{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YU6FNLFM6II4E3GXAZ44XYUGUI","short_pith_number":"pith:YU6FNLFM","schema_version":"1.0","canonical_sha256":"c53c56acacf211c26cd70679cbe286a23d49e52dcdd015ed4a19d31bf2a6326f","source":{"kind":"arxiv","id":"1503.06694","version":1},"attestation_state":"computed","paper":{"title":"Singular Sets and the Lavrentiev Phenomenon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Richard Gratwick","submitted_at":"2015-03-23T15:51:44Z","abstract_excerpt":"We show that non-occurrence of the Lavrentiev phenomenon does not imply that the singular set is small. Precisely, given a compact Lebesgue null subset of the line $E$ and an arbitrary superlinearity, there exists a smooth, strictly convex Lagrangian with this superlinear growth, such that all minimizers of the associated variational problem have singular set exactly $E$, but still admit approximation in energy by smooth functions."},"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":"1503.06694","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-03-23T15:51:44Z","cross_cats_sorted":[],"title_canon_sha256":"97295d9d2770168d15439d063e99414181f8f06bc8dfbf1a91d41a0d121b1980","abstract_canon_sha256":"fd11d91b64610c4aaa3740d9bcc4110f1b5d1d2978d4d1b6f0f8a61e4250b728"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:14.644071Z","signature_b64":"xPIR3PkGLPfQ+dAKXhSwgc65X4Q6zFMKyuH4HM3P5itiXNHZqe6UKE/fc/kjl4NMFN5iCaxI/vSG8UeEutFODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c53c56acacf211c26cd70679cbe286a23d49e52dcdd015ed4a19d31bf2a6326f","last_reissued_at":"2026-05-17T23:40:14.643287Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:14.643287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Singular Sets and the Lavrentiev Phenomenon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Richard Gratwick","submitted_at":"2015-03-23T15:51:44Z","abstract_excerpt":"We show that non-occurrence of the Lavrentiev phenomenon does not imply that the singular set is small. Precisely, given a compact Lebesgue null subset of the line $E$ and an arbitrary superlinearity, there exists a smooth, strictly convex Lagrangian with this superlinear growth, such that all minimizers of the associated variational problem have singular set exactly $E$, but still admit approximation in energy by smooth functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06694","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":"1503.06694","created_at":"2026-05-17T23:40:14.643420+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.06694v1","created_at":"2026-05-17T23:40:14.643420+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06694","created_at":"2026-05-17T23:40:14.643420+00:00"},{"alias_kind":"pith_short_12","alias_value":"YU6FNLFM6II4","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"YU6FNLFM6II4E3GX","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"YU6FNLFM","created_at":"2026-05-18T12:29:52.810259+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/YU6FNLFM6II4E3GXAZ44XYUGUI","json":"https://pith.science/pith/YU6FNLFM6II4E3GXAZ44XYUGUI.json","graph_json":"https://pith.science/api/pith-number/YU6FNLFM6II4E3GXAZ44XYUGUI/graph.json","events_json":"https://pith.science/api/pith-number/YU6FNLFM6II4E3GXAZ44XYUGUI/events.json","paper":"https://pith.science/paper/YU6FNLFM"},"agent_actions":{"view_html":"https://pith.science/pith/YU6FNLFM6II4E3GXAZ44XYUGUI","download_json":"https://pith.science/pith/YU6FNLFM6II4E3GXAZ44XYUGUI.json","view_paper":"https://pith.science/paper/YU6FNLFM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.06694&json=true","fetch_graph":"https://pith.science/api/pith-number/YU6FNLFM6II4E3GXAZ44XYUGUI/graph.json","fetch_events":"https://pith.science/api/pith-number/YU6FNLFM6II4E3GXAZ44XYUGUI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YU6FNLFM6II4E3GXAZ44XYUGUI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YU6FNLFM6II4E3GXAZ44XYUGUI/action/storage_attestation","attest_author":"https://pith.science/pith/YU6FNLFM6II4E3GXAZ44XYUGUI/action/author_attestation","sign_citation":"https://pith.science/pith/YU6FNLFM6II4E3GXAZ44XYUGUI/action/citation_signature","submit_replication":"https://pith.science/pith/YU6FNLFM6II4E3GXAZ44XYUGUI/action/replication_record"}},"created_at":"2026-05-17T23:40:14.643420+00:00","updated_at":"2026-05-17T23:40:14.643420+00:00"}