{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6G7AWJ436GMTE3DSWXRSJWL6EY","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":"c3dc6c3e1bcde252f23f8a7a56ba86c615e7e2823d75adae669ca93392464143","cross_cats_sorted":["hep-ph","hep-th","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-18T21:43:01Z","title_canon_sha256":"1523a6f1b81c18407f20457d013d76a1f01eecd461bb464495c1152bb1137f7f"},"schema_version":"1.0","source":{"id":"1602.05985","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05985","created_at":"2026-05-18T01:20:21Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05985v1","created_at":"2026-05-18T01:20:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05985","created_at":"2026-05-18T01:20:21Z"},{"alias_kind":"pith_short_12","alias_value":"6G7AWJ436GMT","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6G7AWJ436GMTE3DS","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6G7AWJ43","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:5fa2c281d4dda14bf8b71a73828fb6cfee1ae82fed67f860a7df901b9f8ca017","target":"graph","created_at":"2026-05-18T01:20:21Z","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":"$E_8$ is prominent in mathematics and theoretical physics, and is generally viewed as an exceptional symmetry in an eight-dimensional space very different from the space we inhabit; for instance the Lie group $E_8$ features heavily in ten-dimensional superstring theory. Contrary to that point of view, here we show that the $E_8$ root system can in fact be constructed from the icosahedron alone and can thus be viewed purely in terms of three-dimensional geometry. The $240$ roots of $E_8$ arise in the 8D Clifford algebra of 3D space as a double cover of the $120$ elements of the icosahedral grou","authors_text":"Pierre-Philippe Dechant","cross_cats":["hep-ph","hep-th","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-18T21:43:01Z","title":"The Birth of $E_8$ out of the Spinors of the Icosahedron"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05985","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:a4f815051d94204ac9894f960c385c645defb594c7d57309004fc1191b42ea7c","target":"record","created_at":"2026-05-18T01:20:21Z","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":"c3dc6c3e1bcde252f23f8a7a56ba86c615e7e2823d75adae669ca93392464143","cross_cats_sorted":["hep-ph","hep-th","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-18T21:43:01Z","title_canon_sha256":"1523a6f1b81c18407f20457d013d76a1f01eecd461bb464495c1152bb1137f7f"},"schema_version":"1.0","source":{"id":"1602.05985","kind":"arxiv","version":1}},"canonical_sha256":"f1be0b279bf199326c72b5e324d97e2630e0fc51aa9d7a8d5e68717589269ae1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1be0b279bf199326c72b5e324d97e2630e0fc51aa9d7a8d5e68717589269ae1","first_computed_at":"2026-05-18T01:20:21.905701Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:21.905701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pn4hyLcwLrGFLdx5APwUeDSwxU/ZZyViCj3tCD6ZAhphQnAujDejVFN9WwoSYykqvBrS36Ogo8Rr99hAk+8+Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:21.906215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05985","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4f815051d94204ac9894f960c385c645defb594c7d57309004fc1191b42ea7c","sha256:5fa2c281d4dda14bf8b71a73828fb6cfee1ae82fed67f860a7df901b9f8ca017"],"state_sha256":"cb53d26181ec33e991126530169b1c2aa3dfae8b11928a4dcb7046ce1230c8f8"}