{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MGO3H2YCA7CELTZPFDQR4ICMLJ","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":"a11d680edf536f41dfa50e0edd2110cf3d7a51b33cf63ca2980cc7ef54590f6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-22T08:26:50Z","title_canon_sha256":"f1137f0e4e00c99aeff8b4e3b35cf9d26c92186516ef0b9fbe664966b57cb589"},"schema_version":"1.0","source":{"id":"1707.07121","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07121","created_at":"2026-05-18T00:24:30Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07121v6","created_at":"2026-05-18T00:24:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07121","created_at":"2026-05-18T00:24:30Z"},{"alias_kind":"pith_short_12","alias_value":"MGO3H2YCA7CE","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MGO3H2YCA7CELTZP","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MGO3H2YC","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:700f26c724f2a9dfdf3d99df3fba29d8e119f60d4023d2999873a556d9fe2edc","target":"graph","created_at":"2026-05-18T00:24:30Z","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":"For a $C^2$ function $u$ and an elliptic operator $L$, we prove a quantitative estimate for the derivative $du$ in terms of local bounds on $u$ and $Lu$. An integral version of this estimate is then used to derive a condition for the zero-mean value property of $\\Delta u$. An extension to differential forms is also given. Our approach is probabilistic and could easily be adapted to other settings.","authors_text":"Anton Thalmaier, James Thompson, Li-Juan Cheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-22T08:26:50Z","title":"Quantitative $C^1$-estimates by Bismut formulae"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07121","kind":"arxiv","version":6},"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:cd5f2e31a2c67bb9ca98f2d5957591b586fc29e7c49f373a749c5736d7b886d5","target":"record","created_at":"2026-05-18T00:24:30Z","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":"a11d680edf536f41dfa50e0edd2110cf3d7a51b33cf63ca2980cc7ef54590f6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-22T08:26:50Z","title_canon_sha256":"f1137f0e4e00c99aeff8b4e3b35cf9d26c92186516ef0b9fbe664966b57cb589"},"schema_version":"1.0","source":{"id":"1707.07121","kind":"arxiv","version":6}},"canonical_sha256":"619db3eb0207c445cf2f28e11e204c5a6621080f3749c441b39f4820fad1309b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"619db3eb0207c445cf2f28e11e204c5a6621080f3749c441b39f4820fad1309b","first_computed_at":"2026-05-18T00:24:30.979539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:30.979539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oETxYdnpiTYIwwoIaFM9NQTubyaUZyD9gOEVR7AC6z5qdo2oTtuhu5mVtbovnm3ZpryOD1Tll85q7l3gWdntBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:30.980807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.07121","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd5f2e31a2c67bb9ca98f2d5957591b586fc29e7c49f373a749c5736d7b886d5","sha256:700f26c724f2a9dfdf3d99df3fba29d8e119f60d4023d2999873a556d9fe2edc"],"state_sha256":"10d3de3fc887fd18071af678f771b1bdc244cfdc9a4fe93d549613b8084a9e60"}