{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZOZFMPUEFO44CWVWO55YKE23HC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4d2fbe41f4221296b2e6a525abd6ecbf3b85a89fb5df4652da4aca02f0ee5f95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-07T19:12:34Z","title_canon_sha256":"0dc6d4fa1cb09493e14f031723e9f5d50fc147a4bd760c11ff3a6173c12e26b9"},"schema_version":"1.0","source":{"id":"1703.02560","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.02560","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"arxiv_version","alias_value":"1703.02560v5","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02560","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"pith_short_12","alias_value":"ZOZFMPUEFO44","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZOZFMPUEFO44CWVW","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZOZFMPUE","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:26f88cf78368df30e84a30ae1a5c745ac2012730b09f24f4e54c6efd58e17dfb","target":"graph","created_at":"2026-05-17T23:48:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We define a Gauss map $\\gamma:M\\rightarrow\\mathbb{S}^{6}$ of an oriented hypersurface $M$ of the unit sphere $\\mathbb{S}^{7}$ and prove that $\\gamma$ is harmonic if and only if $M$ has CMC. Results on the geometry and topology of CMC hypersurfaces of $\\mathbb{S}^{7}$, under hypothesis on the image of $\\gamma$, are then obtained. By a Hopf symmetrization process we define a Gauss map for hypersurfaces of $\\mathbb{CP}^{3}$ and obtain similar results for CMC hypersurfaces of this space.","authors_text":"Eduardo Longa, Fidelis Bittencourt, Jaime Ripoll, Pedro Fusieger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-07T19:12:34Z","title":"Gauss map and the topology of constant mean curvature hypersurfaces of $\\mathbb{S}^{7}$ and $\\mathbb{CP}^{3}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02560","kind":"arxiv","version":5},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:acdcc3955488837b2944f87be6532a74e4301eb7dde10b567e75ed7773357ab5","target":"record","created_at":"2026-05-17T23:48:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4d2fbe41f4221296b2e6a525abd6ecbf3b85a89fb5df4652da4aca02f0ee5f95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-07T19:12:34Z","title_canon_sha256":"0dc6d4fa1cb09493e14f031723e9f5d50fc147a4bd760c11ff3a6173c12e26b9"},"schema_version":"1.0","source":{"id":"1703.02560","kind":"arxiv","version":5}},"canonical_sha256":"cbb2563e842bb9c15ab6777b85135b38b2652a19c43865f1729ba5d569ce33ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbb2563e842bb9c15ab6777b85135b38b2652a19c43865f1729ba5d569ce33ac","first_computed_at":"2026-05-17T23:48:06.961144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:06.961144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9Oex+RJfJ5aIMQ5slL5IwVKa/SzRYC4RBnqQJhCz7QwnU4fc3zcYWGDJ6T9NtVwN6MwDu/cLPOyKHo8BAeteBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:06.961647Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.02560","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acdcc3955488837b2944f87be6532a74e4301eb7dde10b567e75ed7773357ab5","sha256:26f88cf78368df30e84a30ae1a5c745ac2012730b09f24f4e54c6efd58e17dfb"],"state_sha256":"59ce2a6290f442455a28fa0a5fae1601390fa15fd144f5e8a9e6f9d3b5f288b2"}