{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ZLQOPWYPNNZEMLBD7473O3TDQB","short_pith_number":"pith:ZLQOPWYP","schema_version":"1.0","canonical_sha256":"cae0e7db0f6b72462c23ff3fb76e63806303a754641f1ee16f0a3a36889519e8","source":{"kind":"arxiv","id":"1407.8046","version":3},"attestation_state":"computed","paper":{"title":"Deformations of homogeneous associative submanifolds in nearly parallel $G_{2}$-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kotaro Kawai","submitted_at":"2014-07-30T13:58:21Z","abstract_excerpt":"A nearly parallel $G_{2}$-manifold $Y$ is a Riemannian 7-manifold whose cone $C(Y) = \\mathbb{R}_{>0} \\times Y$ has the holonomy group contained in ${\\rm Spin(7)}$. In other words, it is a spin 7-manifold with a real Killing spinor. We have a special class of calibrated submanifolds called Cayley submanifolds in $C(Y)$. An associative submanifold in $Y$ is a minimal 3-submanifold whose cone is Cayley. We study its deformations, namely, Cayley cone deformations, explicitly when it is homogeneous in the 7-sphere $S^{7}$."},"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":"1407.8046","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-30T13:58:21Z","cross_cats_sorted":[],"title_canon_sha256":"cc1b30107d1b80e7e27893e28f436dd00725b6a200ad71d264c61f96d07c8ecf","abstract_canon_sha256":"ff197c1ff8ad8baa9e844e72cc46c377eb696802a9378a6e15d8e3d1dfdc71f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:25.028075Z","signature_b64":"NWgnlO4FOh0l+ncv5x52qkOOiSjWKNcLkHX+Bsq5VoIQJX9VE426ED9ObLsXKaxuLjxhn/8zOIro7nArLFmnBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cae0e7db0f6b72462c23ff3fb76e63806303a754641f1ee16f0a3a36889519e8","last_reissued_at":"2026-05-18T00:15:25.027497Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:25.027497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deformations of homogeneous associative submanifolds in nearly parallel $G_{2}$-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kotaro Kawai","submitted_at":"2014-07-30T13:58:21Z","abstract_excerpt":"A nearly parallel $G_{2}$-manifold $Y$ is a Riemannian 7-manifold whose cone $C(Y) = \\mathbb{R}_{>0} \\times Y$ has the holonomy group contained in ${\\rm Spin(7)}$. In other words, it is a spin 7-manifold with a real Killing spinor. We have a special class of calibrated submanifolds called Cayley submanifolds in $C(Y)$. An associative submanifold in $Y$ is a minimal 3-submanifold whose cone is Cayley. We study its deformations, namely, Cayley cone deformations, explicitly when it is homogeneous in the 7-sphere $S^{7}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8046","kind":"arxiv","version":3},"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":"1407.8046","created_at":"2026-05-18T00:15:25.027604+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.8046v3","created_at":"2026-05-18T00:15:25.027604+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.8046","created_at":"2026-05-18T00:15:25.027604+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZLQOPWYPNNZE","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZLQOPWYPNNZEMLBD","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZLQOPWYP","created_at":"2026-05-18T12:28:59.999130+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/ZLQOPWYPNNZEMLBD7473O3TDQB","json":"https://pith.science/pith/ZLQOPWYPNNZEMLBD7473O3TDQB.json","graph_json":"https://pith.science/api/pith-number/ZLQOPWYPNNZEMLBD7473O3TDQB/graph.json","events_json":"https://pith.science/api/pith-number/ZLQOPWYPNNZEMLBD7473O3TDQB/events.json","paper":"https://pith.science/paper/ZLQOPWYP"},"agent_actions":{"view_html":"https://pith.science/pith/ZLQOPWYPNNZEMLBD7473O3TDQB","download_json":"https://pith.science/pith/ZLQOPWYPNNZEMLBD7473O3TDQB.json","view_paper":"https://pith.science/paper/ZLQOPWYP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.8046&json=true","fetch_graph":"https://pith.science/api/pith-number/ZLQOPWYPNNZEMLBD7473O3TDQB/graph.json","fetch_events":"https://pith.science/api/pith-number/ZLQOPWYPNNZEMLBD7473O3TDQB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZLQOPWYPNNZEMLBD7473O3TDQB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZLQOPWYPNNZEMLBD7473O3TDQB/action/storage_attestation","attest_author":"https://pith.science/pith/ZLQOPWYPNNZEMLBD7473O3TDQB/action/author_attestation","sign_citation":"https://pith.science/pith/ZLQOPWYPNNZEMLBD7473O3TDQB/action/citation_signature","submit_replication":"https://pith.science/pith/ZLQOPWYPNNZEMLBD7473O3TDQB/action/replication_record"}},"created_at":"2026-05-18T00:15:25.027604+00:00","updated_at":"2026-05-18T00:15:25.027604+00:00"}