{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:W73TT3EKMFHRGDTAYANRIHPHJU","short_pith_number":"pith:W73TT3EK","schema_version":"1.0","canonical_sha256":"b7f739ec8a614f130e60c01b141de74d2df8a4799c36dc00ad0a175ca7517a65","source":{"kind":"arxiv","id":"2211.15632","version":2},"attestation_state":"computed","paper":{"title":"A variational method for functionals depending on eigenvalues","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.FA"],"primary_cat":"math.AP","authors_text":"Romain Petrides","submitted_at":"2022-11-28T18:35:19Z","abstract_excerpt":"We perform a systematic variational method for functionals depending on eigenvalues of Riemannian manifolds. It is based on a new concept of Palais Smale sequences that can be constructed thanks to a generalization of classical min-max methods on $C^1$ functionals to locally-Lipschitz functionals. We prove convergence results on these Palais-Smale sequences emerging from combinations of Laplace eigenvalues or combinations of Steklov eigenvalues in dimension 2."},"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":"2211.15632","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-11-28T18:35:19Z","cross_cats_sorted":["math.DG","math.FA"],"title_canon_sha256":"f8cd612bdafe3660fb161622d2de894fbc990547683b81e01bbe72a234caed63","abstract_canon_sha256":"a60d64fb7c63f8d6d982a4f1b3220fc7de768cd12deae1cb8266110aa23687f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:18:18.038250Z","signature_b64":"aiTRP4EGN3FSRZ6is5nYpZbxZOpXs41bAfzquPKcy6ptXTbXwFLkUe2oWyPKyGBNneVahcL59GMsmKFD8c2JAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7f739ec8a614f130e60c01b141de74d2df8a4799c36dc00ad0a175ca7517a65","last_reissued_at":"2026-07-05T09:18:18.037819Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:18:18.037819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A variational method for functionals depending on eigenvalues","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.FA"],"primary_cat":"math.AP","authors_text":"Romain Petrides","submitted_at":"2022-11-28T18:35:19Z","abstract_excerpt":"We perform a systematic variational method for functionals depending on eigenvalues of Riemannian manifolds. It is based on a new concept of Palais Smale sequences that can be constructed thanks to a generalization of classical min-max methods on $C^1$ functionals to locally-Lipschitz functionals. We prove convergence results on these Palais-Smale sequences emerging from combinations of Laplace eigenvalues or combinations of Steklov eigenvalues in dimension 2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.15632","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/2211.15632/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":"2211.15632","created_at":"2026-07-05T09:18:18.037867+00:00"},{"alias_kind":"arxiv_version","alias_value":"2211.15632v2","created_at":"2026-07-05T09:18:18.037867+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.15632","created_at":"2026-07-05T09:18:18.037867+00:00"},{"alias_kind":"pith_short_12","alias_value":"W73TT3EKMFHR","created_at":"2026-07-05T09:18:18.037867+00:00"},{"alias_kind":"pith_short_16","alias_value":"W73TT3EKMFHRGDTA","created_at":"2026-07-05T09:18:18.037867+00:00"},{"alias_kind":"pith_short_8","alias_value":"W73TT3EK","created_at":"2026-07-05T09:18:18.037867+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.31869","citing_title":"Eigenvalue optimization via a first-variation formula","ref_index":75,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/W73TT3EKMFHRGDTAYANRIHPHJU","json":"https://pith.science/pith/W73TT3EKMFHRGDTAYANRIHPHJU.json","graph_json":"https://pith.science/api/pith-number/W73TT3EKMFHRGDTAYANRIHPHJU/graph.json","events_json":"https://pith.science/api/pith-number/W73TT3EKMFHRGDTAYANRIHPHJU/events.json","paper":"https://pith.science/paper/W73TT3EK"},"agent_actions":{"view_html":"https://pith.science/pith/W73TT3EKMFHRGDTAYANRIHPHJU","download_json":"https://pith.science/pith/W73TT3EKMFHRGDTAYANRIHPHJU.json","view_paper":"https://pith.science/paper/W73TT3EK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2211.15632&json=true","fetch_graph":"https://pith.science/api/pith-number/W73TT3EKMFHRGDTAYANRIHPHJU/graph.json","fetch_events":"https://pith.science/api/pith-number/W73TT3EKMFHRGDTAYANRIHPHJU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W73TT3EKMFHRGDTAYANRIHPHJU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W73TT3EKMFHRGDTAYANRIHPHJU/action/storage_attestation","attest_author":"https://pith.science/pith/W73TT3EKMFHRGDTAYANRIHPHJU/action/author_attestation","sign_citation":"https://pith.science/pith/W73TT3EKMFHRGDTAYANRIHPHJU/action/citation_signature","submit_replication":"https://pith.science/pith/W73TT3EKMFHRGDTAYANRIHPHJU/action/replication_record"}},"created_at":"2026-07-05T09:18:18.037867+00:00","updated_at":"2026-07-05T09:18:18.037867+00:00"}