-04T16:15:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:WKXIVAZXARK46SVISBAMP36F2F","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9912130","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1999-12-15T15:13:13Z","cross_cats_sorted":["cond-mat","gr-qc","hep-lat","math-ph","math.MP","math.QA"],"title_canon_sha256":"7da0c9b563b23bc82acb311392f1aec07ffd8eea578d2f5e156a24c7acb9ba02","abstract_canon_sha256":"bbdd49cec793d9b31f66d8a1830077af31a99d71f033c80f256e582ec79085a6"},"schema_version":"1.0"},"canonical_sha256":"b2ae8a83370455cf4aa89040c7efc5d15db04a4f96e35d57dfc7afb73160c99b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:15:05.201379Z","signature_b64":"eU31lFGe+2JqcQ0Lq/DKHD5KCWnlI9y2LZiMkYqdz2E48YZRvG2Nsg8HrLF+mrqgf78pOnlH2ljZ/+gYQfOOBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2ae8a83370455cf4aa89040c7efc5d15db04a4f96e35d57dfc7afb73160c99b","last_reissued_at":"2026-07-04T16:15:05.200983Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:15:05.200983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9912130","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:15:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"caaL6BSRaOGYwwh8CnjlqKxc2SKs0zA12Q7DSmbbMCeIrkS4LV9IMY3H8siL0D+orE+SHtiOLHTWlRjAZgmRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T09:18:46.391930Z"},"content_sha256":"4b43c1a43b525ff25264a0a3c99546727a60172f9404b6be4b41a9311933e983","schema_version":"1.0","event_id":"sha256:4b43c1a43b525ff25264a0a3c99546727a60172f9404b6be4b41a9311933e983"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:WKXIVAZXARK46SVISBAMP36F2F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From Large N Matrices to the Noncommutative Torus","license":"","headline":"","cross_cats":["cond-mat","gr-qc","hep-lat","math-ph","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"F. Lizzi, G. Landi, R.J. Szabo","submitted_at":"1999-12-15T15:13:13Z","abstract_excerpt":"We describe how and to what extent the noncommutative two-torus can be approximated by a tower of finite-dimensional matrix geometries. The approximation is carried out for both irrational and rational deformation parameters by embedding the algebra of the noncommutative torus into an approximately finite algebra. The construction is a rigorous derivation of the recent discretizations of noncommutative gauge theories using finite dimensional matrix models, and it shows precisely how the continuum limits of these models must be taken. We clarify various aspects of Morita equivalence using this "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9912130","kind":"arxiv","version":1},"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/hep-th/9912130/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:15:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NIypi5phdVtx2mVJrXiI9d0FBlhFCO22Xqy41H5fhP/haWG8/M6aChywuMOmpEGT1twz/7QsFgPF5jDHur6VCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T09:18:46.392948Z"},"content_sha256":"32953b2463930c685dcfd0857a34cec5c339a24fd64fbf78f337fab1cd562705","schema_version":"1.0","event_id":"sha256:32953b2463930c685dcfd0857a34cec5c339a24fd64fbf78f337fab1cd562705"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WKXIVAZXARK46SVISBAMP36F2F/bundle.json","state_url":"https://pith.science/pith/WKXIVAZXARK46SVISBAMP36F2F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WKXIVAZXARK46SVISBAMP36F2F/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-15T09:18:46Z","links":{"resolver":"https://pith.science/pith/WKXIVAZXARK46SVISBAMP36F2F","bundle":"https://pith.science/pith/WKXIVAZXARK46SVISBAMP36F2F/bundle.json","state":"https://pith.science/pith/WKXIVAZXARK46SVISBAMP36F2F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WKXIVAZXARK46SVISBAMP36F2F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:WKXIVAZXARK46SVISBAMP36F2F","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":"bbdd49cec793d9b31f66d8a1830077af31a99d71f033c80f256e582ec79085a6","cross_cats_sorted":["cond-mat","gr-qc","hep-lat","math-ph","math.MP","math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"1999-12-15T15:13:13Z","title_canon_sha256":"7da0c9b563b23bc82acb311392f1aec07ffd8eea578d2f5e156a24c7acb9ba02"},"schema_version":"1.0","source":{"id":"hep-th/9912130","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9912130","created_at":"2026-07-04T16:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9912130v1","created_at":"2026-07-04T16:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9912130","created_at":"2026-07-04T16:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"WKXIVAZXARK4","created_at":"2026-07-04T16:15:05Z"},{"alias_kind":"pith_short_16","alias_value":"WKXIVAZXARK46SVI","created_at":"2026-07-04T16:15:05Z"},{"alias_kind":"pith_short_8","alias_value":"WKXIVAZX","created_at":"2026-07-04T16:15:05Z"}],"graph_snapshots":[{"event_id":"sha256:32953b2463930c685dcfd0857a34cec5c339a24fd64fbf78f337fab1cd562705","target":"graph","created_at":"2026-07-04T16:15:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-th/9912130/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We describe how and to what extent the noncommutative two-torus can be approximated by a tower of finite-dimensional matrix geometries. The approximation is carried out for both irrational and rational deformation parameters by embedding the algebra of the noncommutative torus into an approximately finite algebra. The construction is a rigorous derivation of the recent discretizations of noncommutative gauge theories using finite dimensional matrix models, and it shows precisely how the continuum limits of these models must be taken. We clarify various aspects of Morita equivalence using this ","authors_text":"F. Lizzi, G. Landi, R.J. Szabo","cross_cats":["cond-mat","gr-qc","hep-lat","math-ph","math.MP","math.QA"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1999-12-15T15:13:13Z","title":"From Large N Matrices to the Noncommutative Torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9912130","kind":"arxiv","version":1},"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":"sha256:4b43c1a43b525ff25264a0a3c99546727a60172f9404b6be4b41a9311933e983","target":"record","created_at":"2026-07-04T16:15:05Z","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":"bbdd49cec793d9b31f66d8a1830077af31a99d71f033c80f256e582ec79085a6","cross_cats_sorted":["cond-mat","gr-qc","hep-lat","math-ph","math.MP","math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"1999-12-15T15:13:13Z","title_canon_sha256":"7da0c9b563b23bc82acb311392f1aec07ffd8eea578d2f5e156a24c7acb9ba02"},"schema_version":"1.0","source":{"id":"hep-th/9912130","kind":"arxiv","version":1}},"canonical_sha256":"b2ae8a83370455cf4aa89040c7efc5d15db04a4f96e35d57dfc7afb73160c99b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2ae8a83370455cf4aa89040c7efc5d15db04a4f96e35d57dfc7afb73160c99b","first_computed_at":"2026-07-04T16:15:05.200983Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:15:05.200983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eU31lFGe+2JqcQ0Lq/DKHD5KCWnlI9y2LZiMkYqdz2E48YZRvG2Nsg8HrLF+mrqgf78pOnlH2ljZ/+gYQfOOBA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:15:05.201379Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9912130","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b43c1a43b525ff25264a0a3c99546727a60172f9404b6be4b41a9311933e983","sha256:32953b2463930c685dcfd0857a34cec5c339a24fd64fbf78f337fab1cd562705"],"state_sha256":"6af3b5eb6d58c1bfeab80d5028806b35fb11e91b8975c5113959522efb5bc6cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FcQJklXLBPET1hjA6N0xkLtaC84MzD0qGN/9GDkfYTj8FG4ts2E/4a3Qn3K8gwPlQhdsffztZSikQ9vYX5W/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T09:18:46.398909Z","bundle_sha256":"2098f602399a933f1109934667b1cd7a65c0917dd96f31654eea8b2f8271b6e5"}}