{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:3LK3423KXMT2WDTCGWN7ZGCSWX","short_pith_number":"pith:3LK3423K","schema_version":"1.0","canonical_sha256":"dad5be6b6abb27ab0e62359bfc9852b5e3cea6bbf195e6030a96bf88af5d3ffb","source":{"kind":"arxiv","id":"1603.04805","version":1},"attestation_state":"computed","paper":{"title":"The $E_8$ geometry from a Clifford perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.GR","math.MP","math.QA"],"primary_cat":"math.RT","authors_text":"Pierre-Philippe Dechant","submitted_at":"2016-02-18T23:36:40Z","abstract_excerpt":"This paper considers the geometry of $E_8$ from a Clifford point of view in three complementary ways. Firstly, in earlier work, I had shown how to construct the four-dimensional exceptional root systems from the 3D root systems using Clifford techniques, by constructing them in the 4D even subalgebra of the 3D Clifford algebra; for instance the icosahedral root system $H_3$ gives rise to the largest (and therefore exceptional) non-crystallographic root system $H_4$. Arnold's trinities and the McKay correspondence then hint that there might be an indirect connection between the icosahedron and "},"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":"1603.04805","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-02-18T23:36:40Z","cross_cats_sorted":["hep-th","math-ph","math.GR","math.MP","math.QA"],"title_canon_sha256":"bfce6d05856ce5454fd37e8349b4cb10b95a64e1d61e18221c670f135e8d2a3f","abstract_canon_sha256":"48fc27d401404a76ab3b1d0fb1fb60933141e92da043a81ebae68dfb979c9edc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:22.595378Z","signature_b64":"T3zNcwmLvKivG2CSsTzxPH0FkL8wsqNxV0kI7JTnHeOK1MTdB6Yb9HJpCX0pnBX6LwyhRfAkTjtH++NvyvAXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dad5be6b6abb27ab0e62359bfc9852b5e3cea6bbf195e6030a96bf88af5d3ffb","last_reissued_at":"2026-05-18T00:50:22.594728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:22.594728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $E_8$ geometry from a Clifford perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.GR","math.MP","math.QA"],"primary_cat":"math.RT","authors_text":"Pierre-Philippe Dechant","submitted_at":"2016-02-18T23:36:40Z","abstract_excerpt":"This paper considers the geometry of $E_8$ from a Clifford point of view in three complementary ways. Firstly, in earlier work, I had shown how to construct the four-dimensional exceptional root systems from the 3D root systems using Clifford techniques, by constructing them in the 4D even subalgebra of the 3D Clifford algebra; for instance the icosahedral root system $H_3$ gives rise to the largest (and therefore exceptional) non-crystallographic root system $H_4$. Arnold's trinities and the McKay correspondence then hint that there might be an indirect connection between the icosahedron and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04805","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":"1603.04805","created_at":"2026-05-18T00:50:22.594823+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.04805v1","created_at":"2026-05-18T00:50:22.594823+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04805","created_at":"2026-05-18T00:50:22.594823+00:00"},{"alias_kind":"pith_short_12","alias_value":"3LK3423KXMT2","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"3LK3423KXMT2WDTC","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"3LK3423K","created_at":"2026-05-18T12:29:55.572404+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/3LK3423KXMT2WDTCGWN7ZGCSWX","json":"https://pith.science/pith/3LK3423KXMT2WDTCGWN7ZGCSWX.json","graph_json":"https://pith.science/api/pith-number/3LK3423KXMT2WDTCGWN7ZGCSWX/graph.json","events_json":"https://pith.science/api/pith-number/3LK3423KXMT2WDTCGWN7ZGCSWX/events.json","paper":"https://pith.science/paper/3LK3423K"},"agent_actions":{"view_html":"https://pith.science/pith/3LK3423KXMT2WDTCGWN7ZGCSWX","download_json":"https://pith.science/pith/3LK3423KXMT2WDTCGWN7ZGCSWX.json","view_paper":"https://pith.science/paper/3LK3423K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.04805&json=true","fetch_graph":"https://pith.science/api/pith-number/3LK3423KXMT2WDTCGWN7ZGCSWX/graph.json","fetch_events":"https://pith.science/api/pith-number/3LK3423KXMT2WDTCGWN7ZGCSWX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3LK3423KXMT2WDTCGWN7ZGCSWX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3LK3423KXMT2WDTCGWN7ZGCSWX/action/storage_attestation","attest_author":"https://pith.science/pith/3LK3423KXMT2WDTCGWN7ZGCSWX/action/author_attestation","sign_citation":"https://pith.science/pith/3LK3423KXMT2WDTCGWN7ZGCSWX/action/citation_signature","submit_replication":"https://pith.science/pith/3LK3423KXMT2WDTCGWN7ZGCSWX/action/replication_record"}},"created_at":"2026-05-18T00:50:22.594823+00:00","updated_at":"2026-05-18T00:50:22.594823+00:00"}