{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:GKKPYCX3E3JX4LSDCNSKSAO7KR","short_pith_number":"pith:GKKPYCX3","schema_version":"1.0","canonical_sha256":"3294fc0afb26d37e2e431364a901df5476ac18e347e379c725ed39437d58566e","source":{"kind":"arxiv","id":"1109.6773","version":3},"attestation_state":"computed","paper":{"title":"Stationary solutions of the nonlinear Schr\\\"odinger equation with fast-decay potentials concentrating around local maxima","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jean Van Schaftingen, Jonathan Di Cosmo","submitted_at":"2011-09-30T09:43:27Z","abstract_excerpt":"We study positive bound states for the equation $$- \\epsilon^2 \\Delta u + Vu = u^p, \\qquad \\text{in $\\mathbf{R}^N$}, $$ where $\\epsilon > 0$ is a real parameter, $\\frac{N}{N-2} < p < \\frac{N+2}{N-2}$ and $V$ is a nonnegative potential. Using purely variational techniques, we find solutions which concentrate at local maxima of the potential $V$ without any restriction on the potential."},"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":"1109.6773","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-30T09:43:27Z","cross_cats_sorted":[],"title_canon_sha256":"4b1756c6b34a67a1955c3951b912ff98e55c4b3cf7e0e02eca43cf1ca942903f","abstract_canon_sha256":"3c3998c2611ab7fe5c323f57972a9375ebe6cfc0f19faea9c8e6d15a5e80f277"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:43.830199Z","signature_b64":"eeCJGM2fzQMqZMoaQr/Ga0ci9O8R3jvt2a9ZSctRFInLODudq1R5TGf98xufOKZnmLHLPbPDXSCk4MUm1vCMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3294fc0afb26d37e2e431364a901df5476ac18e347e379c725ed39437d58566e","last_reissued_at":"2026-05-18T02:57:43.829735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:43.829735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stationary solutions of the nonlinear Schr\\\"odinger equation with fast-decay potentials concentrating around local maxima","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jean Van Schaftingen, Jonathan Di Cosmo","submitted_at":"2011-09-30T09:43:27Z","abstract_excerpt":"We study positive bound states for the equation $$- \\epsilon^2 \\Delta u + Vu = u^p, \\qquad \\text{in $\\mathbf{R}^N$}, $$ where $\\epsilon > 0$ is a real parameter, $\\frac{N}{N-2} < p < \\frac{N+2}{N-2}$ and $V$ is a nonnegative potential. Using purely variational techniques, we find solutions which concentrate at local maxima of the potential $V$ without any restriction on the potential."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6773","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":""},"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":"1109.6773","created_at":"2026-05-18T02:57:43.829799+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.6773v3","created_at":"2026-05-18T02:57:43.829799+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6773","created_at":"2026-05-18T02:57:43.829799+00:00"},{"alias_kind":"pith_short_12","alias_value":"GKKPYCX3E3JX","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"GKKPYCX3E3JX4LSD","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"GKKPYCX3","created_at":"2026-05-18T12:26:30.835961+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/GKKPYCX3E3JX4LSDCNSKSAO7KR","json":"https://pith.science/pith/GKKPYCX3E3JX4LSDCNSKSAO7KR.json","graph_json":"https://pith.science/api/pith-number/GKKPYCX3E3JX4LSDCNSKSAO7KR/graph.json","events_json":"https://pith.science/api/pith-number/GKKPYCX3E3JX4LSDCNSKSAO7KR/events.json","paper":"https://pith.science/paper/GKKPYCX3"},"agent_actions":{"view_html":"https://pith.science/pith/GKKPYCX3E3JX4LSDCNSKSAO7KR","download_json":"https://pith.science/pith/GKKPYCX3E3JX4LSDCNSKSAO7KR.json","view_paper":"https://pith.science/paper/GKKPYCX3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.6773&json=true","fetch_graph":"https://pith.science/api/pith-number/GKKPYCX3E3JX4LSDCNSKSAO7KR/graph.json","fetch_events":"https://pith.science/api/pith-number/GKKPYCX3E3JX4LSDCNSKSAO7KR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GKKPYCX3E3JX4LSDCNSKSAO7KR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GKKPYCX3E3JX4LSDCNSKSAO7KR/action/storage_attestation","attest_author":"https://pith.science/pith/GKKPYCX3E3JX4LSDCNSKSAO7KR/action/author_attestation","sign_citation":"https://pith.science/pith/GKKPYCX3E3JX4LSDCNSKSAO7KR/action/citation_signature","submit_replication":"https://pith.science/pith/GKKPYCX3E3JX4LSDCNSKSAO7KR/action/replication_record"}},"created_at":"2026-05-18T02:57:43.829799+00:00","updated_at":"2026-05-18T02:57:43.829799+00:00"}