{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:432TRPOHDHRJBJEESQPRILBAX7","short_pith_number":"pith:432TRPOH","schema_version":"1.0","canonical_sha256":"e6f538bdc719e290a484941f142c20bfcd585a070d9de740fc3a422ada91f934","source":{"kind":"arxiv","id":"2103.16892","version":1},"attestation_state":"computed","paper":{"title":"The Existence of G-Invariant constant mean curvature Hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Tongrui Wang, Zhiang Wu","submitted_at":"2021-03-31T08:21:31Z","abstract_excerpt":"In this paper, we consider a closed Riemannian manifold $M^{n+1}$ with dimension $3\\leq n+1\\leq 7$, and a compact Lie group $G$ acting as isometries on $M$ with cohomogeneity at least $3$. Suppose the union of non-principal orbits $M\\setminus M^{reg}$ is a smooth embedded submanifold of $M$ without boundary and ${\\rm dim}(M\\setminus M^{reg})\\leq n-2 $. Then for any $c\\in\\mathbb{R}$, we show the existence of a nontrivial, smooth, closed, $G$-equivariant almost embedded $G$-invariant hypersurface $\\Sigma^n$ of constant mean curvature $c$."},"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":"2103.16892","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-03-31T08:21:31Z","cross_cats_sorted":[],"title_canon_sha256":"67835caa043b6564c213bb83338d5ed16ea07756a3fc38f62b68d24a0e8b382d","abstract_canon_sha256":"364a7b6b212638354425a42e94a4bdb13cd2e10d759b401e4ebe9a906a03339e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:28:09.973810Z","signature_b64":"uiswhYYvu0GC5MgH5vC+6kI2c1etZufXojZMe6tfHbjaEWL1/rraT2JFJfLbneJhR1tBLR8/kZhUIF/kaYgJBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6f538bdc719e290a484941f142c20bfcd585a070d9de740fc3a422ada91f934","last_reissued_at":"2026-07-05T02:28:09.973403Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:28:09.973403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Existence of G-Invariant constant mean curvature Hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Tongrui Wang, Zhiang Wu","submitted_at":"2021-03-31T08:21:31Z","abstract_excerpt":"In this paper, we consider a closed Riemannian manifold $M^{n+1}$ with dimension $3\\leq n+1\\leq 7$, and a compact Lie group $G$ acting as isometries on $M$ with cohomogeneity at least $3$. Suppose the union of non-principal orbits $M\\setminus M^{reg}$ is a smooth embedded submanifold of $M$ without boundary and ${\\rm dim}(M\\setminus M^{reg})\\leq n-2 $. Then for any $c\\in\\mathbb{R}$, we show the existence of a nontrivial, smooth, closed, $G$-equivariant almost embedded $G$-invariant hypersurface $\\Sigma^n$ of constant mean curvature $c$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.16892","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/2103.16892/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":"2103.16892","created_at":"2026-07-05T02:28:09.973461+00:00"},{"alias_kind":"arxiv_version","alias_value":"2103.16892v1","created_at":"2026-07-05T02:28:09.973461+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.16892","created_at":"2026-07-05T02:28:09.973461+00:00"},{"alias_kind":"pith_short_12","alias_value":"432TRPOHDHRJ","created_at":"2026-07-05T02:28:09.973461+00:00"},{"alias_kind":"pith_short_16","alias_value":"432TRPOHDHRJBJEE","created_at":"2026-07-05T02:28:09.973461+00:00"},{"alias_kind":"pith_short_8","alias_value":"432TRPOH","created_at":"2026-07-05T02:28:09.973461+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/432TRPOHDHRJBJEESQPRILBAX7","json":"https://pith.science/pith/432TRPOHDHRJBJEESQPRILBAX7.json","graph_json":"https://pith.science/api/pith-number/432TRPOHDHRJBJEESQPRILBAX7/graph.json","events_json":"https://pith.science/api/pith-number/432TRPOHDHRJBJEESQPRILBAX7/events.json","paper":"https://pith.science/paper/432TRPOH"},"agent_actions":{"view_html":"https://pith.science/pith/432TRPOHDHRJBJEESQPRILBAX7","download_json":"https://pith.science/pith/432TRPOHDHRJBJEESQPRILBAX7.json","view_paper":"https://pith.science/paper/432TRPOH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2103.16892&json=true","fetch_graph":"https://pith.science/api/pith-number/432TRPOHDHRJBJEESQPRILBAX7/graph.json","fetch_events":"https://pith.science/api/pith-number/432TRPOHDHRJBJEESQPRILBAX7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/432TRPOHDHRJBJEESQPRILBAX7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/432TRPOHDHRJBJEESQPRILBAX7/action/storage_attestation","attest_author":"https://pith.science/pith/432TRPOHDHRJBJEESQPRILBAX7/action/author_attestation","sign_citation":"https://pith.science/pith/432TRPOHDHRJBJEESQPRILBAX7/action/citation_signature","submit_replication":"https://pith.science/pith/432TRPOHDHRJBJEESQPRILBAX7/action/replication_record"}},"created_at":"2026-07-05T02:28:09.973461+00:00","updated_at":"2026-07-05T02:28:09.973461+00:00"}