{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HODYDDI37TP7DSEUUNS6RYQD34","short_pith_number":"pith:HODYDDI3","schema_version":"1.0","canonical_sha256":"3b87818d1bfcdff1c894a365e8e203df343b23a740405b9277f2b4caa84aa98c","source":{"kind":"arxiv","id":"1808.00194","version":1},"attestation_state":"computed","paper":{"title":"De Giorgi-Nash-Moser and H{\\\"o}rmander theories: new interplay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cl\\'ement Mouhot","submitted_at":"2018-08-01T07:00:43Z","abstract_excerpt":"We report on recent results and a new line of research at the crossroad of two major theories in the analysis of partial differential equations. The celebrated De Giorgi-Nash-Moser theory shows H{\\\"o}lder estimates and the Harnack inequality for uniformly elliptic or parabolic equations with rough coefficients in divergence form. The theory of hypoellipticity of H{\\\"o}rmander shows, under general \"bracket\" conditions, the regularity of solutions to partial differential equations combining first and second order derivative operators when ellipticity fails in some directions. We discuss recent e"},"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":"1808.00194","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-01T07:00:43Z","cross_cats_sorted":[],"title_canon_sha256":"2f494e0b828edc87b8b12f0f7e0b96930f7225fd28cde283540715bbacd132fd","abstract_canon_sha256":"30d119f283f697a396afcf1ec9f5eb0258aea9a4248ec9a50774719c8e819aef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:08.455522Z","signature_b64":"VSzeP5DbvvLlYfy9ZVqx1MZizPz8WtgxNDcCbNaRnJ7PR+sp4t/Jwj1b231feNvSO7WfJa+AWKcgvJC/7jtpDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b87818d1bfcdff1c894a365e8e203df343b23a740405b9277f2b4caa84aa98c","last_reissued_at":"2026-05-18T00:09:08.455103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:08.455103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"De Giorgi-Nash-Moser and H{\\\"o}rmander theories: new interplay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cl\\'ement Mouhot","submitted_at":"2018-08-01T07:00:43Z","abstract_excerpt":"We report on recent results and a new line of research at the crossroad of two major theories in the analysis of partial differential equations. The celebrated De Giorgi-Nash-Moser theory shows H{\\\"o}lder estimates and the Harnack inequality for uniformly elliptic or parabolic equations with rough coefficients in divergence form. The theory of hypoellipticity of H{\\\"o}rmander shows, under general \"bracket\" conditions, the regularity of solutions to partial differential equations combining first and second order derivative operators when ellipticity fails in some directions. We discuss recent e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00194","kind":"arxiv","version":1},"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":"1808.00194","created_at":"2026-05-18T00:09:08.455172+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.00194v1","created_at":"2026-05-18T00:09:08.455172+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.00194","created_at":"2026-05-18T00:09:08.455172+00:00"},{"alias_kind":"pith_short_12","alias_value":"HODYDDI37TP7","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HODYDDI37TP7DSEU","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HODYDDI3","created_at":"2026-05-18T12:32:28.185984+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.22956","citing_title":"Large-Scale Regularity for the Periodic Kinetic Fokker-Planck equation","ref_index":17,"is_internal_anchor":false},{"citing_arxiv_id":"2604.22944","citing_title":"Nash-Aronson Estimate for the Linear Kinetic Fokker-Planck equation","ref_index":15,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HODYDDI37TP7DSEUUNS6RYQD34","json":"https://pith.science/pith/HODYDDI37TP7DSEUUNS6RYQD34.json","graph_json":"https://pith.science/api/pith-number/HODYDDI37TP7DSEUUNS6RYQD34/graph.json","events_json":"https://pith.science/api/pith-number/HODYDDI37TP7DSEUUNS6RYQD34/events.json","paper":"https://pith.science/paper/HODYDDI3"},"agent_actions":{"view_html":"https://pith.science/pith/HODYDDI37TP7DSEUUNS6RYQD34","download_json":"https://pith.science/pith/HODYDDI37TP7DSEUUNS6RYQD34.json","view_paper":"https://pith.science/paper/HODYDDI3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.00194&json=true","fetch_graph":"https://pith.science/api/pith-number/HODYDDI37TP7DSEUUNS6RYQD34/graph.json","fetch_events":"https://pith.science/api/pith-number/HODYDDI37TP7DSEUUNS6RYQD34/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HODYDDI37TP7DSEUUNS6RYQD34/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HODYDDI37TP7DSEUUNS6RYQD34/action/storage_attestation","attest_author":"https://pith.science/pith/HODYDDI37TP7DSEUUNS6RYQD34/action/author_attestation","sign_citation":"https://pith.science/pith/HODYDDI37TP7DSEUUNS6RYQD34/action/citation_signature","submit_replication":"https://pith.science/pith/HODYDDI37TP7DSEUUNS6RYQD34/action/replication_record"}},"created_at":"2026-05-18T00:09:08.455172+00:00","updated_at":"2026-05-18T00:09:08.455172+00:00"}