{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FYLNST5UEFPCFJZXGT4OD3P6W7","short_pith_number":"pith:FYLNST5U","schema_version":"1.0","canonical_sha256":"2e16d94fb4215e22a73734f8e1edfeb7f72966f6349e0c28657b6e16e776c1df","source":{"kind":"arxiv","id":"1202.5566","version":3},"attestation_state":"computed","paper":{"title":"A note on interior $W^{2,1+\\varepsilon}$ estimates for the Monge-Ampere equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Figalli, Guido De Philippis, Ovidiu Savin","submitted_at":"2012-02-24T21:29:21Z","abstract_excerpt":"By a variant of the techniques introduced by the first two authors in [DF] to prove that second derivatives of solutions to the Monge-Ampere equation are locally in $L\\log L$, we obtain interior $W^{2,1+\\varepsilon}$ estimates."},"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":"1202.5566","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-24T21:29:21Z","cross_cats_sorted":[],"title_canon_sha256":"73234c8ba0fd9ec0340060074a051ea570b1e4d684f219b6d508f07e9f7901e8","abstract_canon_sha256":"7f7741997e9a1e0d80004f322530b8859da2c13d633da188791c859706463375"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:58.805560Z","signature_b64":"hUOwEi3apeavNg11+zcJAEXs1vkcn7u+oRe+dfzgGLMrBk8+3t+htLo0MR5+w/CQ7cTOTH3AJOaJftRGkLzYBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e16d94fb4215e22a73734f8e1edfeb7f72966f6349e0c28657b6e16e776c1df","last_reissued_at":"2026-05-18T03:41:58.804825Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:58.804825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on interior $W^{2,1+\\varepsilon}$ estimates for the Monge-Ampere equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Figalli, Guido De Philippis, Ovidiu Savin","submitted_at":"2012-02-24T21:29:21Z","abstract_excerpt":"By a variant of the techniques introduced by the first two authors in [DF] to prove that second derivatives of solutions to the Monge-Ampere equation are locally in $L\\log L$, we obtain interior $W^{2,1+\\varepsilon}$ estimates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5566","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":"1202.5566","created_at":"2026-05-18T03:41:58.804952+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.5566v3","created_at":"2026-05-18T03:41:58.804952+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5566","created_at":"2026-05-18T03:41:58.804952+00:00"},{"alias_kind":"pith_short_12","alias_value":"FYLNST5UEFPC","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"FYLNST5UEFPCFJZX","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"FYLNST5U","created_at":"2026-05-18T12:27:06.952714+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/FYLNST5UEFPCFJZXGT4OD3P6W7","json":"https://pith.science/pith/FYLNST5UEFPCFJZXGT4OD3P6W7.json","graph_json":"https://pith.science/api/pith-number/FYLNST5UEFPCFJZXGT4OD3P6W7/graph.json","events_json":"https://pith.science/api/pith-number/FYLNST5UEFPCFJZXGT4OD3P6W7/events.json","paper":"https://pith.science/paper/FYLNST5U"},"agent_actions":{"view_html":"https://pith.science/pith/FYLNST5UEFPCFJZXGT4OD3P6W7","download_json":"https://pith.science/pith/FYLNST5UEFPCFJZXGT4OD3P6W7.json","view_paper":"https://pith.science/paper/FYLNST5U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.5566&json=true","fetch_graph":"https://pith.science/api/pith-number/FYLNST5UEFPCFJZXGT4OD3P6W7/graph.json","fetch_events":"https://pith.science/api/pith-number/FYLNST5UEFPCFJZXGT4OD3P6W7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FYLNST5UEFPCFJZXGT4OD3P6W7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FYLNST5UEFPCFJZXGT4OD3P6W7/action/storage_attestation","attest_author":"https://pith.science/pith/FYLNST5UEFPCFJZXGT4OD3P6W7/action/author_attestation","sign_citation":"https://pith.science/pith/FYLNST5UEFPCFJZXGT4OD3P6W7/action/citation_signature","submit_replication":"https://pith.science/pith/FYLNST5UEFPCFJZXGT4OD3P6W7/action/replication_record"}},"created_at":"2026-05-18T03:41:58.804952+00:00","updated_at":"2026-05-18T03:41:58.804952+00:00"}