{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GTLICMTNPVP3QTQUTRUSCJDH6M","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":"16ffc9cfc0dc8461cdcc2de95129ea8f00b675c3da031909cb79b1a646d50362","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-04-30T01:42:12Z","title_canon_sha256":"41621b6aa3f99a5fca429635b0141f1aead41a5652f7b9db7bed6bd32b1b1194"},"schema_version":"1.0","source":{"id":"2504.21253","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.21253","created_at":"2026-07-05T10:56:20Z"},{"alias_kind":"arxiv_version","alias_value":"2504.21253v1","created_at":"2026-07-05T10:56:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.21253","created_at":"2026-07-05T10:56:20Z"},{"alias_kind":"pith_short_12","alias_value":"GTLICMTNPVP3","created_at":"2026-07-05T10:56:20Z"},{"alias_kind":"pith_short_16","alias_value":"GTLICMTNPVP3QTQU","created_at":"2026-07-05T10:56:20Z"},{"alias_kind":"pith_short_8","alias_value":"GTLICMTN","created_at":"2026-07-05T10:56:20Z"}],"graph_snapshots":[{"event_id":"sha256:329459af59985881703fa9e64eb96271c6678515bf4dd32c7893f9b3809e01f7","target":"graph","created_at":"2026-07-05T10:56:20Z","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/2504.21253/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study convex solutions to the Monge-Amp\\`ere obstacle problem \\[ \\operatorname{det} D^2 v=g v^q\\chi_{\\{v>0\\}}, \\quad v \\geq 0, \\] where $q \\in [0,n)$ is a constant and $g$ is a bounded positive function. This problem emerges from the $L_p$ Minkowski problem. We establish $C^{1, \\alpha}$ regularity for the strictly convex part of the free boundary $\\partial\\{v=0\\}$. Furthermore, when $g \\in C^{\\alpha}$, we prove a Schauder-type estimate. As a consequence, when $g\\equiv 1$, we obtain a Liouville theorem for entire solutions with unbounded coincidence sets $\\{v=0\\}$. Combined with existing res","authors_text":"Jingang Xiong, Tianling Jin, Xushan Tu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-04-30T01:42:12Z","title":"Regularity and classification of the free boundary for a Monge-Amp\\`ere obstacle problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.21253","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":"sha256:7a516c38377301b1aac8852af16ce19640cf1b82a4a397a61250b73f0c4e2fb9","target":"record","created_at":"2026-07-05T10:56:20Z","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":"16ffc9cfc0dc8461cdcc2de95129ea8f00b675c3da031909cb79b1a646d50362","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-04-30T01:42:12Z","title_canon_sha256":"41621b6aa3f99a5fca429635b0141f1aead41a5652f7b9db7bed6bd32b1b1194"},"schema_version":"1.0","source":{"id":"2504.21253","kind":"arxiv","version":1}},"canonical_sha256":"34d681326d7d5fb84e149c69212467f314092d02e3d2e3c76f3ee6ab62cf7ad8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34d681326d7d5fb84e149c69212467f314092d02e3d2e3c76f3ee6ab62cf7ad8","first_computed_at":"2026-07-05T10:56:20.883759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:56:20.883759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sA6mjeD9ufPZsqc7XJxzggk8R8vxygIy2h9r2TZozEFr5niWHnjmAZ7IXU2cyARx3H0ZFsJd2+JV5oLdcBNwCg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:56:20.884227Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.21253","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a516c38377301b1aac8852af16ce19640cf1b82a4a397a61250b73f0c4e2fb9","sha256:329459af59985881703fa9e64eb96271c6678515bf4dd32c7893f9b3809e01f7"],"state_sha256":"ea6ee8713bf96aba06d558d38a125d322d6636568b9e88c740545562cdbf2ee5"}