{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:VXHFXX7BDSZQJXLASB4KSOLOTO","short_pith_number":"pith:VXHFXX7B","schema_version":"1.0","canonical_sha256":"adce5bdfe11cb304dd609078a9396e9bab7f890a88b32223889b22b1708ab439","source":{"kind":"arxiv","id":"1903.03103","version":2},"attestation_state":"computed","paper":{"title":"Minimizers of convex functionals with small degeneracy set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Connor Mooney","submitted_at":"2019-03-07T18:56:38Z","abstract_excerpt":"We study the question whether Lipschitz minimizers of $\\int F(\\nabla u)\\,dx$ in $\\mathbb{R}^n$ are $C^1$ when $F$ is strictly convex. Building on work of De Silva-Savin, we confirm the $C^1$ regularity when $D^2F$ is positive and bounded away from finitely many points that lie in a $2$-plane. We then construct a counterexample in $\\mathbb{R}^4$, where $F$ is strictly convex but $D^2F$ degenerates on the intersection of a Simons cone with $S^3$. Finally we highlight a connection between the case $n = 3$ and a result of Alexandrov in classical differential geometry, and we make a conjecture abou"},"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":"1903.03103","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-07T18:56:38Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"974d344053efe06b59388cd562e4867dee62770cc0f9e1c2a3f7f3ba870dca67","abstract_canon_sha256":"0802f1ee49bc937ffd46edcbce878ecc55354515f0b4c169ac34177be61a11cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:13.710844Z","signature_b64":"N5CSG4B7AEdph/adhOstQoMKJeBH1sT/eIcCCyEvPOxvi6YDZzNQD8X+r1zn09ZClDlYWFeg71l1o2eUzGSPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adce5bdfe11cb304dd609078a9396e9bab7f890a88b32223889b22b1708ab439","last_reissued_at":"2026-05-17T23:51:13.710380Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:13.710380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimizers of convex functionals with small degeneracy set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Connor Mooney","submitted_at":"2019-03-07T18:56:38Z","abstract_excerpt":"We study the question whether Lipschitz minimizers of $\\int F(\\nabla u)\\,dx$ in $\\mathbb{R}^n$ are $C^1$ when $F$ is strictly convex. Building on work of De Silva-Savin, we confirm the $C^1$ regularity when $D^2F$ is positive and bounded away from finitely many points that lie in a $2$-plane. We then construct a counterexample in $\\mathbb{R}^4$, where $F$ is strictly convex but $D^2F$ degenerates on the intersection of a Simons cone with $S^3$. Finally we highlight a connection between the case $n = 3$ and a result of Alexandrov in classical differential geometry, and we make a conjecture abou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03103","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":""},"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":"1903.03103","created_at":"2026-05-17T23:51:13.710453+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.03103v2","created_at":"2026-05-17T23:51:13.710453+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.03103","created_at":"2026-05-17T23:51:13.710453+00:00"},{"alias_kind":"pith_short_12","alias_value":"VXHFXX7BDSZQ","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"VXHFXX7BDSZQJXLA","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"VXHFXX7B","created_at":"2026-05-18T12:33:30.264802+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/VXHFXX7BDSZQJXLASB4KSOLOTO","json":"https://pith.science/pith/VXHFXX7BDSZQJXLASB4KSOLOTO.json","graph_json":"https://pith.science/api/pith-number/VXHFXX7BDSZQJXLASB4KSOLOTO/graph.json","events_json":"https://pith.science/api/pith-number/VXHFXX7BDSZQJXLASB4KSOLOTO/events.json","paper":"https://pith.science/paper/VXHFXX7B"},"agent_actions":{"view_html":"https://pith.science/pith/VXHFXX7BDSZQJXLASB4KSOLOTO","download_json":"https://pith.science/pith/VXHFXX7BDSZQJXLASB4KSOLOTO.json","view_paper":"https://pith.science/paper/VXHFXX7B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.03103&json=true","fetch_graph":"https://pith.science/api/pith-number/VXHFXX7BDSZQJXLASB4KSOLOTO/graph.json","fetch_events":"https://pith.science/api/pith-number/VXHFXX7BDSZQJXLASB4KSOLOTO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VXHFXX7BDSZQJXLASB4KSOLOTO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VXHFXX7BDSZQJXLASB4KSOLOTO/action/storage_attestation","attest_author":"https://pith.science/pith/VXHFXX7BDSZQJXLASB4KSOLOTO/action/author_attestation","sign_citation":"https://pith.science/pith/VXHFXX7BDSZQJXLASB4KSOLOTO/action/citation_signature","submit_replication":"https://pith.science/pith/VXHFXX7BDSZQJXLASB4KSOLOTO/action/replication_record"}},"created_at":"2026-05-17T23:51:13.710453+00:00","updated_at":"2026-05-17T23:51:13.710453+00:00"}