{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:QHBR5OEKA2HO7TYAO543M6ZTSA","short_pith_number":"pith:QHBR5OEK","canonical_record":{"source":{"id":"hep-th/0310026","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2003-10-03T16:48:33Z","cross_cats_sorted":["gr-qc","math.QA"],"title_canon_sha256":"a8398887bf153d2188c0a87ad24294a2da9f661ac0f3c941f0292940db12b62e","abstract_canon_sha256":"01d42bb2177de948886ea497a9e4616c696259b1838851d1f4d4e5d9b2e24217"},"schema_version":"1.0"},"canonical_sha256":"81c31eb88a068eefcf007779b67b33901beab9c00dbcce857879628558ce4962","source":{"kind":"arxiv","id":"hep-th/0310026","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0310026","created_at":"2026-07-04T16:41:24Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0310026v4","created_at":"2026-07-04T16:41:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0310026","created_at":"2026-07-04T16:41:24Z"},{"alias_kind":"pith_short_12","alias_value":"QHBR5OEKA2HO","created_at":"2026-07-04T16:41:24Z"},{"alias_kind":"pith_short_16","alias_value":"QHBR5OEKA2HO7TYA","created_at":"2026-07-04T16:41:24Z"},{"alias_kind":"pith_short_8","alias_value":"QHBR5OEK","created_at":"2026-07-04T16:41:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:QHBR5OEKA2HO7TYAO543M6ZTSA","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0310026","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2003-10-03T16:48:33Z","cross_cats_sorted":["gr-qc","math.QA"],"title_canon_sha256":"a8398887bf153d2188c0a87ad24294a2da9f661ac0f3c941f0292940db12b62e","abstract_canon_sha256":"01d42bb2177de948886ea497a9e4616c696259b1838851d1f4d4e5d9b2e24217"},"schema_version":"1.0"},"canonical_sha256":"81c31eb88a068eefcf007779b67b33901beab9c00dbcce857879628558ce4962","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:41:24.867639Z","signature_b64":"BekjkVGRhUOvK8T+0U3PN+q2MYGUkT0ZUnzF8MbACQgvx5sze0+zalRQTh/9xrQh8tbgGraNbt0AODIpTinVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81c31eb88a068eefcf007779b67b33901beab9c00dbcce857879628558ce4962","last_reissued_at":"2026-07-04T16:41:24.867214Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:41:24.867214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0310026","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:41:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xbajGzc9eVzLvddQsoE4gIj60CN3me1FDjJD+tuMOj1OT+BYWaJaYHEDHREVpzlhb12Yi/i5sEIU54C6ZdUMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T12:23:02.453879Z"},"content_sha256":"bb4bd2b93dd63438a92d1bb6e75c5550a34fe4e5bdca4f0862947c6dde8af5cc","schema_version":"1.0","event_id":"sha256:bb4bd2b93dd63438a92d1bb6e75c5550a34fe4e5bdca4f0862947c6dde8af5cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:QHBR5OEKA2HO7TYAO543M6ZTSA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topology Change for Fuzzy Physics: Fuzzy Spaces as Hopf Algebras","license":"","headline":"","cross_cats":["gr-qc","math.QA"],"primary_cat":"hep-th","authors_text":"A. P. Balachandran, S. Kurkcuoglu","submitted_at":"2003-10-03T16:48:33Z","abstract_excerpt":"Fuzzy spaces are obtained by quantizing adjoint orbits of compact semi-simple Lie groups. Fuzzy spheres emerge from quantizing S^2 and are associated with the group SU(2) in this manner. They are useful for regularizing quantum field theories and modeling spacetimes by non-commutative manifolds. We show that fuzzy spaces are Hopf algebras and in fact have more structure than the latter. They are thus candidates for quantum symmetries. Using their generalized Hopf algebraic structures, we can also model processes where one fuzzy space splits into several fuzzy spaces. For example we can discuss"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0310026","kind":"arxiv","version":4},"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/0310026/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":"2026-07-04T16:41:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LWThoY6IbH8PavanSHde4qnsEHPWTTULcmb8S0BGJL8EkygJq663iuxTRkuwEKNJ4BrdLE68m3LplxSfrFZAAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T12:23:02.454416Z"},"content_sha256":"b0210c5de3f12bac875f7cbd9c1ad84ab74ba6743a3adbea0b36f48c1688a614","schema_version":"1.0","event_id":"sha256:b0210c5de3f12bac875f7cbd9c1ad84ab74ba6743a3adbea0b36f48c1688a614"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QHBR5OEKA2HO7TYAO543M6ZTSA/bundle.json","state_url":"https://pith.science/pith/QHBR5OEKA2HO7TYAO543M6ZTSA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QHBR5OEKA2HO7TYAO543M6ZTSA/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":"2026-08-04T12:23:02Z","links":{"resolver":"https://pith.science/pith/QHBR5OEKA2HO7TYAO543M6ZTSA","bundle":"https://pith.science/pith/QHBR5OEKA2HO7TYAO543M6ZTSA/bundle.json","state":"https://pith.science/pith/QHBR5OEKA2HO7TYAO543M6ZTSA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QHBR5OEKA2HO7TYAO543M6ZTSA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:QHBR5OEKA2HO7TYAO543M6ZTSA","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":"01d42bb2177de948886ea497a9e4616c696259b1838851d1f4d4e5d9b2e24217","cross_cats_sorted":["gr-qc","math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"2003-10-03T16:48:33Z","title_canon_sha256":"a8398887bf153d2188c0a87ad24294a2da9f661ac0f3c941f0292940db12b62e"},"schema_version":"1.0","source":{"id":"hep-th/0310026","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0310026","created_at":"2026-07-04T16:41:24Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0310026v4","created_at":"2026-07-04T16:41:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0310026","created_at":"2026-07-04T16:41:24Z"},{"alias_kind":"pith_short_12","alias_value":"QHBR5OEKA2HO","created_at":"2026-07-04T16:41:24Z"},{"alias_kind":"pith_short_16","alias_value":"QHBR5OEKA2HO7TYA","created_at":"2026-07-04T16:41:24Z"},{"alias_kind":"pith_short_8","alias_value":"QHBR5OEK","created_at":"2026-07-04T16:41:24Z"}],"graph_snapshots":[{"event_id":"sha256:b0210c5de3f12bac875f7cbd9c1ad84ab74ba6743a3adbea0b36f48c1688a614","target":"graph","created_at":"2026-07-04T16:41:24Z","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/0310026/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Fuzzy spaces are obtained by quantizing adjoint orbits of compact semi-simple Lie groups. Fuzzy spheres emerge from quantizing S^2 and are associated with the group SU(2) in this manner. They are useful for regularizing quantum field theories and modeling spacetimes by non-commutative manifolds. We show that fuzzy spaces are Hopf algebras and in fact have more structure than the latter. They are thus candidates for quantum symmetries. Using their generalized Hopf algebraic structures, we can also model processes where one fuzzy space splits into several fuzzy spaces. For example we can discuss","authors_text":"A. P. Balachandran, S. Kurkcuoglu","cross_cats":["gr-qc","math.QA"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2003-10-03T16:48:33Z","title":"Topology Change for Fuzzy Physics: Fuzzy Spaces as Hopf Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0310026","kind":"arxiv","version":4},"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:bb4bd2b93dd63438a92d1bb6e75c5550a34fe4e5bdca4f0862947c6dde8af5cc","target":"record","created_at":"2026-07-04T16:41:24Z","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":"01d42bb2177de948886ea497a9e4616c696259b1838851d1f4d4e5d9b2e24217","cross_cats_sorted":["gr-qc","math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"2003-10-03T16:48:33Z","title_canon_sha256":"a8398887bf153d2188c0a87ad24294a2da9f661ac0f3c941f0292940db12b62e"},"schema_version":"1.0","source":{"id":"hep-th/0310026","kind":"arxiv","version":4}},"canonical_sha256":"81c31eb88a068eefcf007779b67b33901beab9c00dbcce857879628558ce4962","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81c31eb88a068eefcf007779b67b33901beab9c00dbcce857879628558ce4962","first_computed_at":"2026-07-04T16:41:24.867214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:41:24.867214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BekjkVGRhUOvK8T+0U3PN+q2MYGUkT0ZUnzF8MbACQgvx5sze0+zalRQTh/9xrQh8tbgGraNbt0AODIpTinVCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:41:24.867639Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0310026","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb4bd2b93dd63438a92d1bb6e75c5550a34fe4e5bdca4f0862947c6dde8af5cc","sha256:b0210c5de3f12bac875f7cbd9c1ad84ab74ba6743a3adbea0b36f48c1688a614"],"state_sha256":"6893ff25e6adcba46add3d130bb81b6bd2f95f84adccd5a152be8e21b2c5d092"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z8eq4KbGR1AtiY8aXIjVjA8o1HRkOJDzmjTNrJgrpCGmbbXbLDQ1zNhwdcoKS43Y71Tb6Slipj3VtdqGTvjiBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T12:23:02.458713Z","bundle_sha256":"6775714e329b48057faf281cdadcbc12e918bf3f6326ff91ab8502b7b1217a68"}}