{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:UFS6BKBFGJYDEAOJWGRP5CVKEV","short_pith_number":"pith:UFS6BKBF","schema_version":"1.0","canonical_sha256":"a165e0a82532703201c9b1a2fe8aaa25753429e1c1854f408eb3762dab2d6092","source":{"kind":"arxiv","id":"2011.05171","version":4},"attestation_state":"computed","paper":{"title":"Subgroups of Clifford algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Robert A. Wilson","submitted_at":"2020-10-27T08:37:22Z","abstract_excerpt":"Clifford algebras are used for constructing spin groups, and are therefore of particular importance in the theory of quantum mechanics. But the spin group is not the only subgroup of the Clifford algebra. An algebraist's perspective on these groups and algebras may suggest ways in which they might be applied more widely to describe the fundamental properties of matter. I do not claim to build a physical theory on top of the fundamental algebra, and my suggestions for possible physical interpretations are indicative only, and may not work. Nevertheless, both the existence of three generations o"},"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":"2011.05171","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-10-27T08:37:22Z","cross_cats_sorted":[],"title_canon_sha256":"0c999ffc9f297a65bbda5a01ab09ca1a5811f6c1e35dadda06c8964368a971df","abstract_canon_sha256":"82142d8d9285bbff31aa53a75b2cafe6cc3c327e04b15cc6d3d661784a057efc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:57:50.807898Z","signature_b64":"PB2hIPYSfkVQJzovENDhd2p3K4bBVFAphKkPxtN5SSy3ejioqnoUh3nvvk4yHWzaAylzonBjEfcYZAdOlSw7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a165e0a82532703201c9b1a2fe8aaa25753429e1c1854f408eb3762dab2d6092","last_reissued_at":"2026-07-05T02:57:50.807431Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:57:50.807431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subgroups of Clifford algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Robert A. Wilson","submitted_at":"2020-10-27T08:37:22Z","abstract_excerpt":"Clifford algebras are used for constructing spin groups, and are therefore of particular importance in the theory of quantum mechanics. But the spin group is not the only subgroup of the Clifford algebra. An algebraist's perspective on these groups and algebras may suggest ways in which they might be applied more widely to describe the fundamental properties of matter. I do not claim to build a physical theory on top of the fundamental algebra, and my suggestions for possible physical interpretations are indicative only, and may not work. Nevertheless, both the existence of three generations o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.05171","kind":"arxiv","version":4},"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/2011.05171/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":"2011.05171","created_at":"2026-07-05T02:57:50.807489+00:00"},{"alias_kind":"arxiv_version","alias_value":"2011.05171v4","created_at":"2026-07-05T02:57:50.807489+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.05171","created_at":"2026-07-05T02:57:50.807489+00:00"},{"alias_kind":"pith_short_12","alias_value":"UFS6BKBFGJYD","created_at":"2026-07-05T02:57:50.807489+00:00"},{"alias_kind":"pith_short_16","alias_value":"UFS6BKBFGJYDEAOJ","created_at":"2026-07-05T02:57:50.807489+00:00"},{"alias_kind":"pith_short_8","alias_value":"UFS6BKBF","created_at":"2026-07-05T02:57:50.807489+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.05223","citing_title":"Sharp Lower Bound on the Minimax Risk for Multinomial Uniformity Testing via a Conditional Central Limit Theorem","ref_index":49,"is_internal_anchor":true},{"citing_arxiv_id":"2606.10992","citing_title":"Surface Crevasse Evolution Observed Using Matched Field Processing and Source Relocation at Hansbreen, Svalbard","ref_index":294,"is_internal_anchor":false},{"citing_arxiv_id":"2505.07923","citing_title":"A Superalgebra Within: representations of lightest standard model particles form a $\\mathbb{Z}_2^5$-graded algebra","ref_index":34,"is_internal_anchor":false},{"citing_arxiv_id":"2601.07857","citing_title":"Electroweak Structure and Three Fermion Generations in Clifford Algebra with S3 Family Symmetry","ref_index":36,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UFS6BKBFGJYDEAOJWGRP5CVKEV","json":"https://pith.science/pith/UFS6BKBFGJYDEAOJWGRP5CVKEV.json","graph_json":"https://pith.science/api/pith-number/UFS6BKBFGJYDEAOJWGRP5CVKEV/graph.json","events_json":"https://pith.science/api/pith-number/UFS6BKBFGJYDEAOJWGRP5CVKEV/events.json","paper":"https://pith.science/paper/UFS6BKBF"},"agent_actions":{"view_html":"https://pith.science/pith/UFS6BKBFGJYDEAOJWGRP5CVKEV","download_json":"https://pith.science/pith/UFS6BKBFGJYDEAOJWGRP5CVKEV.json","view_paper":"https://pith.science/paper/UFS6BKBF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2011.05171&json=true","fetch_graph":"https://pith.science/api/pith-number/UFS6BKBFGJYDEAOJWGRP5CVKEV/graph.json","fetch_events":"https://pith.science/api/pith-number/UFS6BKBFGJYDEAOJWGRP5CVKEV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UFS6BKBFGJYDEAOJWGRP5CVKEV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UFS6BKBFGJYDEAOJWGRP5CVKEV/action/storage_attestation","attest_author":"https://pith.science/pith/UFS6BKBFGJYDEAOJWGRP5CVKEV/action/author_attestation","sign_citation":"https://pith.science/pith/UFS6BKBFGJYDEAOJWGRP5CVKEV/action/citation_signature","submit_replication":"https://pith.science/pith/UFS6BKBFGJYDEAOJWGRP5CVKEV/action/replication_record"}},"created_at":"2026-07-05T02:57:50.807489+00:00","updated_at":"2026-07-05T02:57:50.807489+00:00"}