{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:KV6PNFGI6DT6UT6RTE7FCHABRM","short_pith_number":"pith:KV6PNFGI","schema_version":"1.0","canonical_sha256":"557cf694c8f0e7ea4fd1993e511c018b3fcf24503f88a3e965f17f11f8bef4a3","source":{"kind":"arxiv","id":"1309.7325","version":2},"attestation_state":"computed","paper":{"title":"A rational construction of Lie algebras of type E_7","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RA","authors_text":"Victor Petrov","submitted_at":"2013-09-27T18:36:33Z","abstract_excerpt":"We give an explicit construction of Lie algebras of type $E_7$ out of a Lie algebra of type $D_6$ with some restrictions. Up to odd degree extensions, every Lie algebra of type $E_7$ arises this way. For Lie algebras that admit a $56$-dimensional representation we provide a more symmetric construction based on an observation of Manivel; the input is seven quaternion algebras subject to some relations."},"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":"1309.7325","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-27T18:36:33Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"8e280f8ce03d784c3f701f02b84ad4fd2e1d6ada063110d6f27ed3c943ba4c5f","abstract_canon_sha256":"95ec6dcf586f7897c4e6ff1a05012d9ba66bacf0401d8048cd18f53163f66318"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:23.617970Z","signature_b64":"AyFydTQ3FOaDtcEIrTjzZ1gJNdm+en8d4N9Mo3MTTlgm4YHSdoGyJ7SLqOZOME2emdGjEBKIkljJA0l4YKrpCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"557cf694c8f0e7ea4fd1993e511c018b3fcf24503f88a3e965f17f11f8bef4a3","last_reissued_at":"2026-05-18T01:37:23.617282Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:23.617282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A rational construction of Lie algebras of type E_7","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RA","authors_text":"Victor Petrov","submitted_at":"2013-09-27T18:36:33Z","abstract_excerpt":"We give an explicit construction of Lie algebras of type $E_7$ out of a Lie algebra of type $D_6$ with some restrictions. Up to odd degree extensions, every Lie algebra of type $E_7$ arises this way. For Lie algebras that admit a $56$-dimensional representation we provide a more symmetric construction based on an observation of Manivel; the input is seven quaternion algebras subject to some relations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7325","kind":"arxiv","version":2},"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":"1309.7325","created_at":"2026-05-18T01:37:23.617402+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.7325v2","created_at":"2026-05-18T01:37:23.617402+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7325","created_at":"2026-05-18T01:37:23.617402+00:00"},{"alias_kind":"pith_short_12","alias_value":"KV6PNFGI6DT6","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"KV6PNFGI6DT6UT6R","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"KV6PNFGI","created_at":"2026-05-18T12:27:51.066281+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/KV6PNFGI6DT6UT6RTE7FCHABRM","json":"https://pith.science/pith/KV6PNFGI6DT6UT6RTE7FCHABRM.json","graph_json":"https://pith.science/api/pith-number/KV6PNFGI6DT6UT6RTE7FCHABRM/graph.json","events_json":"https://pith.science/api/pith-number/KV6PNFGI6DT6UT6RTE7FCHABRM/events.json","paper":"https://pith.science/paper/KV6PNFGI"},"agent_actions":{"view_html":"https://pith.science/pith/KV6PNFGI6DT6UT6RTE7FCHABRM","download_json":"https://pith.science/pith/KV6PNFGI6DT6UT6RTE7FCHABRM.json","view_paper":"https://pith.science/paper/KV6PNFGI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.7325&json=true","fetch_graph":"https://pith.science/api/pith-number/KV6PNFGI6DT6UT6RTE7FCHABRM/graph.json","fetch_events":"https://pith.science/api/pith-number/KV6PNFGI6DT6UT6RTE7FCHABRM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KV6PNFGI6DT6UT6RTE7FCHABRM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KV6PNFGI6DT6UT6RTE7FCHABRM/action/storage_attestation","attest_author":"https://pith.science/pith/KV6PNFGI6DT6UT6RTE7FCHABRM/action/author_attestation","sign_citation":"https://pith.science/pith/KV6PNFGI6DT6UT6RTE7FCHABRM/action/citation_signature","submit_replication":"https://pith.science/pith/KV6PNFGI6DT6UT6RTE7FCHABRM/action/replication_record"}},"created_at":"2026-05-18T01:37:23.617402+00:00","updated_at":"2026-05-18T01:37:23.617402+00:00"}