{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SAP3R7R22MQ6GZCTFH3EONOMPI","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":"6818ee337dc7c01aa4b2925e8831ad4529e80c8a1a38e845f1a7004432f42eb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-25T23:23:36Z","title_canon_sha256":"51820e7991a97212f57cf1d05bb71b1c964217bed60e53f74cf6e51f0980eb0f"},"schema_version":"1.0","source":{"id":"1704.07929","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.07929","created_at":"2026-05-18T00:45:31Z"},{"alias_kind":"arxiv_version","alias_value":"1704.07929v1","created_at":"2026-05-18T00:45:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07929","created_at":"2026-05-18T00:45:31Z"},{"alias_kind":"pith_short_12","alias_value":"SAP3R7R22MQ6","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SAP3R7R22MQ6GZCT","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SAP3R7R2","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:b852d6012aafbbf96a87d78d4dd3f0f805fd37375e61159f4296a86ddcb0cea3","target":"graph","created_at":"2026-05-18T00:45:31Z","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 the Fermi Lectures on the obstacle problem in 1998, Caffarelli gave a proof of the mean value theorem which extends to general divergence form uniformly elliptic operators. In the general setting, the result shows that for any such operator $L$ and at any point $x_0$ in the domain, there exists a nested family of sets $\\{ D_r(x_0) \\}$ where the average over any of those sets is related to the value of the function at $x_0.$ Although it is known that the $\\{ D_r(x_0) \\}$ are nested and are comparable to balls in the sense that there exists $c, C$ depending only on $L$ such that $B_{cr}(x_0) ","authors_text":"Ashok Aryal, Ivan Blank","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-25T23:23:36Z","title":"Geometry of mean value sets for general divergence form uniformly elliptic operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07929","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":"sha256:328965035c5f9749258bbfbfa1743a041282eadc13b4bddca6d5edb9d47b94a4","target":"record","created_at":"2026-05-18T00:45:31Z","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":"6818ee337dc7c01aa4b2925e8831ad4529e80c8a1a38e845f1a7004432f42eb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-25T23:23:36Z","title_canon_sha256":"51820e7991a97212f57cf1d05bb71b1c964217bed60e53f74cf6e51f0980eb0f"},"schema_version":"1.0","source":{"id":"1704.07929","kind":"arxiv","version":1}},"canonical_sha256":"901fb8fe3ad321e3645329f64735cc7a1bdc2b1b6aa0976e9dda6ed75ab23145","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"901fb8fe3ad321e3645329f64735cc7a1bdc2b1b6aa0976e9dda6ed75ab23145","first_computed_at":"2026-05-18T00:45:31.495378Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:31.495378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s5Ml4n1vgr2/Pd5LOAm4OYb6qso6wX0FtgFlHPxvjZO2hlvGOqzv1iJBE3pWLwSH435u4Ulrmc2o8tES4V9tAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:31.495807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.07929","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:328965035c5f9749258bbfbfa1743a041282eadc13b4bddca6d5edb9d47b94a4","sha256:b852d6012aafbbf96a87d78d4dd3f0f805fd37375e61159f4296a86ddcb0cea3"],"state_sha256":"a8a7bed96855bfac4fc9c57d175dc08b378bc94ecbfaaf569294c39cce93cea8"}