{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CDE4HXICJ2BXVR2WW73XTTHOO3","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":"e7a524c8794c7717af91d074cef3e093e42d2185ac21fee863d1a6ae05eafd2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-05-30T09:49:35Z","title_canon_sha256":"45b84040167b9944de50651a17cd4b4376ef16ce02d709d043c991cf913fe27b"},"schema_version":"1.0","source":{"id":"2505.24410","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.24410","created_at":"2026-07-05T11:55:19Z"},{"alias_kind":"arxiv_version","alias_value":"2505.24410v2","created_at":"2026-07-05T11:55:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24410","created_at":"2026-07-05T11:55:19Z"},{"alias_kind":"pith_short_12","alias_value":"CDE4HXICJ2BX","created_at":"2026-07-05T11:55:19Z"},{"alias_kind":"pith_short_16","alias_value":"CDE4HXICJ2BXVR2W","created_at":"2026-07-05T11:55:19Z"},{"alias_kind":"pith_short_8","alias_value":"CDE4HXIC","created_at":"2026-07-05T11:55:19Z"}],"graph_snapshots":[{"event_id":"sha256:6ac2580d046350516ad27b533b48790a4dc8c22c0564560bfad791649fe7da86","target":"graph","created_at":"2026-07-05T11:55:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.24410/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the regularity of the solution for the obstacle problem associated with the linearized Monge-Amp\\`ere operator: \\begin{align*}\n  \\begin{cases}\n  &u\\geq\\varphi \\text{\\quad in } \\Omega\n  &L_{ w}u=\\tr( W D^{2}u)\\leq 0 \\text{\\quad in } \\Omega\n  &L_{ w}u= 0 \\text{\\quad in } \\{u>\\varphi\\}\n  &u=0 \\text{\\quad on } \\partial\\Omega,\n  \\end{cases} \\end{align*} where $ W=(\\det D^{2} w) D^{2} w^{-1}$ is the matrix of cofactor of $D^{2} w$, $w$ satisfies $\\lambda \\leq \\det D^{2} w \\leq \\Lambda$ and $ w=0$ on $\\partial \\Omega$, $\\varphi$ is the obstacle with at least $C^{2}(\\bar{\\Omega","authors_text":"Meng Ji","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-05-30T09:49:35Z","title":"$C^{1,\\alpha}$ regularity of the solution for the obstacle problem for the linearized Monge-Amp\\`ere operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24410","kind":"arxiv","version":2},"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":"sha256:575ccac3b800d445f9980b04d4fcd2a06648c1a47f767ea958e5194104c368e5","target":"record","created_at":"2026-07-05T11:55:19Z","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":"e7a524c8794c7717af91d074cef3e093e42d2185ac21fee863d1a6ae05eafd2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-05-30T09:49:35Z","title_canon_sha256":"45b84040167b9944de50651a17cd4b4376ef16ce02d709d043c991cf913fe27b"},"schema_version":"1.0","source":{"id":"2505.24410","kind":"arxiv","version":2}},"canonical_sha256":"10c9c3dd024e837ac756b7f779ccee76f55390c3e0347261ec9c467df0572c08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10c9c3dd024e837ac756b7f779ccee76f55390c3e0347261ec9c467df0572c08","first_computed_at":"2026-07-05T11:55:19.685040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:55:19.685040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g6qexD6HNXtbw/hnxK8Bw0PcUHdq6ie+t2Gj0CQ+reugNyKG16WAjz5Zb+w9eIshbNoCnzpRq9vcdovpIbOIBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:55:19.685439Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.24410","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:575ccac3b800d445f9980b04d4fcd2a06648c1a47f767ea958e5194104c368e5","sha256:6ac2580d046350516ad27b533b48790a4dc8c22c0564560bfad791649fe7da86"],"state_sha256":"8d910c003a81b203f33333b169e63b6ee08ccfe9e1298f04b40444f6921ec549"}