{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:K4EDK5HMQRJOQ4XZ26XDRYXAUA","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":"65354e57d3098368a0b6926285a2456fcaf906d7e173de4780fce0cb1d26c583","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-17T06:01:16Z","title_canon_sha256":"879f5f3e60c8af8b9c88a1ca2d09ea07ffc0b8cb6c3ecc76460e9bb8b9f41c08"},"schema_version":"1.0","source":{"id":"1505.04358","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04358","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04358v2","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04358","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"pith_short_12","alias_value":"K4EDK5HMQRJO","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"K4EDK5HMQRJOQ4XZ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"K4EDK5HM","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:d6ec9a34a688c3a017bac362222fdbd424ef9ea89dc91e1189cc45abe5da3b91","target":"graph","created_at":"2026-05-18T01:23:32Z","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 study a fully nonlinear PDE involving a linear combination of symmetric polynomials of the K\\\"ahler form on a K\\\"ahler manifold. A $C^0$ \\emph{a priori} estimate is proven in general and a gradient estimate is proven in certain cases. Independently, we also provide a method-of-continuity proof via a path of K\\\"ahler metrics to recover the existence of solutions in some of the known cases. Known results are then applied to an analytic problem arising from Chern-Weil theory and to a special Lagrangian-type equation arising from mirror symmetry.","authors_text":"Vamsi Pingali","cross_cats":["math-ph","math.CV","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-17T06:01:16Z","title":"A priori estimates for a generalised Monge-Amp\\`ere PDE on some compact K\\\"ahler manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04358","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":"sha256:11d6ce14966ed4b24979910d9a578527f83489cb89f5e5db6cb4c14e9944920a","target":"record","created_at":"2026-05-18T01:23:32Z","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":"65354e57d3098368a0b6926285a2456fcaf906d7e173de4780fce0cb1d26c583","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-17T06:01:16Z","title_canon_sha256":"879f5f3e60c8af8b9c88a1ca2d09ea07ffc0b8cb6c3ecc76460e9bb8b9f41c08"},"schema_version":"1.0","source":{"id":"1505.04358","kind":"arxiv","version":2}},"canonical_sha256":"57083574ec8452e872f9d7ae38e2e0a0204f8fae0fb0a6d852179e88e22561fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57083574ec8452e872f9d7ae38e2e0a0204f8fae0fb0a6d852179e88e22561fd","first_computed_at":"2026-05-18T01:23:32.216110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:32.216110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JkL44lencCxLW37t2QsQWuCjKnwHWjBax2KwatLmr9Rf2InR68wOY00EiL7I1uDlOd08p79aci3msiPK30kCCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:32.216731Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.04358","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11d6ce14966ed4b24979910d9a578527f83489cb89f5e5db6cb4c14e9944920a","sha256:d6ec9a34a688c3a017bac362222fdbd424ef9ea89dc91e1189cc45abe5da3b91"],"state_sha256":"9cc11047cf90f76997f0ed52334d5f8de6c7aa56146ae550b70d3dfe54c0c3bd"}