{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:QUNBU2Q6H5NOJ43VE4WS7UVCZ5","short_pith_number":"pith:QUNBU2Q6","canonical_record":{"source":{"id":"2406.18483","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-06-26T16:48:53Z","cross_cats_sorted":["math-ph","math.DG","math.MP","math.QA"],"title_canon_sha256":"61635b8c3af259b9c1ad0afef13282d46fb284037c87f39afbe4a66afaadb100","abstract_canon_sha256":"d0b058549d699a6a4126453b3dfc5c5afa04dee68f2fc911f5f396210c8aea96"},"schema_version":"1.0"},"canonical_sha256":"851a1a6a1e3f5ae4f375272d2fd2a2cf52ab1bd270e450b3b66827a0f4fa4aae","source":{"kind":"arxiv","id":"2406.18483","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.18483","created_at":"2026-07-05T08:37:09Z"},{"alias_kind":"arxiv_version","alias_value":"2406.18483v1","created_at":"2026-07-05T08:37:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.18483","created_at":"2026-07-05T08:37:09Z"},{"alias_kind":"pith_short_12","alias_value":"QUNBU2Q6H5NO","created_at":"2026-07-05T08:37:09Z"},{"alias_kind":"pith_short_16","alias_value":"QUNBU2Q6H5NOJ43V","created_at":"2026-07-05T08:37:09Z"},{"alias_kind":"pith_short_8","alias_value":"QUNBU2Q6","created_at":"2026-07-05T08:37:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:QUNBU2Q6H5NOJ43VE4WS7UVCZ5","target":"record","payload":{"canonical_record":{"source":{"id":"2406.18483","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-06-26T16:48:53Z","cross_cats_sorted":["math-ph","math.DG","math.MP","math.QA"],"title_canon_sha256":"61635b8c3af259b9c1ad0afef13282d46fb284037c87f39afbe4a66afaadb100","abstract_canon_sha256":"d0b058549d699a6a4126453b3dfc5c5afa04dee68f2fc911f5f396210c8aea96"},"schema_version":"1.0"},"canonical_sha256":"851a1a6a1e3f5ae4f375272d2fd2a2cf52ab1bd270e450b3b66827a0f4fa4aae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:37:09.825328Z","signature_b64":"w6dBHnW/2Xo5wPviWdL8MuXmp7ZFyOr9NOXehkPOR7nTpyxh4Yu3fa0yRWZ8SZ7xIqeuU/Vv2ny0YVF7BiF1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"851a1a6a1e3f5ae4f375272d2fd2a2cf52ab1bd270e450b3b66827a0f4fa4aae","last_reissued_at":"2026-07-05T08:37:09.824806Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:37:09.824806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.18483","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":"2026-07-05T08:37:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DrQL9TMFsh3eZB0ubGu81ACk6DXfTNJuye8DuQF5K4l/6fYaxsfIiAQTYWNiLqBV45wLXpdyTKeqKA9e9d7/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:41:23.539207Z"},"content_sha256":"f6c1a2fcdeed8df8a3d8f060a3c7591002ce5067b47874eba2fd3d27e3bf6e97","schema_version":"1.0","event_id":"sha256:f6c1a2fcdeed8df8a3d8f060a3c7591002ce5067b47874eba2fd3d27e3bf6e97"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:QUNBU2Q6H5NOJ43VE4WS7UVCZ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Curvature and Weitzenbock formula for the Podle\\'{s} quantum sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP","math.QA"],"primary_cat":"math.OA","authors_text":"Adam Rennie, Bram Mesland","submitted_at":"2024-06-26T16:48:53Z","abstract_excerpt":"We prove that there is a unique Levi-Civita connection on the one-forms of the Dabrowski-Sitarz spectral triple for the Podle\\'{s} sphere $S^{2}_{q}$. We compute the full curvature tensor, as well as the Ricci and scalar curvature of the Podle\\'{s} sphere using the framework of \\cite{MRLC}. The scalar curvature is a constant, and as the parameter $q\\to 1$, the scalar curvature converges to the classical value $2$. We prove a generalised Weitzenbock formula for the spinor bundle, which differs from the classical Lichnerowicz formula for $q\\neq 1$, yet recovers it for $q\\to 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.18483","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/2406.18483/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":"2026-07-05T08:37:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BKlDkYPwmyg+r1QGjeRHROJNFH3SSzddrZfyi1cpwrvkQTb1UM4todWkcTZOp6bnSGcebh7rZLmglvxO/H4mCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:41:23.539602Z"},"content_sha256":"85daafa3f6e1c1c19bd8b24d68e3540534d03b5360d404ccf3cde8336f14930f","schema_version":"1.0","event_id":"sha256:85daafa3f6e1c1c19bd8b24d68e3540534d03b5360d404ccf3cde8336f14930f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QUNBU2Q6H5NOJ43VE4WS7UVCZ5/bundle.json","state_url":"https://pith.science/pith/QUNBU2Q6H5NOJ43VE4WS7UVCZ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QUNBU2Q6H5NOJ43VE4WS7UVCZ5/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":"2026-08-13T04:41:23Z","links":{"resolver":"https://pith.science/pith/QUNBU2Q6H5NOJ43VE4WS7UVCZ5","bundle":"https://pith.science/pith/QUNBU2Q6H5NOJ43VE4WS7UVCZ5/bundle.json","state":"https://pith.science/pith/QUNBU2Q6H5NOJ43VE4WS7UVCZ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QUNBU2Q6H5NOJ43VE4WS7UVCZ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QUNBU2Q6H5NOJ43VE4WS7UVCZ5","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":"d0b058549d699a6a4126453b3dfc5c5afa04dee68f2fc911f5f396210c8aea96","cross_cats_sorted":["math-ph","math.DG","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-06-26T16:48:53Z","title_canon_sha256":"61635b8c3af259b9c1ad0afef13282d46fb284037c87f39afbe4a66afaadb100"},"schema_version":"1.0","source":{"id":"2406.18483","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.18483","created_at":"2026-07-05T08:37:09Z"},{"alias_kind":"arxiv_version","alias_value":"2406.18483v1","created_at":"2026-07-05T08:37:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.18483","created_at":"2026-07-05T08:37:09Z"},{"alias_kind":"pith_short_12","alias_value":"QUNBU2Q6H5NO","created_at":"2026-07-05T08:37:09Z"},{"alias_kind":"pith_short_16","alias_value":"QUNBU2Q6H5NOJ43V","created_at":"2026-07-05T08:37:09Z"},{"alias_kind":"pith_short_8","alias_value":"QUNBU2Q6","created_at":"2026-07-05T08:37:09Z"}],"graph_snapshots":[{"event_id":"sha256:85daafa3f6e1c1c19bd8b24d68e3540534d03b5360d404ccf3cde8336f14930f","target":"graph","created_at":"2026-07-05T08:37:09Z","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/2406.18483/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that there is a unique Levi-Civita connection on the one-forms of the Dabrowski-Sitarz spectral triple for the Podle\\'{s} sphere $S^{2}_{q}$. We compute the full curvature tensor, as well as the Ricci and scalar curvature of the Podle\\'{s} sphere using the framework of \\cite{MRLC}. The scalar curvature is a constant, and as the parameter $q\\to 1$, the scalar curvature converges to the classical value $2$. We prove a generalised Weitzenbock formula for the spinor bundle, which differs from the classical Lichnerowicz formula for $q\\neq 1$, yet recovers it for $q\\to 1$.","authors_text":"Adam Rennie, Bram Mesland","cross_cats":["math-ph","math.DG","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-06-26T16:48:53Z","title":"Curvature and Weitzenbock formula for the Podle\\'{s} quantum sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.18483","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:f6c1a2fcdeed8df8a3d8f060a3c7591002ce5067b47874eba2fd3d27e3bf6e97","target":"record","created_at":"2026-07-05T08:37:09Z","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":"d0b058549d699a6a4126453b3dfc5c5afa04dee68f2fc911f5f396210c8aea96","cross_cats_sorted":["math-ph","math.DG","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-06-26T16:48:53Z","title_canon_sha256":"61635b8c3af259b9c1ad0afef13282d46fb284037c87f39afbe4a66afaadb100"},"schema_version":"1.0","source":{"id":"2406.18483","kind":"arxiv","version":1}},"canonical_sha256":"851a1a6a1e3f5ae4f375272d2fd2a2cf52ab1bd270e450b3b66827a0f4fa4aae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"851a1a6a1e3f5ae4f375272d2fd2a2cf52ab1bd270e450b3b66827a0f4fa4aae","first_computed_at":"2026-07-05T08:37:09.824806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:37:09.824806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w6dBHnW/2Xo5wPviWdL8MuXmp7ZFyOr9NOXehkPOR7nTpyxh4Yu3fa0yRWZ8SZ7xIqeuU/Vv2ny0YVF7BiF1DA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:37:09.825328Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.18483","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6c1a2fcdeed8df8a3d8f060a3c7591002ce5067b47874eba2fd3d27e3bf6e97","sha256:85daafa3f6e1c1c19bd8b24d68e3540534d03b5360d404ccf3cde8336f14930f"],"state_sha256":"13295ec85e98702e959a7667fbf559083678cce9f0bf13f0d551abf92ce5db14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f/HzisMT+fnFepIYlzvdOKm1hHqistB63o1KAVKW+oE/RQrMq77tqW9gNZG245TSqOPBnXc9FJw6Fporxt8bAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T04:41:23.542074Z","bundle_sha256":"bc22ba5b67756a75f50582ae4354f9b69de657af36b7f80998d527e064b148b7"}}