{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:YXLBDTACS4IZRT7GA7CB4MRFLL","short_pith_number":"pith:YXLBDTAC","canonical_record":{"source":{"id":"hep-th/0103023","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2001-03-05T00:53:24Z","cross_cats_sorted":["gr-qc","hep-lat","math.QA"],"title_canon_sha256":"aea11af2de46c3e66b81ef3a65389ba21dcaf269059d8769f99b2608b13270db","abstract_canon_sha256":"a59470c6c1326e4ec1912442e16b57f93a43d435eb886df1b415b64b027d18f1"},"schema_version":"1.0"},"canonical_sha256":"c5d611cc02971198cfe607c41e32255aecfad4cc260c356c5f53f58e2d508ba7","source":{"kind":"arxiv","id":"hep-th/0103023","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0103023","created_at":"2026-07-04T15:23:14Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0103023v2","created_at":"2026-07-04T15:23:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0103023","created_at":"2026-07-04T15:23:14Z"},{"alias_kind":"pith_short_12","alias_value":"YXLBDTACS4IZ","created_at":"2026-07-04T15:23:14Z"},{"alias_kind":"pith_short_16","alias_value":"YXLBDTACS4IZRT7G","created_at":"2026-07-04T15:23:14Z"},{"alias_kind":"pith_short_8","alias_value":"YXLBDTAC","created_at":"2026-07-04T15:23:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:YXLBDTACS4IZRT7GA7CB4MRFLL","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0103023","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2001-03-05T00:53:24Z","cross_cats_sorted":["gr-qc","hep-lat","math.QA"],"title_canon_sha256":"aea11af2de46c3e66b81ef3a65389ba21dcaf269059d8769f99b2608b13270db","abstract_canon_sha256":"a59470c6c1326e4ec1912442e16b57f93a43d435eb886df1b415b64b027d18f1"},"schema_version":"1.0"},"canonical_sha256":"c5d611cc02971198cfe607c41e32255aecfad4cc260c356c5f53f58e2d508ba7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:23:14.149507Z","signature_b64":"2bb1kgxWAk1rnO3qsgT/4dOmSJrzETyxwE5hd7bwfyJBvLlN5lNA6LFB3Ia1i8yLfETjTyZHhnihqQuBjtU8Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5d611cc02971198cfe607c41e32255aecfad4cc260c356c5f53f58e2d508ba7","last_reissued_at":"2026-07-04T15:23:14.149029Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:23:14.149029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0103023","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:23:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dYlrzYQf+OT5RkZ39ODZIVFfLbNcI5YJKzGts4vWPgJIKM6WhkPJ+1PPsL5fVF54FAUUUmpgBgCJ+gasu3lHDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T20:43:00.944219Z"},"content_sha256":"e8007c24356d73e3bf22f58fc2495d3db5dd66e50ddef4e6f76bf2f56c93c07b","schema_version":"1.0","event_id":"sha256:e8007c24356d73e3bf22f58fc2495d3db5dd66e50ddef4e6f76bf2f56c93c07b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:YXLBDTACS4IZRT7GA7CB4MRFLL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fuzzy CP2","license":"","headline":"","cross_cats":["gr-qc","hep-lat","math.QA"],"primary_cat":"hep-th","authors_text":"A.P.Balachandran, B.Ydri, G.Alexanian, G.Immirzi","submitted_at":"2001-03-05T00:53:24Z","abstract_excerpt":"Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold''. Such discretization by quantization is remarkably successful in preserving symmetries and topological features, and altogether overcoming the fermion-doubling problem. In this paper, we report on our work on the ``fuzzification'' of the four-dimensional CP2 and its QFT's. CP2 is not spin, but spin${}_c$. Its Dirac operator has many unique features. They are explained and their fuzzy ve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0103023","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/0103023/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":"2026-07-04T15:23:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mhB+BPX7/6sxUcbutCXXMqcOeRSZA25FWmrJojQbVSF2vfHUuOmlH55UiSVOgQSC6T8xjAnSzkX9Y6HEEbQgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T20:43:00.945073Z"},"content_sha256":"5db523d6c3dd2b2e786da4a789d7976803c9c65090b7797f1ce5d13f828d4594","schema_version":"1.0","event_id":"sha256:5db523d6c3dd2b2e786da4a789d7976803c9c65090b7797f1ce5d13f828d4594"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YXLBDTACS4IZRT7GA7CB4MRFLL/bundle.json","state_url":"https://pith.science/pith/YXLBDTACS4IZRT7GA7CB4MRFLL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YXLBDTACS4IZRT7GA7CB4MRFLL/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":"2026-08-11T20:43:00Z","links":{"resolver":"https://pith.science/pith/YXLBDTACS4IZRT7GA7CB4MRFLL","bundle":"https://pith.science/pith/YXLBDTACS4IZRT7GA7CB4MRFLL/bundle.json","state":"https://pith.science/pith/YXLBDTACS4IZRT7GA7CB4MRFLL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YXLBDTACS4IZRT7GA7CB4MRFLL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:YXLBDTACS4IZRT7GA7CB4MRFLL","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":"a59470c6c1326e4ec1912442e16b57f93a43d435eb886df1b415b64b027d18f1","cross_cats_sorted":["gr-qc","hep-lat","math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"2001-03-05T00:53:24Z","title_canon_sha256":"aea11af2de46c3e66b81ef3a65389ba21dcaf269059d8769f99b2608b13270db"},"schema_version":"1.0","source":{"id":"hep-th/0103023","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0103023","created_at":"2026-07-04T15:23:14Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0103023v2","created_at":"2026-07-04T15:23:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0103023","created_at":"2026-07-04T15:23:14Z"},{"alias_kind":"pith_short_12","alias_value":"YXLBDTACS4IZ","created_at":"2026-07-04T15:23:14Z"},{"alias_kind":"pith_short_16","alias_value":"YXLBDTACS4IZRT7G","created_at":"2026-07-04T15:23:14Z"},{"alias_kind":"pith_short_8","alias_value":"YXLBDTAC","created_at":"2026-07-04T15:23:14Z"}],"graph_snapshots":[{"event_id":"sha256:5db523d6c3dd2b2e786da4a789d7976803c9c65090b7797f1ce5d13f828d4594","target":"graph","created_at":"2026-07-04T15:23:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-th/0103023/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold''. Such discretization by quantization is remarkably successful in preserving symmetries and topological features, and altogether overcoming the fermion-doubling problem. In this paper, we report on our work on the ``fuzzification'' of the four-dimensional CP2 and its QFT's. CP2 is not spin, but spin${}_c$. Its Dirac operator has many unique features. They are explained and their fuzzy ve","authors_text":"A.P.Balachandran, B.Ydri, G.Alexanian, G.Immirzi","cross_cats":["gr-qc","hep-lat","math.QA"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2001-03-05T00:53:24Z","title":"Fuzzy CP2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0103023","kind":"arxiv","version":2},"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:e8007c24356d73e3bf22f58fc2495d3db5dd66e50ddef4e6f76bf2f56c93c07b","target":"record","created_at":"2026-07-04T15:23:14Z","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":"a59470c6c1326e4ec1912442e16b57f93a43d435eb886df1b415b64b027d18f1","cross_cats_sorted":["gr-qc","hep-lat","math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"2001-03-05T00:53:24Z","title_canon_sha256":"aea11af2de46c3e66b81ef3a65389ba21dcaf269059d8769f99b2608b13270db"},"schema_version":"1.0","source":{"id":"hep-th/0103023","kind":"arxiv","version":2}},"canonical_sha256":"c5d611cc02971198cfe607c41e32255aecfad4cc260c356c5f53f58e2d508ba7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5d611cc02971198cfe607c41e32255aecfad4cc260c356c5f53f58e2d508ba7","first_computed_at":"2026-07-04T15:23:14.149029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:23:14.149029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2bb1kgxWAk1rnO3qsgT/4dOmSJrzETyxwE5hd7bwfyJBvLlN5lNA6LFB3Ia1i8yLfETjTyZHhnihqQuBjtU8Dw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:23:14.149507Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0103023","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8007c24356d73e3bf22f58fc2495d3db5dd66e50ddef4e6f76bf2f56c93c07b","sha256:5db523d6c3dd2b2e786da4a789d7976803c9c65090b7797f1ce5d13f828d4594"],"state_sha256":"02c1db8517fbe6b51bf247b9248c3859f7df0a7196024dcb237835002d034a75"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ASbbof+mMj8MNRG6heeMpDLYY4PToVKDP10dLPdgJ77B075Ds7Ik5LSlE4zP2l9yhif3YfRkVpfGb2IEilu3BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T20:43:00.950520Z","bundle_sha256":"73c932c0cb88afaf599b0c153b66270e859378c7a60e8b672b162948883ab289"}}