{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:Q745FZ6FTMJXN47SXORUIIXJ5R","short_pith_number":"pith:Q745FZ6F","schema_version":"1.0","canonical_sha256":"87f9d2e7c59b1376f3f2bba34422e9ec6b0647d95d78950f4d378198affabaad","source":{"kind":"arxiv","id":"1504.05925","version":2},"attestation_state":"computed","paper":{"title":"Homogeneous spin Riemannian manifolds with the simplest Dirac operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jos\\'e A. Oubi\\~na, Jos\\'e C. Gonz\\'alez-D\\'avila, P. M. Gadea","submitted_at":"2015-04-22T19:05:11Z","abstract_excerpt":"We show the existence of nonsymmetric homogeneous spin Riemannian manifolds whose Dirac operator is like that on a Riemannian symmetric spin space. Such manifolds are exactly the homogeneous spin Riemannian manifolds $(M,g)$ which are traceless cyclic with respect to some quotient expression $M=G/K$ and reductive decomposition $\\mathfrak{g} = \\mathfrak{k} \\oplus \\mathfrak{m}$. Using transversally symmetric fibrations of noncompact type, we give a list of them."},"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":"1504.05925","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-22T19:05:11Z","cross_cats_sorted":[],"title_canon_sha256":"1752faeeb3d9e0b0dea61c0278d80e71a4ef4f0eeb7bd3eed7a59d6cda22bc5a","abstract_canon_sha256":"09552513560f454edcd95adf484c3dc5a926e1800101d9eb77d9d64eac77d4af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:05.140108Z","signature_b64":"rD5lOnYnMqmUqEtkAFhy0L7th+tlzFWS7hB4LoPyp4ZKbeIqaa/qaCLjam8L6gG9C4YOIqKgioOv18XxzZX2DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87f9d2e7c59b1376f3f2bba34422e9ec6b0647d95d78950f4d378198affabaad","last_reissued_at":"2026-05-18T01:21:05.139641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:05.139641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homogeneous spin Riemannian manifolds with the simplest Dirac operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jos\\'e A. Oubi\\~na, Jos\\'e C. Gonz\\'alez-D\\'avila, P. M. Gadea","submitted_at":"2015-04-22T19:05:11Z","abstract_excerpt":"We show the existence of nonsymmetric homogeneous spin Riemannian manifolds whose Dirac operator is like that on a Riemannian symmetric spin space. Such manifolds are exactly the homogeneous spin Riemannian manifolds $(M,g)$ which are traceless cyclic with respect to some quotient expression $M=G/K$ and reductive decomposition $\\mathfrak{g} = \\mathfrak{k} \\oplus \\mathfrak{m}$. Using transversally symmetric fibrations of noncompact type, we give a list of them."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05925","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":"1504.05925","created_at":"2026-05-18T01:21:05.139714+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.05925v2","created_at":"2026-05-18T01:21:05.139714+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05925","created_at":"2026-05-18T01:21:05.139714+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q745FZ6FTMJX","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q745FZ6FTMJXN47S","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q745FZ6F","created_at":"2026-05-18T12:29:37.295048+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/Q745FZ6FTMJXN47SXORUIIXJ5R","json":"https://pith.science/pith/Q745FZ6FTMJXN47SXORUIIXJ5R.json","graph_json":"https://pith.science/api/pith-number/Q745FZ6FTMJXN47SXORUIIXJ5R/graph.json","events_json":"https://pith.science/api/pith-number/Q745FZ6FTMJXN47SXORUIIXJ5R/events.json","paper":"https://pith.science/paper/Q745FZ6F"},"agent_actions":{"view_html":"https://pith.science/pith/Q745FZ6FTMJXN47SXORUIIXJ5R","download_json":"https://pith.science/pith/Q745FZ6FTMJXN47SXORUIIXJ5R.json","view_paper":"https://pith.science/paper/Q745FZ6F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.05925&json=true","fetch_graph":"https://pith.science/api/pith-number/Q745FZ6FTMJXN47SXORUIIXJ5R/graph.json","fetch_events":"https://pith.science/api/pith-number/Q745FZ6FTMJXN47SXORUIIXJ5R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q745FZ6FTMJXN47SXORUIIXJ5R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q745FZ6FTMJXN47SXORUIIXJ5R/action/storage_attestation","attest_author":"https://pith.science/pith/Q745FZ6FTMJXN47SXORUIIXJ5R/action/author_attestation","sign_citation":"https://pith.science/pith/Q745FZ6FTMJXN47SXORUIIXJ5R/action/citation_signature","submit_replication":"https://pith.science/pith/Q745FZ6FTMJXN47SXORUIIXJ5R/action/replication_record"}},"created_at":"2026-05-18T01:21:05.139714+00:00","updated_at":"2026-05-18T01:21:05.139714+00:00"}