{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:VREA766Z6Z2SL5UNRJFS5LYRHY","short_pith_number":"pith:VREA766Z","schema_version":"1.0","canonical_sha256":"ac480ffbd9f67525f68d8a4b2eaf113e048623b90475dd31835d6a601010a2cb","source":{"kind":"arxiv","id":"2502.07098","version":3},"attestation_state":"computed","paper":{"title":"Infinitely Many Surfaces with Prescribed Mean Curvature in the Presence of a Strictly Stable Minimal Surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jared Marx-Kuo, Pedro Gaspar","submitted_at":"2025-02-10T22:43:05Z","abstract_excerpt":"We construct infinitely many distinct hypersurfaces with prescribed mean curvature (PMC) for a large class of prescribing functions when $(M^{n+1}, g)$ is a closed smooth manifold containing a minimal surface that is strictly stable (or more generally, admits a contracting neighborhood). In particular, we construct infinitely many distinct PMCs when $H_n(M, \\mathbb{Z}_2) \\neq 0$, or if $(M, g)$ does not satisfy the Frankel property. Our construction synthesizes ideas from Song's construction of infinitely many minimal surfaces in the non-generic setting, Dey's construction of multiple constant"},"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":"2502.07098","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-02-10T22:43:05Z","cross_cats_sorted":[],"title_canon_sha256":"9b16f20746425b2bdc31d077689b00af2de49ccdf0d10f514a9bdb6571035223","abstract_canon_sha256":"49166d97d593988ea3f9676647cdbc1158c79b8d8c10de59694c962b93980298"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:57:55.744633Z","signature_b64":"zMFZv/eJZAxCkKJreGs8aXypsU1xdIpmgPoz//ENdngh93oX+E59EMUDaY/v2k6RTVYaAGa6GHTGGUw0e5alCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac480ffbd9f67525f68d8a4b2eaf113e048623b90475dd31835d6a601010a2cb","last_reissued_at":"2026-07-05T10:57:55.744127Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:57:55.744127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinitely Many Surfaces with Prescribed Mean Curvature in the Presence of a Strictly Stable Minimal Surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jared Marx-Kuo, Pedro Gaspar","submitted_at":"2025-02-10T22:43:05Z","abstract_excerpt":"We construct infinitely many distinct hypersurfaces with prescribed mean curvature (PMC) for a large class of prescribing functions when $(M^{n+1}, g)$ is a closed smooth manifold containing a minimal surface that is strictly stable (or more generally, admits a contracting neighborhood). In particular, we construct infinitely many distinct PMCs when $H_n(M, \\mathbb{Z}_2) \\neq 0$, or if $(M, g)$ does not satisfy the Frankel property. Our construction synthesizes ideas from Song's construction of infinitely many minimal surfaces in the non-generic setting, Dey's construction of multiple constant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07098","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.07098/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":"2502.07098","created_at":"2026-07-05T10:57:55.744184+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.07098v3","created_at":"2026-07-05T10:57:55.744184+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07098","created_at":"2026-07-05T10:57:55.744184+00:00"},{"alias_kind":"pith_short_12","alias_value":"VREA766Z6Z2S","created_at":"2026-07-05T10:57:55.744184+00:00"},{"alias_kind":"pith_short_16","alias_value":"VREA766Z6Z2SL5UN","created_at":"2026-07-05T10:57:55.744184+00:00"},{"alias_kind":"pith_short_8","alias_value":"VREA766Z","created_at":"2026-07-05T10:57:55.744184+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/VREA766Z6Z2SL5UNRJFS5LYRHY","json":"https://pith.science/pith/VREA766Z6Z2SL5UNRJFS5LYRHY.json","graph_json":"https://pith.science/api/pith-number/VREA766Z6Z2SL5UNRJFS5LYRHY/graph.json","events_json":"https://pith.science/api/pith-number/VREA766Z6Z2SL5UNRJFS5LYRHY/events.json","paper":"https://pith.science/paper/VREA766Z"},"agent_actions":{"view_html":"https://pith.science/pith/VREA766Z6Z2SL5UNRJFS5LYRHY","download_json":"https://pith.science/pith/VREA766Z6Z2SL5UNRJFS5LYRHY.json","view_paper":"https://pith.science/paper/VREA766Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.07098&json=true","fetch_graph":"https://pith.science/api/pith-number/VREA766Z6Z2SL5UNRJFS5LYRHY/graph.json","fetch_events":"https://pith.science/api/pith-number/VREA766Z6Z2SL5UNRJFS5LYRHY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VREA766Z6Z2SL5UNRJFS5LYRHY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VREA766Z6Z2SL5UNRJFS5LYRHY/action/storage_attestation","attest_author":"https://pith.science/pith/VREA766Z6Z2SL5UNRJFS5LYRHY/action/author_attestation","sign_citation":"https://pith.science/pith/VREA766Z6Z2SL5UNRJFS5LYRHY/action/citation_signature","submit_replication":"https://pith.science/pith/VREA766Z6Z2SL5UNRJFS5LYRHY/action/replication_record"}},"created_at":"2026-07-05T10:57:55.744184+00:00","updated_at":"2026-07-05T10:57:55.744184+00:00"}