{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2KZVBOH4DPQ5HJM3SGQK7TA5AZ","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":"dd6c6f0fff42f7996ada25b73e911aadf8ba11ac4a1c06b411b07e0a2d7a927a","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-25T09:57:29Z","title_canon_sha256":"20c9fee4822792a11875bbdc36ab09d5220e435b076578cc0bc2dc82e8e426fc"},"schema_version":"1.0","source":{"id":"1503.07318","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07318","created_at":"2026-05-18T02:20:21Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07318v1","created_at":"2026-05-18T02:20:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07318","created_at":"2026-05-18T02:20:21Z"},{"alias_kind":"pith_short_12","alias_value":"2KZVBOH4DPQ5","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2KZVBOH4DPQ5HJM3","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2KZVBOH4","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:c5db6c965421fe6426efd34de3550cb8d7819ea509db5327acdecc09cf1aaeb9","target":"graph","created_at":"2026-05-18T02:20:21Z","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":"In this paper, we prove $L^p$ estimates for the fractional derivatives of solutions to elliptic fractional partial differential equations whose coefficients are $VMO$. In particular, our work extends the optimal regularity known in the second order elliptic setting to a spectrum of fractional order elliptic equations.","authors_text":"Armin Schikorra, Daniel Spector, Tien-Tsan Shieh","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-25T09:57:29Z","title":"$L^p$-theory for fractional gradient PDE with VMO coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07318","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":"sha256:60b701050ec8be2adc89a92599c835de376eb7ad5d7369163956cf3406730a3f","target":"record","created_at":"2026-05-18T02:20:21Z","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":"dd6c6f0fff42f7996ada25b73e911aadf8ba11ac4a1c06b411b07e0a2d7a927a","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-25T09:57:29Z","title_canon_sha256":"20c9fee4822792a11875bbdc36ab09d5220e435b076578cc0bc2dc82e8e426fc"},"schema_version":"1.0","source":{"id":"1503.07318","kind":"arxiv","version":1}},"canonical_sha256":"d2b350b8fc1be1d3a59b91a0afcc1d065d1507da87df8b0ad65ddd07c2685b2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2b350b8fc1be1d3a59b91a0afcc1d065d1507da87df8b0ad65ddd07c2685b2d","first_computed_at":"2026-05-18T02:20:21.437482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:21.437482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZZ9hmrUxbc0kmiqqjYY0JhW9qUeh0vXUtIqT80Kfj7YGOWgiJS7Tetsa7VwUHA+Rh6z+YxH4jcymdON5G6GBBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:21.438101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.07318","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60b701050ec8be2adc89a92599c835de376eb7ad5d7369163956cf3406730a3f","sha256:c5db6c965421fe6426efd34de3550cb8d7819ea509db5327acdecc09cf1aaeb9"],"state_sha256":"f152eea36006de2d593f29b7ca3f3c2830bf1941e3964bdf46fe208ef7892b71"}