{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7NEHQD7V4XY4WC5D3XRBIAU6YP","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":"874355849a22bac9665c1d99525f0955632624e77976374d789e835e414916ec","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-05-24T13:20:39Z","title_canon_sha256":"c94ce588b4bf718767a5b870e66bc698b34ef3e9cb0b4aaa0c8e08897c27bd04"},"schema_version":"1.0","source":{"id":"1905.10222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.10222","created_at":"2026-07-05T02:59:01Z"},{"alias_kind":"arxiv_version","alias_value":"1905.10222v1","created_at":"2026-07-05T02:59:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.10222","created_at":"2026-07-05T02:59:01Z"},{"alias_kind":"pith_short_12","alias_value":"7NEHQD7V4XY4","created_at":"2026-07-05T02:59:01Z"},{"alias_kind":"pith_short_16","alias_value":"7NEHQD7V4XY4WC5D","created_at":"2026-07-05T02:59:01Z"},{"alias_kind":"pith_short_8","alias_value":"7NEHQD7V","created_at":"2026-07-05T02:59:01Z"}],"graph_snapshots":[{"event_id":"sha256:21340d2c1b0254f291f6bdf293e4931916201b3cdf6499847303fa50c86fe7e3","target":"graph","created_at":"2026-07-05T02:59:01Z","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/1905.10222/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove that for any K\\\"ahler metrics $\\omega_0$ and $\\chi$ on $M$, there exists $\\omega_\\varphi=\\omega_0+\\sqrt{-1}\\partial\\bar\\partial\\varphi>0$ satisfying the J-equation $\\mathrm{tr}_{\\omega_\\varphi}\\chi=c$ if and only if $(M,[\\omega_0],[\\chi])$ is uniformly J-stable. As a corollary, we can find many constant scalar curvature K\\\"ahler metrics with $c_1<0$. Using the same method, we also prove a similar result for the deformed Hermitian-Yang-Mills equation when the angle is in $(\\frac{n\\pi}{2}-\\frac{\\pi}{4},\\frac{n\\pi}{2})$.","authors_text":"Gao Chen","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-05-24T13:20:39Z","title":"On J-equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10222","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:eb7bb203e8d1e2f9d52b7903fd022c600f2494ebac65b19edce37c4a4e00a28b","target":"record","created_at":"2026-07-05T02:59:01Z","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":"874355849a22bac9665c1d99525f0955632624e77976374d789e835e414916ec","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-05-24T13:20:39Z","title_canon_sha256":"c94ce588b4bf718767a5b870e66bc698b34ef3e9cb0b4aaa0c8e08897c27bd04"},"schema_version":"1.0","source":{"id":"1905.10222","kind":"arxiv","version":1}},"canonical_sha256":"fb48780ff5e5f1cb0ba3dde214029ec3d98e1b5d01f002646fda69e460ea6618","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb48780ff5e5f1cb0ba3dde214029ec3d98e1b5d01f002646fda69e460ea6618","first_computed_at":"2026-07-05T02:59:01.051350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:59:01.051350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k9dhuthCN/ZY/SJ1nXWoeBn7KfxClhz5ZgbrG+jmJ0Sb9klbrg+CcdRdq3Jp+WSC8/4zuH+0c0yh4rNkJgjuAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:59:01.051781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.10222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb7bb203e8d1e2f9d52b7903fd022c600f2494ebac65b19edce37c4a4e00a28b","sha256:21340d2c1b0254f291f6bdf293e4931916201b3cdf6499847303fa50c86fe7e3"],"state_sha256":"1fd89fda0253dba30bf963cc9f37d21d3182ab210476215afc8c1223fabad796"}