{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CEU77XPEV222SWBVE32GFLNFZF","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":"f1e28c5196b57f452b5356288a3905b89a78e1f04e5aa5bdd4b6546aa6693ef4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-02T15:19:58Z","title_canon_sha256":"096e49698b555093c378d0a4a83cf849f5ce69ee920c009886c4b06859b65309"},"schema_version":"1.0","source":{"id":"1103.0456","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0456","created_at":"2026-05-18T04:27:34Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0456v1","created_at":"2026-05-18T04:27:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0456","created_at":"2026-05-18T04:27:34Z"},{"alias_kind":"pith_short_12","alias_value":"CEU77XPEV222","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CEU77XPEV222SWBV","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CEU77XPE","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:65e199064d2d2ff398b3a6e0742494e25c2cfc6ac8330adc5c514de71a8a0985","target":"graph","created_at":"2026-05-18T04:27:34Z","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 obtain global $W^{2,p}$ estimates for the Monge-Ampere equation under natural assumptions on the domain and boundary data.","authors_text":"Ovidiu Savin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-02T15:19:58Z","title":"Global $W^{2,p}$ estimates for the Monge-Ampere equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0456","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":"sha256:0c213c71f88199a119a0a1eebb97dac32dfd339dfd0ce66223a80be811e133a4","target":"record","created_at":"2026-05-18T04:27:34Z","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":"f1e28c5196b57f452b5356288a3905b89a78e1f04e5aa5bdd4b6546aa6693ef4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-02T15:19:58Z","title_canon_sha256":"096e49698b555093c378d0a4a83cf849f5ce69ee920c009886c4b06859b65309"},"schema_version":"1.0","source":{"id":"1103.0456","kind":"arxiv","version":1}},"canonical_sha256":"1129ffdde4aeb5a9583526f462ada5c9575ca4c689025fbc7cbf2a7ca86088a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1129ffdde4aeb5a9583526f462ada5c9575ca4c689025fbc7cbf2a7ca86088a6","first_computed_at":"2026-05-18T04:27:34.845909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:34.845909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hV50VgZqnhanQcO/uTXgJNkHQGhkBfP4AxlnzTNjbqk44sAQC06TgzIWerQqcBKi81HoDotPQHX4EQx0zhatBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:34.846694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.0456","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c213c71f88199a119a0a1eebb97dac32dfd339dfd0ce66223a80be811e133a4","sha256:65e199064d2d2ff398b3a6e0742494e25c2cfc6ac8330adc5c514de71a8a0985"],"state_sha256":"25875e2bd9a6e0b8a4b618df4b39698ecdc526a48961642c0f2ffbfc35161cd0"}