{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7P4D5HHNDGUQUKQV4HAFZJHCXF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"813a6ab70e30f860c26e81d1a3f43ea8395688986cc8fd19af8f575679b23b92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-12-13T21:19:50Z","title_canon_sha256":"dacd373520dc9b1418c8a6fcd8279fe43748103cf775cb27e173429ee6ff9882"},"schema_version":"1.0","source":{"id":"1112.3047","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3047","created_at":"2026-05-18T04:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3047v1","created_at":"2026-05-18T04:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3047","created_at":"2026-05-18T04:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"7P4D5HHNDGUQ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7P4D5HHNDGUQUKQV","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7P4D5HHN","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:4280099d4ecd0a7d35c53985fcdb6036f478cf18e607fcae4cbcf21e481b1607","target":"graph","created_at":"2026-05-18T04:06:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Bertfried Fauser, Rafal Ablamowicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-12-13T21:19:50Z","title":"Transposition anti-involution in Clifford algebras and invariance groups of scalar products on spinor spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3047","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f93bdc105d7b0c2f68fefeac00609524ff9f26abf9c295df7e0a55d646985dfc","target":"record","created_at":"2026-05-18T04:06:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"813a6ab70e30f860c26e81d1a3f43ea8395688986cc8fd19af8f575679b23b92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-12-13T21:19:50Z","title_canon_sha256":"dacd373520dc9b1418c8a6fcd8279fe43748103cf775cb27e173429ee6ff9882"},"schema_version":"1.0","source":{"id":"1112.3047","kind":"arxiv","version":1}},"canonical_sha256":"fbf83e9ced19a90a2a15e1c05ca4e2b94561a23ba7ed8a905595d568353306b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbf83e9ced19a90a2a15e1c05ca4e2b94561a23ba7ed8a905595d568353306b4","first_computed_at":"2026-05-18T04:06:21.363578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:21.363578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EIS4YbtU6J3VAL1X32zR4XDewMobFyofJ11nrSuiwRr2zitbQdn2hyZKvDfze+mYXGh2RJVeTfEf8RyNOXGUCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:21.364226Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.3047","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f93bdc105d7b0c2f68fefeac00609524ff9f26abf9c295df7e0a55d646985dfc","sha256:4280099d4ecd0a7d35c53985fcdb6036f478cf18e607fcae4cbcf21e481b1607"],"state_sha256":"c8faa063dc4fcf62d9886d656b4a556b681ca19b4618afe71d0cdaf6e4e8b47a"}