{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:2FV3CUYGTU6MATSLMW26FYZFAZ","short_pith_number":"pith:2FV3CUYG","schema_version":"1.0","canonical_sha256":"d16bb153069d3cc04e4b65b5e2e325064a1123f3397b7fa4df668c25f0502993","source":{"kind":"arxiv","id":"1112.3159","version":1},"attestation_state":"computed","paper":{"title":"A remark on natural constraints in variational methods and an application to superlinear Schr\\\"odinger systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Benedetta Noris, Gianmaria Verzini","submitted_at":"2011-12-14T10:31:57Z","abstract_excerpt":"For a regular functional J defined on a Hilbert space X, we consider the set N of points x of X such that the projection of the gradient of J at x onto a closed linear subspace V(x) of X vanishes. We study sufficient conditions for a constrained critical point of J restricted to N to be a free critical point of J, providing a unified approach to different natural constraints known in the literature, such as the Birkhoff-Hestenes natural isoperimetric conditions and the Nehari manifold. As an application, we prove multiplicity of solutions to a class of superlinear Schr\\\"odinger systems on sing"},"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":"1112.3159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-14T10:31:57Z","cross_cats_sorted":[],"title_canon_sha256":"d3c8fd377a449f1f73f9239efa0415aa96b29e72c6eb9151915da4bfa1e53c39","abstract_canon_sha256":"a132b40fbf0816c3822d983d6115712ee80d4bf17650de2ff95b9cfccd85f957"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:19.974342Z","signature_b64":"LsxauZfvtV0fDw1I17dtDj+xnj3k23hWZNMXdV4mmcmEFPTGQcKEJFeaObzWH5//U5K1KHuzdNgJKRVWDEU5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d16bb153069d3cc04e4b65b5e2e325064a1123f3397b7fa4df668c25f0502993","last_reissued_at":"2026-05-18T04:06:19.973794Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:19.973794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A remark on natural constraints in variational methods and an application to superlinear Schr\\\"odinger systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Benedetta Noris, Gianmaria Verzini","submitted_at":"2011-12-14T10:31:57Z","abstract_excerpt":"For a regular functional J defined on a Hilbert space X, we consider the set N of points x of X such that the projection of the gradient of J at x onto a closed linear subspace V(x) of X vanishes. We study sufficient conditions for a constrained critical point of J restricted to N to be a free critical point of J, providing a unified approach to different natural constraints known in the literature, such as the Birkhoff-Hestenes natural isoperimetric conditions and the Nehari manifold. As an application, we prove multiplicity of solutions to a class of superlinear Schr\\\"odinger systems on sing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3159","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":"1112.3159","created_at":"2026-05-18T04:06:19.973880+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.3159v1","created_at":"2026-05-18T04:06:19.973880+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3159","created_at":"2026-05-18T04:06:19.973880+00:00"},{"alias_kind":"pith_short_12","alias_value":"2FV3CUYGTU6M","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"2FV3CUYGTU6MATSL","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"2FV3CUYG","created_at":"2026-05-18T12:26:18.847500+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/2FV3CUYGTU6MATSLMW26FYZFAZ","json":"https://pith.science/pith/2FV3CUYGTU6MATSLMW26FYZFAZ.json","graph_json":"https://pith.science/api/pith-number/2FV3CUYGTU6MATSLMW26FYZFAZ/graph.json","events_json":"https://pith.science/api/pith-number/2FV3CUYGTU6MATSLMW26FYZFAZ/events.json","paper":"https://pith.science/paper/2FV3CUYG"},"agent_actions":{"view_html":"https://pith.science/pith/2FV3CUYGTU6MATSLMW26FYZFAZ","download_json":"https://pith.science/pith/2FV3CUYGTU6MATSLMW26FYZFAZ.json","view_paper":"https://pith.science/paper/2FV3CUYG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.3159&json=true","fetch_graph":"https://pith.science/api/pith-number/2FV3CUYGTU6MATSLMW26FYZFAZ/graph.json","fetch_events":"https://pith.science/api/pith-number/2FV3CUYGTU6MATSLMW26FYZFAZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2FV3CUYGTU6MATSLMW26FYZFAZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2FV3CUYGTU6MATSLMW26FYZFAZ/action/storage_attestation","attest_author":"https://pith.science/pith/2FV3CUYGTU6MATSLMW26FYZFAZ/action/author_attestation","sign_citation":"https://pith.science/pith/2FV3CUYGTU6MATSLMW26FYZFAZ/action/citation_signature","submit_replication":"https://pith.science/pith/2FV3CUYGTU6MATSLMW26FYZFAZ/action/replication_record"}},"created_at":"2026-05-18T04:06:19.973880+00:00","updated_at":"2026-05-18T04:06:19.973880+00:00"}