{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AXTZGNKZC3D4OLHCBBD32N2OJZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"db5c82f555158c24284ab823b1978ef5fab83216b2fb88c9d1952ebcb177b6f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-16T16:20:26Z","title_canon_sha256":"d8b58ddf69b60c3d12366cd89dd0426156412d79fe0c9f7361c99b6ce9a43393"},"schema_version":"1.0","source":{"id":"1310.4435","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4435","created_at":"2026-05-18T01:24:30Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4435v1","created_at":"2026-05-18T01:24:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4435","created_at":"2026-05-18T01:24:30Z"},{"alias_kind":"pith_short_12","alias_value":"AXTZGNKZC3D4","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AXTZGNKZC3D4OLHC","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AXTZGNKZ","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:57897704422e23bb1d27aa4d385963d733cbb1ba4a8e39b07ac2a7c0d24f988f","target":"graph","created_at":"2026-05-18T01:24:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We establish local higher integrability and differentiability results for minimizers of variational integrals $$ \\mathfrak{F}(v,\\Omega) = \\int_{\\Omega} /! F(Dv(x)) \\, dx $$ over $W^{1,p}$--Sobolev mappings $u \\colon \\Omega \\subset {\\mathbb R}^n \\to {\\mathbb R}^N$ satisfying a Dirichlet boundary condition. The integrands $F$ are assumed to be autonomous, convex and of $(p,q)$ growth, but are otherwise not subjected to any further structure conditions, and we consider exponents in the range $1<p \\leq q < p^{\\ast}$, where $p^{\\ast}$ denotes the Sobolev conjugate exponent of $p$.","authors_text":"Antonia Passarelli di Napoli, Jan Kristensen, Menita Carozza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-16T16:20:26Z","title":"Regularity of minimizers of autonomous convex variational integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4435","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ea08128d1b0747f8fcae9867a8c75e3bed29c249a5499e10e2f1235325ab81ec","target":"record","created_at":"2026-05-18T01:24:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"db5c82f555158c24284ab823b1978ef5fab83216b2fb88c9d1952ebcb177b6f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-16T16:20:26Z","title_canon_sha256":"d8b58ddf69b60c3d12366cd89dd0426156412d79fe0c9f7361c99b6ce9a43393"},"schema_version":"1.0","source":{"id":"1310.4435","kind":"arxiv","version":1}},"canonical_sha256":"05e793355916c7c72ce20847bd374e4e7e732dbbd5a7b097c7414db61620fe0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05e793355916c7c72ce20847bd374e4e7e732dbbd5a7b097c7414db61620fe0e","first_computed_at":"2026-05-18T01:24:30.848663Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:30.848663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rpwdxbbf3RK9QYdPyVZ/B3gYkAM678t028jk8yUkL7zdfsHL25P6YuLsBEZmMNpQGyI8grkTV7KXrDK4iCyWDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:30.849358Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4435","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea08128d1b0747f8fcae9867a8c75e3bed29c249a5499e10e2f1235325ab81ec","sha256:57897704422e23bb1d27aa4d385963d733cbb1ba4a8e39b07ac2a7c0d24f988f"],"state_sha256":"800dc1e472d65b0742e444f50480b0d89873e8eb17c62fcbb2b7a7db6a955849"}