{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YAJIGGVSURJZTDWZPLFNALD4GN","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":"22d033a6a92084844e874a9d6f6fd51cbf080d42dd65463b850304686d2a55b8","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.SG","submitted_at":"2016-03-21T20:28:49Z","title_canon_sha256":"2ad2001e3da7ff4cabf09a57d54b5afaf9f4b357749bf55a401a8840b32b43e2"},"schema_version":"1.0","source":{"id":"1603.06603","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06603","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06603v3","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06603","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"pith_short_12","alias_value":"YAJIGGVSURJZ","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YAJIGGVSURJZTDWZ","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YAJIGGVS","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:c1df3563adb90fd7e470adfb61a4a22b8a4d2c14c2d3cc84d8feadf79dd4340e","target":"graph","created_at":"2026-05-18T00:55:25Z","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 show that the Morita equivalences $\\mathrm{Cliff}(4) \\simeq {\\mathbb H}$, $\\mathrm{Cliff}(7) \\simeq \\mathrm{Cliff}(-1)$, and $\\mathrm{Cliff}(8) \\simeq {\\mathbb R}$ arise from quantizing the Hamiltonian reductions ${\\mathbb R}^{0|4} // \\mathrm{Spin}(3)$, ${\\mathbb R}^{0|7} // G_2$, and ${\\mathbb R}^{0|8} // \\mathrm{Spin}(7)$, respectively.","authors_text":"Theo Johnson-Freyd","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.SG","submitted_at":"2016-03-21T20:28:49Z","title":"The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06603","kind":"arxiv","version":3},"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:e8301781931ce429d9d76b9ec73f65b7de24a22775cd217bb627a97185eed113","target":"record","created_at":"2026-05-18T00:55:25Z","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":"22d033a6a92084844e874a9d6f6fd51cbf080d42dd65463b850304686d2a55b8","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.SG","submitted_at":"2016-03-21T20:28:49Z","title_canon_sha256":"2ad2001e3da7ff4cabf09a57d54b5afaf9f4b357749bf55a401a8840b32b43e2"},"schema_version":"1.0","source":{"id":"1603.06603","kind":"arxiv","version":3}},"canonical_sha256":"c012831ab2a453998ed97acad02c7c3372a1d797b5cf9a34e62703ff8682aaa1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c012831ab2a453998ed97acad02c7c3372a1d797b5cf9a34e62703ff8682aaa1","first_computed_at":"2026-05-18T00:55:25.220973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:25.220973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q7Js41z5Czb2ATO31KQ1zKgnA/UGKrHviwsfMaxJ2YejWEW3CZ5xfEeXT+F5rhFDSk9j3BiIxi95/FlInM/jCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:25.221538Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06603","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8301781931ce429d9d76b9ec73f65b7de24a22775cd217bb627a97185eed113","sha256:c1df3563adb90fd7e470adfb61a4a22b8a4d2c14c2d3cc84d8feadf79dd4340e"],"state_sha256":"a023a80162e08393ef8dce01fcc2b55d4f25ceb8ebabd81f6ee2f4c4c434a2c6"}