{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:K7UIQB6THBU5WNLUCZELXRPCF4","short_pith_number":"pith:K7UIQB6T","schema_version":"1.0","canonical_sha256":"57e88807d33869db35741648bbc5e22f30dde99c5e38c0fcd4d21b1a7ecf2ad4","source":{"kind":"arxiv","id":"1105.1898","version":2},"attestation_state":"computed","paper":{"title":"A note on the geometrical interpretation of quantum groups and non-commutative spaces in gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Carlo Rovelli, Eugenio Bianchi","submitted_at":"2011-05-10T10:10:25Z","abstract_excerpt":"Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We consider here a different geometrical interpretation of this cut-off, where the relevant non-commutative space is the space of directions around any spacetime point. The limitations in angular resolution expresses the finiteness of the angular size of a Planck-scale minimal surface at a maximum distance 1/\\sqrt{Lambda} related the cosmological constant Lambda."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1105.1898","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-05-10T10:10:25Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"c639e23fdca07bbeb598a5679f12cac89413dca9c9ab22177bbbda91b09186ad","abstract_canon_sha256":"04bf16333a778e69f429fc2e9299c453c7b95fd3df0243af9ded9240301505a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:01.584534Z","signature_b64":"AEGsjZxP1m1WGEo1+LXwrcFa1E+M27a7navizXIBNdGVfLt6tzITb6dxaS81PzLA0S+2CW8fGpvOKQ3N1iYuDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57e88807d33869db35741648bbc5e22f30dde99c5e38c0fcd4d21b1a7ecf2ad4","last_reissued_at":"2026-05-18T04:16:01.583766Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:01.583766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the geometrical interpretation of quantum groups and non-commutative spaces in gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Carlo Rovelli, Eugenio Bianchi","submitted_at":"2011-05-10T10:10:25Z","abstract_excerpt":"Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We consider here a different geometrical interpretation of this cut-off, where the relevant non-commutative space is the space of directions around any spacetime point. The limitations in angular resolution expresses the finiteness of the angular size of a Planck-scale minimal surface at a maximum distance 1/\\sqrt{Lambda} related the cosmological constant Lambda."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1898","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1105.1898","created_at":"2026-05-18T04:16:01.583900+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.1898v2","created_at":"2026-05-18T04:16:01.583900+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1898","created_at":"2026-05-18T04:16:01.583900+00:00"},{"alias_kind":"pith_short_12","alias_value":"K7UIQB6THBU5","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"K7UIQB6THBU5WNLU","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"K7UIQB6T","created_at":"2026-05-18T12:26:32.869790+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.23862","citing_title":"Indefinite probabilities in quantum spacetime: A deepening of unpredictability","ref_index":31,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/K7UIQB6THBU5WNLUCZELXRPCF4","json":"https://pith.science/pith/K7UIQB6THBU5WNLUCZELXRPCF4.json","graph_json":"https://pith.science/api/pith-number/K7UIQB6THBU5WNLUCZELXRPCF4/graph.json","events_json":"https://pith.science/api/pith-number/K7UIQB6THBU5WNLUCZELXRPCF4/events.json","paper":"https://pith.science/paper/K7UIQB6T"},"agent_actions":{"view_html":"https://pith.science/pith/K7UIQB6THBU5WNLUCZELXRPCF4","download_json":"https://pith.science/pith/K7UIQB6THBU5WNLUCZELXRPCF4.json","view_paper":"https://pith.science/paper/K7UIQB6T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.1898&json=true","fetch_graph":"https://pith.science/api/pith-number/K7UIQB6THBU5WNLUCZELXRPCF4/graph.json","fetch_events":"https://pith.science/api/pith-number/K7UIQB6THBU5WNLUCZELXRPCF4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K7UIQB6THBU5WNLUCZELXRPCF4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K7UIQB6THBU5WNLUCZELXRPCF4/action/storage_attestation","attest_author":"https://pith.science/pith/K7UIQB6THBU5WNLUCZELXRPCF4/action/author_attestation","sign_citation":"https://pith.science/pith/K7UIQB6THBU5WNLUCZELXRPCF4/action/citation_signature","submit_replication":"https://pith.science/pith/K7UIQB6THBU5WNLUCZELXRPCF4/action/replication_record"}},"created_at":"2026-05-18T04:16:01.583900+00:00","updated_at":"2026-05-18T04:16:01.583900+00:00"}