{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:EDXYAYMLJXXUBJL6DS7T2JNFSX","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":"93f8b6d192ec5f341ae63eb2ce0bfde859fafdc750a985253e07e678c69fb06d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-02T10:40:55Z","title_canon_sha256":"6093c90baee06d5abe68e76f60c7ab9741695b1591fe4990cbd1d894de5c4584"},"schema_version":"1.0","source":{"id":"1010.0322","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0322","created_at":"2026-05-18T04:39:58Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0322v1","created_at":"2026-05-18T04:39:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0322","created_at":"2026-05-18T04:39:58Z"},{"alias_kind":"pith_short_12","alias_value":"EDXYAYMLJXXU","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EDXYAYMLJXXUBJL6","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EDXYAYML","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:fcdffef769866aa08dba0ff4204b6c792aaf740eb39d53c0f398d3826947eb33","target":"graph","created_at":"2026-05-18T04:39:58Z","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":"We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence form under natural growth conditions. The degeneracy is given by a suitable power of a strong $A_\\infty$ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove $C^{1,\\alpha}$ local estimates for solutions of a degenerate equation in non divergence form.","authors_text":"Giuseppe Di Fazio, Maria Stella Fanciullo, Piero Zamboni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-02T10:40:55Z","title":"Harnack inequality and regularity for degenerate quasilinear elliptic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0322","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":"sha256:33c2b328a32cfcd2515de5aab73ceaee70e50a14021a61fdae0060c86e59ff5e","target":"record","created_at":"2026-05-18T04:39:58Z","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":"93f8b6d192ec5f341ae63eb2ce0bfde859fafdc750a985253e07e678c69fb06d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-02T10:40:55Z","title_canon_sha256":"6093c90baee06d5abe68e76f60c7ab9741695b1591fe4990cbd1d894de5c4584"},"schema_version":"1.0","source":{"id":"1010.0322","kind":"arxiv","version":1}},"canonical_sha256":"20ef80618b4def40a57e1cbf3d25a595feb19cebd305b7ad09659376e7376597","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20ef80618b4def40a57e1cbf3d25a595feb19cebd305b7ad09659376e7376597","first_computed_at":"2026-05-18T04:39:58.638157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:58.638157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S61zO0DzG121MrizuA+AO1QpjNCMIM//fDmk1OZg9HjAk4zCCT8pBETcj63xQX6yt1ki2LKzqjv07J9Iym9JAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:58.638808Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.0322","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33c2b328a32cfcd2515de5aab73ceaee70e50a14021a61fdae0060c86e59ff5e","sha256:fcdffef769866aa08dba0ff4204b6c792aaf740eb39d53c0f398d3826947eb33"],"state_sha256":"59db367b7ffb5096cd9cb0426992f2ade9b239480193fb38de622e16d1c0d720"}