{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:7P4D5HHNDGUQUKQV4HAFZJHCXF","short_pith_number":"pith:7P4D5HHN","schema_version":"1.0","canonical_sha256":"fbf83e9ced19a90a2a15e1c05ca4e2b94561a23ba7ed8a905595d568353306b4","source":{"kind":"arxiv","id":"1112.3047","version":1},"attestation_state":"computed","paper":{"title":"Transposition anti-involution in Clifford algebras and invariance groups of scalar products on spinor spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Bertfried Fauser, Rafal Ablamowicz","submitted_at":"2011-12-13T21:19:50Z","abstract_excerpt":"We introduce on the abstract level in real Clifford algebras \\cl_{p,q} of a non-degenerate quadratic space (V,Q), where Q has signature \\epsilon=(p,q), a transposition anti-involution \\tp. In a spinor representation, the anti-involution \\tp gives transposition, complex Hermitian conjugation or quaternionic Hermitian conjugation when the spinor space \\check{S} is viewed as a \\cl_{p,q}-left and \\check{K}-right module with \\check{K} isomorphic to R or R^2, C, or, H or H^2.\n  \\tp is a lifting to \\cl_{p,q} of an orthogonal involution \\tve: V \\rightarrow V which depends on the signature of Q. The in"},"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":"1112.3047","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-12-13T21:19:50Z","cross_cats_sorted":[],"title_canon_sha256":"dacd373520dc9b1418c8a6fcd8279fe43748103cf775cb27e173429ee6ff9882","abstract_canon_sha256":"813a6ab70e30f860c26e81d1a3f43ea8395688986cc8fd19af8f575679b23b92"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:21.364226Z","signature_b64":"EIS4YbtU6J3VAL1X32zR4XDewMobFyofJ11nrSuiwRr2zitbQdn2hyZKvDfze+mYXGh2RJVeTfEf8RyNOXGUCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbf83e9ced19a90a2a15e1c05ca4e2b94561a23ba7ed8a905595d568353306b4","last_reissued_at":"2026-05-18T04:06:21.363578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:21.363578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transposition anti-involution in Clifford algebras and invariance groups of scalar products on spinor spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Bertfried Fauser, Rafal Ablamowicz","submitted_at":"2011-12-13T21:19:50Z","abstract_excerpt":"We introduce on the abstract level in real Clifford algebras \\cl_{p,q} of a non-degenerate quadratic space (V,Q), where Q has signature \\epsilon=(p,q), a transposition anti-involution \\tp. In a spinor representation, the anti-involution \\tp gives transposition, complex Hermitian conjugation or quaternionic Hermitian conjugation when the spinor space \\check{S} is viewed as a \\cl_{p,q}-left and \\check{K}-right module with \\check{K} isomorphic to R or R^2, C, or, H or H^2.\n  \\tp is a lifting to \\cl_{p,q} of an orthogonal involution \\tve: V \\rightarrow V which depends on the signature of Q. The in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3047","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":""},"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":"1112.3047","created_at":"2026-05-18T04:06:21.363693+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.3047v1","created_at":"2026-05-18T04:06:21.363693+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3047","created_at":"2026-05-18T04:06:21.363693+00:00"},{"alias_kind":"pith_short_12","alias_value":"7P4D5HHNDGUQ","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"7P4D5HHNDGUQUKQV","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"7P4D5HHN","created_at":"2026-05-18T12:26:22.705136+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/7P4D5HHNDGUQUKQV4HAFZJHCXF","json":"https://pith.science/pith/7P4D5HHNDGUQUKQV4HAFZJHCXF.json","graph_json":"https://pith.science/api/pith-number/7P4D5HHNDGUQUKQV4HAFZJHCXF/graph.json","events_json":"https://pith.science/api/pith-number/7P4D5HHNDGUQUKQV4HAFZJHCXF/events.json","paper":"https://pith.science/paper/7P4D5HHN"},"agent_actions":{"view_html":"https://pith.science/pith/7P4D5HHNDGUQUKQV4HAFZJHCXF","download_json":"https://pith.science/pith/7P4D5HHNDGUQUKQV4HAFZJHCXF.json","view_paper":"https://pith.science/paper/7P4D5HHN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.3047&json=true","fetch_graph":"https://pith.science/api/pith-number/7P4D5HHNDGUQUKQV4HAFZJHCXF/graph.json","fetch_events":"https://pith.science/api/pith-number/7P4D5HHNDGUQUKQV4HAFZJHCXF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7P4D5HHNDGUQUKQV4HAFZJHCXF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7P4D5HHNDGUQUKQV4HAFZJHCXF/action/storage_attestation","attest_author":"https://pith.science/pith/7P4D5HHNDGUQUKQV4HAFZJHCXF/action/author_attestation","sign_citation":"https://pith.science/pith/7P4D5HHNDGUQUKQV4HAFZJHCXF/action/citation_signature","submit_replication":"https://pith.science/pith/7P4D5HHNDGUQUKQV4HAFZJHCXF/action/replication_record"}},"created_at":"2026-05-18T04:06:21.363693+00:00","updated_at":"2026-05-18T04:06:21.363693+00:00"}