{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:7NVVTLWRROBFAQ2CTPSX7OM6RH","short_pith_number":"pith:7NVVTLWR","schema_version":"1.0","canonical_sha256":"fb6b59aed18b825043429be57fb99e89d042940cbf37e7632f8355e81f1a34a1","source":{"kind":"arxiv","id":"1905.07735","version":3},"attestation_state":"computed","paper":{"title":"General covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"Q. H. Liu, W. K. Du, X. Y. Zhou, Z. Li, Z. Q. Yang","submitted_at":"2019-05-19T13:02:19Z","abstract_excerpt":"For a particle that is constrained on an ($N-1$)-dimensional ($N\\geq2$) curved surface, the Cartesian components of its momentum in $N$-dimensional flat space is believed to offer a proper form of momentum for the particle on the surface, which is called the geometric momentum as it depends on the mean curvature. Once the momentum is made general covariance, the spin connection part can be interpreted as a gauge potential. The present study consists in two parts, the first is a discussion of the general framework for the general covariant geometric momentum. The second is devoted to a study of"},"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":"1905.07735","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-05-19T13:02:19Z","cross_cats_sorted":["cond-mat.mes-hall","math-ph","math.MP","quant-ph"],"title_canon_sha256":"783896f829481837597e6d7a9fdbb3ad27d257143c8ed988d9062ae39e91b195","abstract_canon_sha256":"90d983ccb3c3e1faf9f9e542c7ff938d5305cfb6a038fdf7cfa80ebe2c058006"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:08:32.044521Z","signature_b64":"KIPwPaMUVmcBGk2i4Y5tr3zdvmFPpoEzEPDPkWAq6v54c1ZecXuz7mmGugCyjZaLfbbchhebIU+46U9Ga6d2Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb6b59aed18b825043429be57fb99e89d042940cbf37e7632f8355e81f1a34a1","last_reissued_at":"2026-07-05T00:08:32.043964Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:08:32.043964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"General covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"Q. H. Liu, W. K. Du, X. Y. Zhou, Z. Li, Z. Q. Yang","submitted_at":"2019-05-19T13:02:19Z","abstract_excerpt":"For a particle that is constrained on an ($N-1$)-dimensional ($N\\geq2$) curved surface, the Cartesian components of its momentum in $N$-dimensional flat space is believed to offer a proper form of momentum for the particle on the surface, which is called the geometric momentum as it depends on the mean curvature. Once the momentum is made general covariance, the spin connection part can be interpreted as a gauge potential. The present study consists in two parts, the first is a discussion of the general framework for the general covariant geometric momentum. The second is devoted to a study of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07735","kind":"arxiv","version":3},"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/1905.07735/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.07735","created_at":"2026-07-05T00:08:32.044034+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.07735v3","created_at":"2026-07-05T00:08:32.044034+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07735","created_at":"2026-07-05T00:08:32.044034+00:00"},{"alias_kind":"pith_short_12","alias_value":"7NVVTLWRROBF","created_at":"2026-07-05T00:08:32.044034+00:00"},{"alias_kind":"pith_short_16","alias_value":"7NVVTLWRROBFAQ2C","created_at":"2026-07-05T00:08:32.044034+00:00"},{"alias_kind":"pith_short_8","alias_value":"7NVVTLWR","created_at":"2026-07-05T00:08:32.044034+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7NVVTLWRROBFAQ2CTPSX7OM6RH","json":"https://pith.science/pith/7NVVTLWRROBFAQ2CTPSX7OM6RH.json","graph_json":"https://pith.science/api/pith-number/7NVVTLWRROBFAQ2CTPSX7OM6RH/graph.json","events_json":"https://pith.science/api/pith-number/7NVVTLWRROBFAQ2CTPSX7OM6RH/events.json","paper":"https://pith.science/paper/7NVVTLWR"},"agent_actions":{"view_html":"https://pith.science/pith/7NVVTLWRROBFAQ2CTPSX7OM6RH","download_json":"https://pith.science/pith/7NVVTLWRROBFAQ2CTPSX7OM6RH.json","view_paper":"https://pith.science/paper/7NVVTLWR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.07735&json=true","fetch_graph":"https://pith.science/api/pith-number/7NVVTLWRROBFAQ2CTPSX7OM6RH/graph.json","fetch_events":"https://pith.science/api/pith-number/7NVVTLWRROBFAQ2CTPSX7OM6RH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7NVVTLWRROBFAQ2CTPSX7OM6RH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7NVVTLWRROBFAQ2CTPSX7OM6RH/action/storage_attestation","attest_author":"https://pith.science/pith/7NVVTLWRROBFAQ2CTPSX7OM6RH/action/author_attestation","sign_citation":"https://pith.science/pith/7NVVTLWRROBFAQ2CTPSX7OM6RH/action/citation_signature","submit_replication":"https://pith.science/pith/7NVVTLWRROBFAQ2CTPSX7OM6RH/action/replication_record"}},"created_at":"2026-07-05T00:08:32.044034+00:00","updated_at":"2026-07-05T00:08:32.044034+00:00"}