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We first compute its ordinary real spectrum using the $G_2$-decomposition of $\\mathbb{O}\\otimes_{\\mathbb{R}}V$. We then analyze the octonionic right-eigenvalue problem $$ h(\\widehat w)=\\widehat w\\lambda, \\qquad \\lambda\\in\\mathbb{O}. $$ After fixing a complex slice $\\mathbb{R}\\oplus\\mathbb{R}\\widehat u\\subset\\mathbb{O}$, the problem becomes a real spectral problem for $H_{u,Q}=h-"},"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":"2606.08299","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-06-06T18:52:03Z","cross_cats_sorted":["math.DG","math.RT"],"title_canon_sha256":"46e0d113dde512cad995e58f60bd4fe3d7651c8f929625fadd16d34345c33af5","abstract_canon_sha256":"2ca2c527600c73f9a56e58e94296ea49aaaba5a19dc9018bd9320c4c47debc3c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:32.944003Z","signature_b64":"dfDFDCAYLTeUAo3JWDNiqSuuN4Yy2xiQso89E6QyVZHaTIhxVKZ8qAnLyCu5Pbli0KtESYD4C/cNe2aJvuy4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e68cdfee9fc04ddaa5b60c6f01abdf9e71100b675224246386144c960947236","last_reissued_at":"2026-06-09T01:05:32.943610Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:32.943610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Octonionic structure operator and its right spectrum","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.RT"],"primary_cat":"math.RA","authors_text":"Sergey Grigorian","submitted_at":"2026-06-06T18:52:03Z","abstract_excerpt":"We study a canonical $G_2$-equivariant operator $h:\\mathbb{O}\\otimes_{\\mathbb{R}}V\\to \\mathbb{O}\\otimes_{\\mathbb{R}}V$ defined using only octonion multiplication, where $V$ is the standard $7$-dimensional $G_2$-module. We first compute its ordinary real spectrum using the $G_2$-decomposition of $\\mathbb{O}\\otimes_{\\mathbb{R}}V$. We then analyze the octonionic right-eigenvalue problem $$ h(\\widehat w)=\\widehat w\\lambda, \\qquad \\lambda\\in\\mathbb{O}. $$ After fixing a complex slice $\\mathbb{R}\\oplus\\mathbb{R}\\widehat u\\subset\\mathbb{O}$, the problem becomes a real spectral problem for $H_{u,Q}=h-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08299","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.08299/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.08299","created_at":"2026-06-09T01:05:32.943674+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.08299v1","created_at":"2026-06-09T01:05:32.943674+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08299","created_at":"2026-06-09T01:05:32.943674+00:00"},{"alias_kind":"pith_short_12","alias_value":"LZUM37XJ7QCN","created_at":"2026-06-09T01:05:32.943674+00:00"},{"alias_kind":"pith_short_16","alias_value":"LZUM37XJ7QCN3KS3","created_at":"2026-06-09T01:05:32.943674+00:00"},{"alias_kind":"pith_short_8","alias_value":"LZUM37XJ","created_at":"2026-06-09T01:05:32.943674+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/LZUM37XJ7QCN3KS3MDDPAGV57H","json":"https://pith.science/pith/LZUM37XJ7QCN3KS3MDDPAGV57H.json","graph_json":"https://pith.science/api/pith-number/LZUM37XJ7QCN3KS3MDDPAGV57H/graph.json","events_json":"https://pith.science/api/pith-number/LZUM37XJ7QCN3KS3MDDPAGV57H/events.json","paper":"https://pith.science/paper/LZUM37XJ"},"agent_actions":{"view_html":"https://pith.science/pith/LZUM37XJ7QCN3KS3MDDPAGV57H","download_json":"https://pith.science/pith/LZUM37XJ7QCN3KS3MDDPAGV57H.json","view_paper":"https://pith.science/paper/LZUM37XJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.08299&json=true","fetch_graph":"https://pith.science/api/pith-number/LZUM37XJ7QCN3KS3MDDPAGV57H/graph.json","fetch_events":"https://pith.science/api/pith-number/LZUM37XJ7QCN3KS3MDDPAGV57H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LZUM37XJ7QCN3KS3MDDPAGV57H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LZUM37XJ7QCN3KS3MDDPAGV57H/action/storage_attestation","attest_author":"https://pith.science/pith/LZUM37XJ7QCN3KS3MDDPAGV57H/action/author_attestation","sign_citation":"https://pith.science/pith/LZUM37XJ7QCN3KS3MDDPAGV57H/action/citation_signature","submit_replication":"https://pith.science/pith/LZUM37XJ7QCN3KS3MDDPAGV57H/action/replication_record"}},"created_at":"2026-06-09T01:05:32.943674+00:00","updated_at":"2026-06-09T01:05:32.943674+00:00"}