{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:YTCADJ4SRSNWVBHDONNA36YRIQ","short_pith_number":"pith:YTCADJ4S","schema_version":"1.0","canonical_sha256":"c4c401a7928c9b6a84e3735a0dfb114436551b2fae0ac37603eafc4f62feac25","source":{"kind":"arxiv","id":"1806.03179","version":1},"attestation_state":"computed","paper":{"title":"Quasi-monotonicity formulas for classical obstacle problems with Sobolev coefficients and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Emanuele Spadaro, Francesco Geraci, Matteo Focardi","submitted_at":"2018-06-08T14:25:33Z","abstract_excerpt":"We establish Weiss' and Monneau's type quasi-monotonicity formulas for quadratic energies having matrix of coefficients in a Sobolev space $W^{1,p}$, $p>n$, and provide an application to the corresponding free boundary analysis for the related classical obstacle problems."},"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":"1806.03179","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-08T14:25:33Z","cross_cats_sorted":[],"title_canon_sha256":"928d60c81e9be3af44b04d75a3a5f4b84a1f9197193b4847ed5c201dca0faaca","abstract_canon_sha256":"147e470041fc0428232997852486a024b8f47ddf154baf2142a1f2b21080d4bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:49.396798Z","signature_b64":"9tYxqBpehqjrtp8HGr5YF9v4vi2Q2XSEgVvVkMxRHpavQFPSTmXlQsegmcGVbX3xNAJ9ykAK3KFhg1ox+SrADw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4c401a7928c9b6a84e3735a0dfb114436551b2fae0ac37603eafc4f62feac25","last_reissued_at":"2026-05-18T00:13:49.396079Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:49.396079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasi-monotonicity formulas for classical obstacle problems with Sobolev coefficients and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Emanuele Spadaro, Francesco Geraci, Matteo Focardi","submitted_at":"2018-06-08T14:25:33Z","abstract_excerpt":"We establish Weiss' and Monneau's type quasi-monotonicity formulas for quadratic energies having matrix of coefficients in a Sobolev space $W^{1,p}$, $p>n$, and provide an application to the corresponding free boundary analysis for the related classical obstacle problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03179","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":"1806.03179","created_at":"2026-05-18T00:13:49.396182+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.03179v1","created_at":"2026-05-18T00:13:49.396182+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03179","created_at":"2026-05-18T00:13:49.396182+00:00"},{"alias_kind":"pith_short_12","alias_value":"YTCADJ4SRSNW","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"YTCADJ4SRSNWVBHD","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"YTCADJ4S","created_at":"2026-05-18T12:33:04.347982+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/YTCADJ4SRSNWVBHDONNA36YRIQ","json":"https://pith.science/pith/YTCADJ4SRSNWVBHDONNA36YRIQ.json","graph_json":"https://pith.science/api/pith-number/YTCADJ4SRSNWVBHDONNA36YRIQ/graph.json","events_json":"https://pith.science/api/pith-number/YTCADJ4SRSNWVBHDONNA36YRIQ/events.json","paper":"https://pith.science/paper/YTCADJ4S"},"agent_actions":{"view_html":"https://pith.science/pith/YTCADJ4SRSNWVBHDONNA36YRIQ","download_json":"https://pith.science/pith/YTCADJ4SRSNWVBHDONNA36YRIQ.json","view_paper":"https://pith.science/paper/YTCADJ4S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.03179&json=true","fetch_graph":"https://pith.science/api/pith-number/YTCADJ4SRSNWVBHDONNA36YRIQ/graph.json","fetch_events":"https://pith.science/api/pith-number/YTCADJ4SRSNWVBHDONNA36YRIQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YTCADJ4SRSNWVBHDONNA36YRIQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YTCADJ4SRSNWVBHDONNA36YRIQ/action/storage_attestation","attest_author":"https://pith.science/pith/YTCADJ4SRSNWVBHDONNA36YRIQ/action/author_attestation","sign_citation":"https://pith.science/pith/YTCADJ4SRSNWVBHDONNA36YRIQ/action/citation_signature","submit_replication":"https://pith.science/pith/YTCADJ4SRSNWVBHDONNA36YRIQ/action/replication_record"}},"created_at":"2026-05-18T00:13:49.396182+00:00","updated_at":"2026-05-18T00:13:49.396182+00:00"}