{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:HF3K4CSPSGQ3ZLVISVVAKY5SRG","short_pith_number":"pith:HF3K4CSP","schema_version":"1.0","canonical_sha256":"3976ae0a4f91a1bcaea8956a0563b2898ee5f30905f9c8333ba8a0346e4e767c","source":{"kind":"arxiv","id":"1901.07252","version":1},"attestation_state":"computed","paper":{"title":"Gradings of Lie algebras, magical spin geometries and matrix factorizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Laurent Manivel (IMT), Roland Abuaf (IF)","submitted_at":"2019-01-22T10:45:42Z","abstract_excerpt":"We describe a remarkable rank fourtenn matrix factorization of the octic Spin(14)-invariant polynomial on either of its half-spin representations. We observe that this representation can be, in a suitable sense, identified with a tensor product of two octonion algebras. Moreover the matrix factorisation can be deduced from a particular Z-grading of the exceptional Lie algebra $\\mathfrak{e}_8$. Intriguingly, the whole story can be extended to the whole Freudenthal-Tits magic square and yields matrix factorizations on other spin representations, as well as for the degree seven invariant on the s"},"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":"1901.07252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-01-22T10:45:42Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"0420cdcba6c263019d36194f828f6bfaac358966e37dc7ac88caedfe4d3869a7","abstract_canon_sha256":"183a9d30d6b4df5533cc96155bcb342e6f9fc2ec8c0245df7e62f654652914da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:47.624073Z","signature_b64":"UnMaWM407Z/YWydF85HfdoGgF4as0EHCaLZtg8WKtYsv6GBgdqgZkqv3zacUuET7H3nEf02KpdwbZxKZmr9PAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3976ae0a4f91a1bcaea8956a0563b2898ee5f30905f9c8333ba8a0346e4e767c","last_reissued_at":"2026-05-17T23:55:47.623427Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:47.623427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gradings of Lie algebras, magical spin geometries and matrix factorizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Laurent Manivel (IMT), Roland Abuaf (IF)","submitted_at":"2019-01-22T10:45:42Z","abstract_excerpt":"We describe a remarkable rank fourtenn matrix factorization of the octic Spin(14)-invariant polynomial on either of its half-spin representations. We observe that this representation can be, in a suitable sense, identified with a tensor product of two octonion algebras. Moreover the matrix factorisation can be deduced from a particular Z-grading of the exceptional Lie algebra $\\mathfrak{e}_8$. Intriguingly, the whole story can be extended to the whole Freudenthal-Tits magic square and yields matrix factorizations on other spin representations, as well as for the degree seven invariant on the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07252","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":"1901.07252","created_at":"2026-05-17T23:55:47.623524+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.07252v1","created_at":"2026-05-17T23:55:47.623524+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07252","created_at":"2026-05-17T23:55:47.623524+00:00"},{"alias_kind":"pith_short_12","alias_value":"HF3K4CSPSGQ3","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"HF3K4CSPSGQ3ZLVI","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"HF3K4CSP","created_at":"2026-05-18T12:33:18.533446+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/HF3K4CSPSGQ3ZLVISVVAKY5SRG","json":"https://pith.science/pith/HF3K4CSPSGQ3ZLVISVVAKY5SRG.json","graph_json":"https://pith.science/api/pith-number/HF3K4CSPSGQ3ZLVISVVAKY5SRG/graph.json","events_json":"https://pith.science/api/pith-number/HF3K4CSPSGQ3ZLVISVVAKY5SRG/events.json","paper":"https://pith.science/paper/HF3K4CSP"},"agent_actions":{"view_html":"https://pith.science/pith/HF3K4CSPSGQ3ZLVISVVAKY5SRG","download_json":"https://pith.science/pith/HF3K4CSPSGQ3ZLVISVVAKY5SRG.json","view_paper":"https://pith.science/paper/HF3K4CSP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.07252&json=true","fetch_graph":"https://pith.science/api/pith-number/HF3K4CSPSGQ3ZLVISVVAKY5SRG/graph.json","fetch_events":"https://pith.science/api/pith-number/HF3K4CSPSGQ3ZLVISVVAKY5SRG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HF3K4CSPSGQ3ZLVISVVAKY5SRG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HF3K4CSPSGQ3ZLVISVVAKY5SRG/action/storage_attestation","attest_author":"https://pith.science/pith/HF3K4CSPSGQ3ZLVISVVAKY5SRG/action/author_attestation","sign_citation":"https://pith.science/pith/HF3K4CSPSGQ3ZLVISVVAKY5SRG/action/citation_signature","submit_replication":"https://pith.science/pith/HF3K4CSPSGQ3ZLVISVVAKY5SRG/action/replication_record"}},"created_at":"2026-05-17T23:55:47.623524+00:00","updated_at":"2026-05-17T23:55:47.623524+00:00"}