{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:NFCYDRWJ2JD6L5SBHRRIFWYYN2","short_pith_number":"pith:NFCYDRWJ","schema_version":"1.0","canonical_sha256":"694581c6c9d247e5f6413c6282db186e9c817d4e27b1e547d6a870f24f2c7e4f","source":{"kind":"arxiv","id":"2402.10656","version":4},"attestation_state":"computed","paper":{"title":"Local interpolation techniques for higher-order singular perturbations of non-convex functionals: free-discontinuity problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Margherita Solci","submitted_at":"2024-02-16T13:05:47Z","abstract_excerpt":"We develop a general approach, using local interpolation inequalities, to non-convex integral functionals depending on the gradient with a singular perturbation by derivatives of order $k\\ge 2$. When applied to functionals giving rise to free-discontinuity energies, such methods permit to change boundary values for derivatives up to order $k-1$ in problems defining density functions for the jump part, thus allowing to prove optimal-profile formulas, and to deduce compactness and lower bounds. As an application, we prove that for $k$-th order perturbations of energies depending on the gradient "},"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":"2402.10656","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-02-16T13:05:47Z","cross_cats_sorted":[],"title_canon_sha256":"d5c582c7d52200aaaa8e61100b20a3be750760ed5705f0627c2d3585c02dd337","abstract_canon_sha256":"15711cd0b4f202d6b5f6948c92b3deeaed0f3c551715bff8fb5f83d3b17318f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:43:05.927955Z","signature_b64":"4gX24zwGeRCCLG0P9Ag5SqTHXLMzJ/V6QXq2XwjQFiy+AL3Xy6fQLVJJ8UoTmF4/5kDX5d2GYvBu7IOKXsuHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"694581c6c9d247e5f6413c6282db186e9c817d4e27b1e547d6a870f24f2c7e4f","last_reissued_at":"2026-07-05T11:43:05.927513Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:43:05.927513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local interpolation techniques for higher-order singular perturbations of non-convex functionals: free-discontinuity problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Margherita Solci","submitted_at":"2024-02-16T13:05:47Z","abstract_excerpt":"We develop a general approach, using local interpolation inequalities, to non-convex integral functionals depending on the gradient with a singular perturbation by derivatives of order $k\\ge 2$. When applied to functionals giving rise to free-discontinuity energies, such methods permit to change boundary values for derivatives up to order $k-1$ in problems defining density functions for the jump part, thus allowing to prove optimal-profile formulas, and to deduce compactness and lower bounds. As an application, we prove that for $k$-th order perturbations of energies depending on the gradient "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.10656","kind":"arxiv","version":4},"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/2402.10656/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":"2402.10656","created_at":"2026-07-05T11:43:05.927570+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.10656v4","created_at":"2026-07-05T11:43:05.927570+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.10656","created_at":"2026-07-05T11:43:05.927570+00:00"},{"alias_kind":"pith_short_12","alias_value":"NFCYDRWJ2JD6","created_at":"2026-07-05T11:43:05.927570+00:00"},{"alias_kind":"pith_short_16","alias_value":"NFCYDRWJ2JD6L5SB","created_at":"2026-07-05T11:43:05.927570+00:00"},{"alias_kind":"pith_short_8","alias_value":"NFCYDRWJ","created_at":"2026-07-05T11:43:05.927570+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.05270","citing_title":"Symmetry breaking for local minimizers of a free discontinuity problem","ref_index":26,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NFCYDRWJ2JD6L5SBHRRIFWYYN2","json":"https://pith.science/pith/NFCYDRWJ2JD6L5SBHRRIFWYYN2.json","graph_json":"https://pith.science/api/pith-number/NFCYDRWJ2JD6L5SBHRRIFWYYN2/graph.json","events_json":"https://pith.science/api/pith-number/NFCYDRWJ2JD6L5SBHRRIFWYYN2/events.json","paper":"https://pith.science/paper/NFCYDRWJ"},"agent_actions":{"view_html":"https://pith.science/pith/NFCYDRWJ2JD6L5SBHRRIFWYYN2","download_json":"https://pith.science/pith/NFCYDRWJ2JD6L5SBHRRIFWYYN2.json","view_paper":"https://pith.science/paper/NFCYDRWJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.10656&json=true","fetch_graph":"https://pith.science/api/pith-number/NFCYDRWJ2JD6L5SBHRRIFWYYN2/graph.json","fetch_events":"https://pith.science/api/pith-number/NFCYDRWJ2JD6L5SBHRRIFWYYN2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NFCYDRWJ2JD6L5SBHRRIFWYYN2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NFCYDRWJ2JD6L5SBHRRIFWYYN2/action/storage_attestation","attest_author":"https://pith.science/pith/NFCYDRWJ2JD6L5SBHRRIFWYYN2/action/author_attestation","sign_citation":"https://pith.science/pith/NFCYDRWJ2JD6L5SBHRRIFWYYN2/action/citation_signature","submit_replication":"https://pith.science/pith/NFCYDRWJ2JD6L5SBHRRIFWYYN2/action/replication_record"}},"created_at":"2026-07-05T11:43:05.927570+00:00","updated_at":"2026-07-05T11:43:05.927570+00:00"}