{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:WBZNL2YMB2RLEGDDTRAAWT6CHT","short_pith_number":"pith:WBZNL2YM","schema_version":"1.0","canonical_sha256":"b072d5eb0c0ea2b218639c400b4fc23ce1a965c48c40164bdbb304a279800750","source":{"kind":"arxiv","id":"2312.11558","version":3},"attestation_state":"computed","paper":{"title":"A unified-description of curvature, torsion, and non-metricity of the metric-affine geometry with the M\\\"{o}bius representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Kyosuke Tomonari","submitted_at":"2023-12-17T10:36:20Z","abstract_excerpt":"We establish the mathematical fundamentals for a unified description of curvature, torsion, and non-metricity 2-forms in the way extending the so-called M\\\"{o}bius representation of the affine group, which is the method to convert the semi-direct product into the ordinary matrix product, to revive the fertility of gauge theories of gravity. First of all, we illustrate the basic concepts for constructing the metric-affine geometry. Then the curvature and torsion 2-forms are described in a unified manner by using the Cartan connection of the M\\\"{o}bius representation of the affine group. In this"},"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":"2312.11558","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2023-12-17T10:36:20Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"949ffb05538266d14d8d08d8db89a93f07737a947797c74a7cded3ad1c92b2fd","abstract_canon_sha256":"9c04d4663378ed05276d55a0099e862cb43bfcca5e578462cc563d5773d48f7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:15:28.729182Z","signature_b64":"xuVnBUkdTO7nB31JG8ZDK/IZmCBQUaCuPPv6smMlEINAyrngOKjgZbdb4GcFPJrU2aMY9JV1jwiHt4SDki8nDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b072d5eb0c0ea2b218639c400b4fc23ce1a965c48c40164bdbb304a279800750","last_reissued_at":"2026-07-05T09:15:28.728706Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:15:28.728706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A unified-description of curvature, torsion, and non-metricity of the metric-affine geometry with the M\\\"{o}bius representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Kyosuke Tomonari","submitted_at":"2023-12-17T10:36:20Z","abstract_excerpt":"We establish the mathematical fundamentals for a unified description of curvature, torsion, and non-metricity 2-forms in the way extending the so-called M\\\"{o}bius representation of the affine group, which is the method to convert the semi-direct product into the ordinary matrix product, to revive the fertility of gauge theories of gravity. First of all, we illustrate the basic concepts for constructing the metric-affine geometry. Then the curvature and torsion 2-forms are described in a unified manner by using the Cartan connection of the M\\\"{o}bius representation of the affine group. In this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.11558","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/2312.11558/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":"2312.11558","created_at":"2026-07-05T09:15:28.728765+00:00"},{"alias_kind":"arxiv_version","alias_value":"2312.11558v3","created_at":"2026-07-05T09:15:28.728765+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.11558","created_at":"2026-07-05T09:15:28.728765+00:00"},{"alias_kind":"pith_short_12","alias_value":"WBZNL2YMB2RL","created_at":"2026-07-05T09:15:28.728765+00:00"},{"alias_kind":"pith_short_16","alias_value":"WBZNL2YMB2RLEGDD","created_at":"2026-07-05T09:15:28.728765+00:00"},{"alias_kind":"pith_short_8","alias_value":"WBZNL2YM","created_at":"2026-07-05T09:15:28.728765+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.22158","citing_title":"Revisiting Coincident GR in Internal STEGR Formulation","ref_index":18,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WBZNL2YMB2RLEGDDTRAAWT6CHT","json":"https://pith.science/pith/WBZNL2YMB2RLEGDDTRAAWT6CHT.json","graph_json":"https://pith.science/api/pith-number/WBZNL2YMB2RLEGDDTRAAWT6CHT/graph.json","events_json":"https://pith.science/api/pith-number/WBZNL2YMB2RLEGDDTRAAWT6CHT/events.json","paper":"https://pith.science/paper/WBZNL2YM"},"agent_actions":{"view_html":"https://pith.science/pith/WBZNL2YMB2RLEGDDTRAAWT6CHT","download_json":"https://pith.science/pith/WBZNL2YMB2RLEGDDTRAAWT6CHT.json","view_paper":"https://pith.science/paper/WBZNL2YM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2312.11558&json=true","fetch_graph":"https://pith.science/api/pith-number/WBZNL2YMB2RLEGDDTRAAWT6CHT/graph.json","fetch_events":"https://pith.science/api/pith-number/WBZNL2YMB2RLEGDDTRAAWT6CHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WBZNL2YMB2RLEGDDTRAAWT6CHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WBZNL2YMB2RLEGDDTRAAWT6CHT/action/storage_attestation","attest_author":"https://pith.science/pith/WBZNL2YMB2RLEGDDTRAAWT6CHT/action/author_attestation","sign_citation":"https://pith.science/pith/WBZNL2YMB2RLEGDDTRAAWT6CHT/action/citation_signature","submit_replication":"https://pith.science/pith/WBZNL2YMB2RLEGDDTRAAWT6CHT/action/replication_record"}},"created_at":"2026-07-05T09:15:28.728765+00:00","updated_at":"2026-07-05T09:15:28.728765+00:00"}