{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:GXR3EWZSCNRINGBSWGMNL27ZGO","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":"859c4dd5590b7dd5f59b9eceedfa8a86b728aa1c43dbf1f521d3240b86ff6d88","cross_cats_sorted":["math.AG","math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-12-14T21:48:05Z","title_canon_sha256":"b6c90d927efa28b392555959801def62c885edc58d7ca564c79ff771f8a81469"},"schema_version":"1.0","source":{"id":"2012.07956","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.07956","created_at":"2026-07-05T01:59:38Z"},{"alias_kind":"arxiv_version","alias_value":"2012.07956v1","created_at":"2026-07-05T01:59:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.07956","created_at":"2026-07-05T01:59:38Z"},{"alias_kind":"pith_short_12","alias_value":"GXR3EWZSCNRI","created_at":"2026-07-05T01:59:38Z"},{"alias_kind":"pith_short_16","alias_value":"GXR3EWZSCNRINGBS","created_at":"2026-07-05T01:59:38Z"},{"alias_kind":"pith_short_8","alias_value":"GXR3EWZS","created_at":"2026-07-05T01:59:38Z"}],"graph_snapshots":[{"event_id":"sha256:9ce548ac757fad2bbb988280679875043a887c9d07d331f49987398b6728de9c","target":"graph","created_at":"2026-07-05T01:59:38Z","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/2012.07956/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The $J$-equation proposed by Donaldson is a complex Hessian quotient equation on K\\\"ahler manifolds. The solvability of the $J$-equation is proved by Song-Weinkove to be equivalent to the existence of a subsolution. It is also conjectured by Lejmi-Szekelyhidi to be equivalent to a stability condition in terms of holomorphic intersection numbers as an analogue of the Nakai-Moishezon criterion in algebraic geometry. The conjecture is recently proved by Chen under a stronger uniform stability condition. In this paper, we establish a Nakai-Moishezon type criterion for pairs of K\\\"ahler classes on ","authors_text":"Jian Song","cross_cats":["math.AG","math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-12-14T21:48:05Z","title":"Nakai-Moishezon criterions for complex Hessian equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.07956","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":"sha256:7f6cc66d903ededb7a8eb304796ee534f3a24c0f5489e6e15fd21faebedf3157","target":"record","created_at":"2026-07-05T01:59:38Z","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":"859c4dd5590b7dd5f59b9eceedfa8a86b728aa1c43dbf1f521d3240b86ff6d88","cross_cats_sorted":["math.AG","math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-12-14T21:48:05Z","title_canon_sha256":"b6c90d927efa28b392555959801def62c885edc58d7ca564c79ff771f8a81469"},"schema_version":"1.0","source":{"id":"2012.07956","kind":"arxiv","version":1}},"canonical_sha256":"35e3b25b321362869832b198d5ebf933be8f5dd7e3a24ba33f8045929f27607e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35e3b25b321362869832b198d5ebf933be8f5dd7e3a24ba33f8045929f27607e","first_computed_at":"2026-07-05T01:59:38.196099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:59:38.196099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OU1+k6PDzM7UJ6FycEdyaUfCJ54fCklnQcWYQcriTu+fMBK36mZTEwSq2DlubiNA2UU/DbPE8/adF9xSQQUVDg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:59:38.196490Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.07956","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f6cc66d903ededb7a8eb304796ee534f3a24c0f5489e6e15fd21faebedf3157","sha256:9ce548ac757fad2bbb988280679875043a887c9d07d331f49987398b6728de9c"],"state_sha256":"d9cbdfcebc8815d7352836d746af4926f99ad0724b1831965725d009853ef09c"}