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These include the invariant Einstein metrics on the Aloff-Wallach spaces $N_{k, l}={\\rm SU}(3)/i_{k, l}(S^{1})$ (which are all nearly ${\\rm G}_2$ except $N_{1,0}$), and Sasaki Einstein circle bundles over certain irreducible Hermitian symmetric spaces. We also prove the instability of most of the simply connected non-symmetric compact homogeneous Einstein spaces of dimensions $5, 6, $ and $7$, including the strict nearly K\\\"ahler ones (except ${\\rm G}_2/{\\rm SU}(3)$)."},"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":"1810.04526","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-10T13:40:23Z","cross_cats_sorted":[],"title_canon_sha256":"420de4e66ea9ea2547c328058f65c1e17f5769c93008a3e7905f1b87505fc8dc","abstract_canon_sha256":"a12968cd83566954226d714c34f7705f22a33ba4f36aed42fa7f973f0d4f017c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:52.974522Z","signature_b64":"+KUko6um7YouYrGkTTxkZAXASbkdyLOPf1GDEu3VNM7exxQEzY7CJqEPyGZDuoxmPiV2SSq7V1/IsRSM28xLCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17b1e648e0ea21e1bbc5bdc3e0b17d3b366bf45f29b036f89bb4a9f7f01be5f7","last_reissued_at":"2026-05-18T00:02:52.973826Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:52.973826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Instability of some Riemannian manifolds with real Killing spinors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Changliang Wang, M. 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