{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:G37SO2MXGQGDRDBMXRR4IP3YL6","short_pith_number":"pith:G37SO2MX","schema_version":"1.0","canonical_sha256":"36ff276997340c388c2cbc63c43f785f9ebba08054d5add6ea5b8ecec67003bf","source":{"kind":"arxiv","id":"1208.4221","version":1},"attestation_state":"computed","paper":{"title":"An explicit embedding of the Tits group in the compact real form of $E_6$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Robert A. Wilson","submitted_at":"2012-08-21T09:11:24Z","abstract_excerpt":"We construct a set of $27\\times 27$ unitary matrices which give an explicit embedding of the Tits group in the compact real form of the Lie group of type $E_6$. A subset gives an embedding of $\\mathrm{PSL}_2(25)$ in $F_4$."},"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":"1208.4221","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-08-21T09:11:24Z","cross_cats_sorted":[],"title_canon_sha256":"89c063cd50f6adff0934816630ded6d5e14ba1b1b2a2263b839c3647abed08e5","abstract_canon_sha256":"fbb87b2eed45a66b112ddf20693c79cd51bdbe2291fb5723a3905836dd719879"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:24.568890Z","signature_b64":"TsMz+OGdXPF7/nEsFtPal30x+FtV7mWTGOKDZg7Dq8fIwUr1z5CCmWe88nJTlyhK8IEQ0jYM+Ab3k/yMuvGlAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36ff276997340c388c2cbc63c43f785f9ebba08054d5add6ea5b8ecec67003bf","last_reissued_at":"2026-05-18T03:48:24.568293Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:24.568293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An explicit embedding of the Tits group in the compact real form of $E_6$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Robert A. Wilson","submitted_at":"2012-08-21T09:11:24Z","abstract_excerpt":"We construct a set of $27\\times 27$ unitary matrices which give an explicit embedding of the Tits group in the compact real form of the Lie group of type $E_6$. A subset gives an embedding of $\\mathrm{PSL}_2(25)$ in $F_4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4221","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":"1208.4221","created_at":"2026-05-18T03:48:24.568391+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.4221v1","created_at":"2026-05-18T03:48:24.568391+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4221","created_at":"2026-05-18T03:48:24.568391+00:00"},{"alias_kind":"pith_short_12","alias_value":"G37SO2MXGQGD","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"G37SO2MXGQGDRDBM","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"G37SO2MX","created_at":"2026-05-18T12:27:06.952714+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/G37SO2MXGQGDRDBMXRR4IP3YL6","json":"https://pith.science/pith/G37SO2MXGQGDRDBMXRR4IP3YL6.json","graph_json":"https://pith.science/api/pith-number/G37SO2MXGQGDRDBMXRR4IP3YL6/graph.json","events_json":"https://pith.science/api/pith-number/G37SO2MXGQGDRDBMXRR4IP3YL6/events.json","paper":"https://pith.science/paper/G37SO2MX"},"agent_actions":{"view_html":"https://pith.science/pith/G37SO2MXGQGDRDBMXRR4IP3YL6","download_json":"https://pith.science/pith/G37SO2MXGQGDRDBMXRR4IP3YL6.json","view_paper":"https://pith.science/paper/G37SO2MX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.4221&json=true","fetch_graph":"https://pith.science/api/pith-number/G37SO2MXGQGDRDBMXRR4IP3YL6/graph.json","fetch_events":"https://pith.science/api/pith-number/G37SO2MXGQGDRDBMXRR4IP3YL6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G37SO2MXGQGDRDBMXRR4IP3YL6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G37SO2MXGQGDRDBMXRR4IP3YL6/action/storage_attestation","attest_author":"https://pith.science/pith/G37SO2MXGQGDRDBMXRR4IP3YL6/action/author_attestation","sign_citation":"https://pith.science/pith/G37SO2MXGQGDRDBMXRR4IP3YL6/action/citation_signature","submit_replication":"https://pith.science/pith/G37SO2MXGQGDRDBMXRR4IP3YL6/action/replication_record"}},"created_at":"2026-05-18T03:48:24.568391+00:00","updated_at":"2026-05-18T03:48:24.568391+00:00"}