{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:UI2BUMRAFJ7QRWEF2BYLXI6AZZ","short_pith_number":"pith:UI2BUMRA","schema_version":"1.0","canonical_sha256":"a2341a32202a7f08d885d070bba3c0ce4a95e59cee3fc03fb4c0231ad8ebe4d7","source":{"kind":"arxiv","id":"2011.05568","version":1},"attestation_state":"computed","paper":{"title":"Notes on spinors in low dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GR","authors_text":"Robert L. Bryant","submitted_at":"2020-11-09T15:19:33Z","abstract_excerpt":"The purpose of these old notes (written in 1998 during a research project on holonomy of pseudo-Riemannian manifolds of type (10,1)) is to determine the orbit structure of the groups Spin(p,q) acting on their spinor spaces for the values (p,q) = (8,0), (9,0), (9,1), (10,0), (10,1), and (10,2). I'm making them available on the arXiv because I continue to get requests for them as well as questions about how they can be cited."},"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":"2011.05568","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2020-11-09T15:19:33Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"54f40c068de47d98a2aec1cb207b03021b33f293b86f91c138e3d573be58dc51","abstract_canon_sha256":"dcc35a7acc36fcadb1a09513d8cb756fe06bd37901bc161db052365957daa993"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:50:51.275205Z","signature_b64":"Wz1YX82cZo69vpbRvIv5k+++odA/vHk4c0I9GKjEV7rMxvbcDIeJ6R3TNLfUN70ofs2x9TYG01FRpdPSyFmWCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2341a32202a7f08d885d070bba3c0ce4a95e59cee3fc03fb4c0231ad8ebe4d7","last_reissued_at":"2026-07-05T01:50:51.274873Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:50:51.274873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Notes on spinors in low dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GR","authors_text":"Robert L. Bryant","submitted_at":"2020-11-09T15:19:33Z","abstract_excerpt":"The purpose of these old notes (written in 1998 during a research project on holonomy of pseudo-Riemannian manifolds of type (10,1)) is to determine the orbit structure of the groups Spin(p,q) acting on their spinor spaces for the values (p,q) = (8,0), (9,0), (9,1), (10,0), (10,1), and (10,2). I'm making them available on the arXiv because I continue to get requests for them as well as questions about how they can be cited."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.05568","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/2011.05568/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":"2011.05568","created_at":"2026-07-05T01:50:51.274929+00:00"},{"alias_kind":"arxiv_version","alias_value":"2011.05568v1","created_at":"2026-07-05T01:50:51.274929+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.05568","created_at":"2026-07-05T01:50:51.274929+00:00"},{"alias_kind":"pith_short_12","alias_value":"UI2BUMRAFJ7Q","created_at":"2026-07-05T01:50:51.274929+00:00"},{"alias_kind":"pith_short_16","alias_value":"UI2BUMRAFJ7QRWEF","created_at":"2026-07-05T01:50:51.274929+00:00"},{"alias_kind":"pith_short_8","alias_value":"UI2BUMRA","created_at":"2026-07-05T01:50:51.274929+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2504.16465","citing_title":"Octonions, complex structures and Standard Model fermions","ref_index":22,"is_internal_anchor":false},{"citing_arxiv_id":"2601.18433","citing_title":"Massless Representations in Conformal Space and Their de Sitter Restrictions","ref_index":102,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UI2BUMRAFJ7QRWEF2BYLXI6AZZ","json":"https://pith.science/pith/UI2BUMRAFJ7QRWEF2BYLXI6AZZ.json","graph_json":"https://pith.science/api/pith-number/UI2BUMRAFJ7QRWEF2BYLXI6AZZ/graph.json","events_json":"https://pith.science/api/pith-number/UI2BUMRAFJ7QRWEF2BYLXI6AZZ/events.json","paper":"https://pith.science/paper/UI2BUMRA"},"agent_actions":{"view_html":"https://pith.science/pith/UI2BUMRAFJ7QRWEF2BYLXI6AZZ","download_json":"https://pith.science/pith/UI2BUMRAFJ7QRWEF2BYLXI6AZZ.json","view_paper":"https://pith.science/paper/UI2BUMRA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2011.05568&json=true","fetch_graph":"https://pith.science/api/pith-number/UI2BUMRAFJ7QRWEF2BYLXI6AZZ/graph.json","fetch_events":"https://pith.science/api/pith-number/UI2BUMRAFJ7QRWEF2BYLXI6AZZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UI2BUMRAFJ7QRWEF2BYLXI6AZZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UI2BUMRAFJ7QRWEF2BYLXI6AZZ/action/storage_attestation","attest_author":"https://pith.science/pith/UI2BUMRAFJ7QRWEF2BYLXI6AZZ/action/author_attestation","sign_citation":"https://pith.science/pith/UI2BUMRAFJ7QRWEF2BYLXI6AZZ/action/citation_signature","submit_replication":"https://pith.science/pith/UI2BUMRAFJ7QRWEF2BYLXI6AZZ/action/replication_record"}},"created_at":"2026-07-05T01:50:51.274929+00:00","updated_at":"2026-07-05T01:50:51.274929+00:00"}