{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:DL7VVOLAW6L5SJBBMOLQVYOO3N","short_pith_number":"pith:DL7VVOLA","schema_version":"1.0","canonical_sha256":"1aff5ab960b797d9242163970ae1cedb4a814e1fd5d148ca21509287be56223a","source":{"kind":"arxiv","id":"1405.6752","version":1},"attestation_state":"computed","paper":{"title":"On the Ambrosetti-Malchiodi-Ni Conjecture for general submanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Felipe Subiabre S\\'anchez, Fethi Mahmoudi, Wei Yao","submitted_at":"2014-05-26T22:25:58Z","abstract_excerpt":"We study positive solutions of the following semilinear equation $$\\varepsilon^2\\Delta_{\\bar g} u - V(z) u+ u^{p} =0\\,\\hbox{ on }\\,M, $$ where $(M, \\bar g )$ is a compact smooth $n$-dimensional Riemannian manifold without boundary or the Euclidean space $\\mathbb R^n$, $\\varepsilon$ is a small positive parameter, $p>1$ and $V$ is a uniformly positive smooth potential. Given $k=1,\\dots,n-1$, and $1 < p < \\frac{n+2-k}{n-2-k}$. Assuming that $K$ is a $k$-dimensional smooth, embedded compact submanifold of $M$, which is stationary and non-degenerate with respect to the functional $\\int_K V^{\\frac{p"},"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":"1405.6752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-26T22:25:58Z","cross_cats_sorted":[],"title_canon_sha256":"0b64cd7a71b9e321ab854225e6e3ebdea827233c55c4e44a240876bcd5482e36","abstract_canon_sha256":"cd657dfdccdfd53f241e7dc846845c25364750efe3d15a9fe78b2032e767e95d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:00.409613Z","signature_b64":"jrV/9PFMOCDT+xx+iyt9+IJE0KtNz4kHvIMvDLJOwjT5jw0s6e7fooFQAtecKcra7vI9DomzMAuSfZWWtOH2Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1aff5ab960b797d9242163970ae1cedb4a814e1fd5d148ca21509287be56223a","last_reissued_at":"2026-05-18T02:51:00.408976Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:00.408976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Ambrosetti-Malchiodi-Ni Conjecture for general submanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Felipe Subiabre S\\'anchez, Fethi Mahmoudi, Wei Yao","submitted_at":"2014-05-26T22:25:58Z","abstract_excerpt":"We study positive solutions of the following semilinear equation $$\\varepsilon^2\\Delta_{\\bar g} u - V(z) u+ u^{p} =0\\,\\hbox{ on }\\,M, $$ where $(M, \\bar g )$ is a compact smooth $n$-dimensional Riemannian manifold without boundary or the Euclidean space $\\mathbb R^n$, $\\varepsilon$ is a small positive parameter, $p>1$ and $V$ is a uniformly positive smooth potential. Given $k=1,\\dots,n-1$, and $1 < p < \\frac{n+2-k}{n-2-k}$. Assuming that $K$ is a $k$-dimensional smooth, embedded compact submanifold of $M$, which is stationary and non-degenerate with respect to the functional $\\int_K V^{\\frac{p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6752","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":""},"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":"1405.6752","created_at":"2026-05-18T02:51:00.409077+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.6752v1","created_at":"2026-05-18T02:51:00.409077+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6752","created_at":"2026-05-18T02:51:00.409077+00:00"},{"alias_kind":"pith_short_12","alias_value":"DL7VVOLAW6L5","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"DL7VVOLAW6L5SJBB","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"DL7VVOLA","created_at":"2026-05-18T12:28:25.294606+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/DL7VVOLAW6L5SJBBMOLQVYOO3N","json":"https://pith.science/pith/DL7VVOLAW6L5SJBBMOLQVYOO3N.json","graph_json":"https://pith.science/api/pith-number/DL7VVOLAW6L5SJBBMOLQVYOO3N/graph.json","events_json":"https://pith.science/api/pith-number/DL7VVOLAW6L5SJBBMOLQVYOO3N/events.json","paper":"https://pith.science/paper/DL7VVOLA"},"agent_actions":{"view_html":"https://pith.science/pith/DL7VVOLAW6L5SJBBMOLQVYOO3N","download_json":"https://pith.science/pith/DL7VVOLAW6L5SJBBMOLQVYOO3N.json","view_paper":"https://pith.science/paper/DL7VVOLA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.6752&json=true","fetch_graph":"https://pith.science/api/pith-number/DL7VVOLAW6L5SJBBMOLQVYOO3N/graph.json","fetch_events":"https://pith.science/api/pith-number/DL7VVOLAW6L5SJBBMOLQVYOO3N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DL7VVOLAW6L5SJBBMOLQVYOO3N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DL7VVOLAW6L5SJBBMOLQVYOO3N/action/storage_attestation","attest_author":"https://pith.science/pith/DL7VVOLAW6L5SJBBMOLQVYOO3N/action/author_attestation","sign_citation":"https://pith.science/pith/DL7VVOLAW6L5SJBBMOLQVYOO3N/action/citation_signature","submit_replication":"https://pith.science/pith/DL7VVOLAW6L5SJBBMOLQVYOO3N/action/replication_record"}},"created_at":"2026-05-18T02:51:00.409077+00:00","updated_at":"2026-05-18T02:51:00.409077+00:00"}