{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:BKQYS7XDHSIMBF6IVAULX5M36Y","short_pith_number":"pith:BKQYS7XD","schema_version":"1.0","canonical_sha256":"0aa1897ee33c90c097c8a828bbf59bf6366ec3e49f7b1c2bc7fada6e05f5a853","source":{"kind":"arxiv","id":"1306.2429","version":3},"attestation_state":"computed","paper":{"title":"Estimates on elliptic equations that hold only where the gradient is large","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cyril Imbert (LAMA), Luis Silvestre","submitted_at":"2013-06-11T06:23:13Z","abstract_excerpt":"We consider a function which is a viscosity solution of a uniformly elliptic equation only at those points where the gradient is large. We prove that the H{\\\"o}lder estimates and the Harnack inequality, as in the theory of Krylov and Safonov, apply to these functions."},"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":"1306.2429","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-11T06:23:13Z","cross_cats_sorted":[],"title_canon_sha256":"84fcfbe34c9d5767a6d0b51dafce5a80c2fd7ff769d1d656c8ad364f7a87df48","abstract_canon_sha256":"1b2f0bec24ef80b7f51bc9ce409d5ae41ddd1f62d24bf50a236ab51799983b9b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:24.297517Z","signature_b64":"jtzl02Gn+0July7RmaA1QfrgVqfyoFxJqScxmxUPn6FTb5VrWTQanV0pmLlNmJMR/FbcQJ2Nvh06ANIgfBEHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0aa1897ee33c90c097c8a828bbf59bf6366ec3e49f7b1c2bc7fada6e05f5a853","last_reissued_at":"2026-05-18T01:15:24.296804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:24.296804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Estimates on elliptic equations that hold only where the gradient is large","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cyril Imbert (LAMA), Luis Silvestre","submitted_at":"2013-06-11T06:23:13Z","abstract_excerpt":"We consider a function which is a viscosity solution of a uniformly elliptic equation only at those points where the gradient is large. We prove that the H{\\\"o}lder estimates and the Harnack inequality, as in the theory of Krylov and Safonov, apply to these functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2429","kind":"arxiv","version":3},"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":"1306.2429","created_at":"2026-05-18T01:15:24.296915+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.2429v3","created_at":"2026-05-18T01:15:24.296915+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2429","created_at":"2026-05-18T01:15:24.296915+00:00"},{"alias_kind":"pith_short_12","alias_value":"BKQYS7XDHSIM","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"BKQYS7XDHSIMBF6I","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"BKQYS7XD","created_at":"2026-05-18T12:27:38.830355+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/BKQYS7XDHSIMBF6IVAULX5M36Y","json":"https://pith.science/pith/BKQYS7XDHSIMBF6IVAULX5M36Y.json","graph_json":"https://pith.science/api/pith-number/BKQYS7XDHSIMBF6IVAULX5M36Y/graph.json","events_json":"https://pith.science/api/pith-number/BKQYS7XDHSIMBF6IVAULX5M36Y/events.json","paper":"https://pith.science/paper/BKQYS7XD"},"agent_actions":{"view_html":"https://pith.science/pith/BKQYS7XDHSIMBF6IVAULX5M36Y","download_json":"https://pith.science/pith/BKQYS7XDHSIMBF6IVAULX5M36Y.json","view_paper":"https://pith.science/paper/BKQYS7XD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.2429&json=true","fetch_graph":"https://pith.science/api/pith-number/BKQYS7XDHSIMBF6IVAULX5M36Y/graph.json","fetch_events":"https://pith.science/api/pith-number/BKQYS7XDHSIMBF6IVAULX5M36Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BKQYS7XDHSIMBF6IVAULX5M36Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BKQYS7XDHSIMBF6IVAULX5M36Y/action/storage_attestation","attest_author":"https://pith.science/pith/BKQYS7XDHSIMBF6IVAULX5M36Y/action/author_attestation","sign_citation":"https://pith.science/pith/BKQYS7XDHSIMBF6IVAULX5M36Y/action/citation_signature","submit_replication":"https://pith.science/pith/BKQYS7XDHSIMBF6IVAULX5M36Y/action/replication_record"}},"created_at":"2026-05-18T01:15:24.296915+00:00","updated_at":"2026-05-18T01:15:24.296915+00:00"}