{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UKWVMB5SN6YRGOSP2TZHEV3ZIY","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":"d20ea5e35b23824490dbd311cc26bb245608385f321bb3847f7e695690d9351f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-03T04:52:09Z","title_canon_sha256":"cc13b74dfe5d53c2ddeea9435441d5b4c0227ca05de80576b4f1c9bd8c5f2456"},"schema_version":"1.0","source":{"id":"1509.00943","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00943","created_at":"2026-05-18T00:22:16Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00943v4","created_at":"2026-05-18T00:22:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00943","created_at":"2026-05-18T00:22:16Z"},{"alias_kind":"pith_short_12","alias_value":"UKWVMB5SN6YR","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UKWVMB5SN6YRGOSP","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UKWVMB5S","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:47b389365d9d4f5aa7a2453c790fd14f48a57090dd61a5232620c2617558b36b","target":"graph","created_at":"2026-05-18T00:22:16Z","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 prove a priori estimates for a generalised Monge-Amp\\`ere PDE with \"non-constant coefficients\" thus improving a result of Sun in the K\\\"ahler case. We apply this result to the deformed Hermitian Yang-Mills (dHYM) equation of Jacob-Yau to obtain an existence result and a priori estimates for some ranges of the phase angle assuming the existence of a subsolution. We then generalise a theorem of Collins-Sz\\`ekelyhidi on toric varieties and use it to address a conjecture of Collins-Jacob-Yau.","authors_text":"Vamsi P. Pingali","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-03T04:52:09Z","title":"A note on the deformed Hermitian Yang-Mills PDE"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00943","kind":"arxiv","version":4},"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":"sha256:7e02dae9828547a61f5f06a02073c940d2c76994370c9cd8a99f3fd74722ad13","target":"record","created_at":"2026-05-18T00:22:16Z","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":"d20ea5e35b23824490dbd311cc26bb245608385f321bb3847f7e695690d9351f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-03T04:52:09Z","title_canon_sha256":"cc13b74dfe5d53c2ddeea9435441d5b4c0227ca05de80576b4f1c9bd8c5f2456"},"schema_version":"1.0","source":{"id":"1509.00943","kind":"arxiv","version":4}},"canonical_sha256":"a2ad5607b26fb1133a4fd4f27257794636cef03ddfa1c6e85f2b7a370480df94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2ad5607b26fb1133a4fd4f27257794636cef03ddfa1c6e85f2b7a370480df94","first_computed_at":"2026-05-18T00:22:16.573841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:16.573841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fCQs8AjAmxh3p24UtaGM200G1Ug/2Vnp2V/qMqWIrWerdPGG/GXdiniJfEmM+Vympv7sr75CV67UFRd3Q162Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:16.574230Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.00943","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e02dae9828547a61f5f06a02073c940d2c76994370c9cd8a99f3fd74722ad13","sha256:47b389365d9d4f5aa7a2453c790fd14f48a57090dd61a5232620c2617558b36b"],"state_sha256":"b506ae67540a284f513927b02558fd8c38afad43de0c01966d047323caf8d50b"}