{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:MINJXE4KVXQCZFKR5XO7B3X7NN","short_pith_number":"pith:MINJXE4K","schema_version":"1.0","canonical_sha256":"621a9b938aade02c9551edddf0eeff6b580fecf43e1afa2650224dbe8fabd368","source":{"kind":"arxiv","id":"1607.06648","version":1},"attestation_state":"computed","paper":{"title":"A sharp estimate a la calderon-zygmund for the p--laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filippo Santambrogio (LM-Orsay), I2M), Lorenzo Brasco (DPT OF MATH., Univ. of Ferrara","submitted_at":"2016-07-22T12:22:10Z","abstract_excerpt":"We consider local weak solutions of the Poisson equation for the p--Laplace operator. We prove a higher differentiability result, under an essentially sharp condition on the right-hand side. The result comes with a local scaling invariant a priori estimate."},"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":"1607.06648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-22T12:22:10Z","cross_cats_sorted":[],"title_canon_sha256":"4db51256ca0c1de15d20874f6152925ede5316d6f8502119f150f1f4938db157","abstract_canon_sha256":"fd0161bed82b9dd2205083ca0451091c287d15e2d8dc7df5757c0d198d9361d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:39.385797Z","signature_b64":"ggAkI6PaLNfGS69X9IJ6h8PaCtVjmZij682iwaro5TV+w7iGFCy1hnkwknMw5hiBOfO4/iTY9dv0Y1AbQ7OCDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"621a9b938aade02c9551edddf0eeff6b580fecf43e1afa2650224dbe8fabd368","last_reissued_at":"2026-05-18T01:10:39.385255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:39.385255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A sharp estimate a la calderon-zygmund for the p--laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filippo Santambrogio (LM-Orsay), I2M), Lorenzo Brasco (DPT OF MATH., Univ. of Ferrara","submitted_at":"2016-07-22T12:22:10Z","abstract_excerpt":"We consider local weak solutions of the Poisson equation for the p--Laplace operator. We prove a higher differentiability result, under an essentially sharp condition on the right-hand side. The result comes with a local scaling invariant a priori estimate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06648","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":"1607.06648","created_at":"2026-05-18T01:10:39.385357+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.06648v1","created_at":"2026-05-18T01:10:39.385357+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06648","created_at":"2026-05-18T01:10:39.385357+00:00"},{"alias_kind":"pith_short_12","alias_value":"MINJXE4KVXQC","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"MINJXE4KVXQCZFKR","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"MINJXE4K","created_at":"2026-05-18T12:30:32.724797+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/MINJXE4KVXQCZFKR5XO7B3X7NN","json":"https://pith.science/pith/MINJXE4KVXQCZFKR5XO7B3X7NN.json","graph_json":"https://pith.science/api/pith-number/MINJXE4KVXQCZFKR5XO7B3X7NN/graph.json","events_json":"https://pith.science/api/pith-number/MINJXE4KVXQCZFKR5XO7B3X7NN/events.json","paper":"https://pith.science/paper/MINJXE4K"},"agent_actions":{"view_html":"https://pith.science/pith/MINJXE4KVXQCZFKR5XO7B3X7NN","download_json":"https://pith.science/pith/MINJXE4KVXQCZFKR5XO7B3X7NN.json","view_paper":"https://pith.science/paper/MINJXE4K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.06648&json=true","fetch_graph":"https://pith.science/api/pith-number/MINJXE4KVXQCZFKR5XO7B3X7NN/graph.json","fetch_events":"https://pith.science/api/pith-number/MINJXE4KVXQCZFKR5XO7B3X7NN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MINJXE4KVXQCZFKR5XO7B3X7NN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MINJXE4KVXQCZFKR5XO7B3X7NN/action/storage_attestation","attest_author":"https://pith.science/pith/MINJXE4KVXQCZFKR5XO7B3X7NN/action/author_attestation","sign_citation":"https://pith.science/pith/MINJXE4KVXQCZFKR5XO7B3X7NN/action/citation_signature","submit_replication":"https://pith.science/pith/MINJXE4KVXQCZFKR5XO7B3X7NN/action/replication_record"}},"created_at":"2026-05-18T01:10:39.385357+00:00","updated_at":"2026-05-18T01:10:39.385357+00:00"}