{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KWP4LIPSX7AANHMS3JR6CHIIJ5","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":"7a6bf42efc87643f8577b822ee49b050a1bed30c84892bc87b988b4747f46f7a","cross_cats_sorted":["math.AG","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-03-21T14:45:37Z","title_canon_sha256":"b7cf2e9fb582d5f65d4554d342b277a666d9535f336759362e15678c3edc60a8"},"schema_version":"1.0","source":{"id":"1803.07948","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07948","created_at":"2026-07-05T00:35:09Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07948v5","created_at":"2026-07-05T00:35:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07948","created_at":"2026-07-05T00:35:09Z"},{"alias_kind":"pith_short_12","alias_value":"KWP4LIPSX7AA","created_at":"2026-07-05T00:35:09Z"},{"alias_kind":"pith_short_16","alias_value":"KWP4LIPSX7AANHMS","created_at":"2026-07-05T00:35:09Z"},{"alias_kind":"pith_short_8","alias_value":"KWP4LIPS","created_at":"2026-07-05T00:35:09Z"}],"graph_snapshots":[{"event_id":"sha256:099c48284e8484b1c5b06580608b2b237c80f3f7c39b881aed88fa12957bda75","target":"graph","created_at":"2026-07-05T00:35:09Z","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/1803.07948/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the reversed Alexandrov-Fenchel inequality for mixed Monge-Amp\\`ere masses of plurisubharmonic functions, which generalizes a result of Demailly and Pham. As applications to convex geometry, this gives a complex analytic proof of the reversed Alexandrov-Fenchel inequality for mixed covolumes, which generalizes recent results in convex geometry of Kaveh-Khovanskii, Khovanskii-Timorin, Milman-Rotem and R. Schneider on reversed (or complemented) Brunn-Minkowski and Alexandrov-Fenchel inequalities. Also for toric plurisubharmonic functions in the Cegrell class, we confirm Demailly's conje","authors_text":"Alexander Rashkovskii, Dano Kim","cross_cats":["math.AG","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-03-21T14:45:37Z","title":"Higher Lelong numbers and convex geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07948","kind":"arxiv","version":5},"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":"sha256:0530d8138ab27eed7f6a7a7ba2053e59812db97f93e9f6f4b022408c02e2d0e5","target":"record","created_at":"2026-07-05T00:35:09Z","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":"7a6bf42efc87643f8577b822ee49b050a1bed30c84892bc87b988b4747f46f7a","cross_cats_sorted":["math.AG","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-03-21T14:45:37Z","title_canon_sha256":"b7cf2e9fb582d5f65d4554d342b277a666d9535f336759362e15678c3edc60a8"},"schema_version":"1.0","source":{"id":"1803.07948","kind":"arxiv","version":5}},"canonical_sha256":"559fc5a1f2bfc0069d92da63e11d084f40df83288632dc5d9a4ecf673e87d22f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"559fc5a1f2bfc0069d92da63e11d084f40df83288632dc5d9a4ecf673e87d22f","first_computed_at":"2026-07-05T00:35:09.038031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:35:09.038031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9Tnd2XA3ieck6Ma8u4+QKgVYCRoZQdcnvvnmM9K82kUAIes2OVZeU7rp0NLIFsX8MCcHyRR3qetd7LnYTwiMDA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:35:09.038465Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.07948","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0530d8138ab27eed7f6a7a7ba2053e59812db97f93e9f6f4b022408c02e2d0e5","sha256:099c48284e8484b1c5b06580608b2b237c80f3f7c39b881aed88fa12957bda75"],"state_sha256":"d2932063ad5d49d7d8835e99abeab62d8260d7e4c5f96d759c1bbb5798473ba0"}