{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:U4LAYKLZN34WLWKWXLWAABOGNU","short_pith_number":"pith:U4LAYKLZ","schema_version":"1.0","canonical_sha256":"a7160c29796ef965d956baec0005c66d1baf8a9c22cc802665fb94a50a8ee589","source":{"kind":"arxiv","id":"2010.05847","version":2},"attestation_state":"computed","paper":{"title":"The inhomogeneous Allen--Cahn equation and the existence of prescribed-mean-curvature hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Costante Bellettini, Neshan Wickramasekera","submitted_at":"2020-10-12T16:51:54Z","abstract_excerpt":"We prove that for any given compact Riemannian manifold $N$ of dimension $n+1 \\geq 3$ and any non-negative Lipschitz function $g$ on $N$, there exists a quasi-embedded, boundaryless hypersurface $M \\subset N,$ of class $C^{2, \\alpha}$ for any $\\alpha \\in (0,1),$ such that $M$ is the image of a two-sided immersion whose mean curvature is given by $g\\nu$ for an appropriate choice of continuous unit normal $\\nu$ to the immersion; and moreover, the singular set $\\Sigma = \\overline{M} \\setminus M$ is empty if $2 \\leq n \\leq 6,$ finite if $n=7$ and satisfies ${\\mathcal H}^{n-7 + \\gamma}(\\Sigma) = 0$"},"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":"2010.05847","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-10-12T16:51:54Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"5d999e2b3172cef4981368a50c524dc9b3b44fc69645994a1904c352af36aa8d","abstract_canon_sha256":"fbe77ac60d61e609bd7c141d2a801b2844e7ccbc774cf3c3c90f11c83d196407"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:16:15.585692Z","signature_b64":"SL2Gb+ufqakIf7GYyf4AherhpyXZvasGe8n/eX2ZV6lYavbnhX02Scwi3V449SV3YWl+mxDuoW5m38LVbbyFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7160c29796ef965d956baec0005c66d1baf8a9c22cc802665fb94a50a8ee589","last_reissued_at":"2026-07-05T02:16:15.585162Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:16:15.585162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The inhomogeneous Allen--Cahn equation and the existence of prescribed-mean-curvature hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Costante Bellettini, Neshan Wickramasekera","submitted_at":"2020-10-12T16:51:54Z","abstract_excerpt":"We prove that for any given compact Riemannian manifold $N$ of dimension $n+1 \\geq 3$ and any non-negative Lipschitz function $g$ on $N$, there exists a quasi-embedded, boundaryless hypersurface $M \\subset N,$ of class $C^{2, \\alpha}$ for any $\\alpha \\in (0,1),$ such that $M$ is the image of a two-sided immersion whose mean curvature is given by $g\\nu$ for an appropriate choice of continuous unit normal $\\nu$ to the immersion; and moreover, the singular set $\\Sigma = \\overline{M} \\setminus M$ is empty if $2 \\leq n \\leq 6,$ finite if $n=7$ and satisfies ${\\mathcal H}^{n-7 + \\gamma}(\\Sigma) = 0$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.05847","kind":"arxiv","version":2},"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/2010.05847/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":"2010.05847","created_at":"2026-07-05T02:16:15.585222+00:00"},{"alias_kind":"arxiv_version","alias_value":"2010.05847v2","created_at":"2026-07-05T02:16:15.585222+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.05847","created_at":"2026-07-05T02:16:15.585222+00:00"},{"alias_kind":"pith_short_12","alias_value":"U4LAYKLZN34W","created_at":"2026-07-05T02:16:15.585222+00:00"},{"alias_kind":"pith_short_16","alias_value":"U4LAYKLZN34WLWKW","created_at":"2026-07-05T02:16:15.585222+00:00"},{"alias_kind":"pith_short_8","alias_value":"U4LAYKLZ","created_at":"2026-07-05T02:16:15.585222+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.01511","citing_title":"A Branch Set Stratification for Stationary Varifolds with Epsilon-Regularity","ref_index":4,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U4LAYKLZN34WLWKWXLWAABOGNU","json":"https://pith.science/pith/U4LAYKLZN34WLWKWXLWAABOGNU.json","graph_json":"https://pith.science/api/pith-number/U4LAYKLZN34WLWKWXLWAABOGNU/graph.json","events_json":"https://pith.science/api/pith-number/U4LAYKLZN34WLWKWXLWAABOGNU/events.json","paper":"https://pith.science/paper/U4LAYKLZ"},"agent_actions":{"view_html":"https://pith.science/pith/U4LAYKLZN34WLWKWXLWAABOGNU","download_json":"https://pith.science/pith/U4LAYKLZN34WLWKWXLWAABOGNU.json","view_paper":"https://pith.science/paper/U4LAYKLZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2010.05847&json=true","fetch_graph":"https://pith.science/api/pith-number/U4LAYKLZN34WLWKWXLWAABOGNU/graph.json","fetch_events":"https://pith.science/api/pith-number/U4LAYKLZN34WLWKWXLWAABOGNU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U4LAYKLZN34WLWKWXLWAABOGNU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U4LAYKLZN34WLWKWXLWAABOGNU/action/storage_attestation","attest_author":"https://pith.science/pith/U4LAYKLZN34WLWKWXLWAABOGNU/action/author_attestation","sign_citation":"https://pith.science/pith/U4LAYKLZN34WLWKWXLWAABOGNU/action/citation_signature","submit_replication":"https://pith.science/pith/U4LAYKLZN34WLWKWXLWAABOGNU/action/replication_record"}},"created_at":"2026-07-05T02:16:15.585222+00:00","updated_at":"2026-07-05T02:16:15.585222+00:00"}