{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:LUOXF43QJVMETQ4KYAUX7FWCZ3","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":"5349bf909d7e8599840cfb484162bea01f70495e520ff3464e173a9788e47b9f","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-05-06T07:55:37Z","title_canon_sha256":"780219a48698aca83df610e45bb3c02596fe26cca4f54acaea92c609e47fede1"},"schema_version":"1.0","source":{"id":"2005.02639","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.02639","created_at":"2026-07-05T01:19:39Z"},{"alias_kind":"arxiv_version","alias_value":"2005.02639v2","created_at":"2026-07-05T01:19:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.02639","created_at":"2026-07-05T01:19:39Z"},{"alias_kind":"pith_short_12","alias_value":"LUOXF43QJVME","created_at":"2026-07-05T01:19:39Z"},{"alias_kind":"pith_short_16","alias_value":"LUOXF43QJVMETQ4K","created_at":"2026-07-05T01:19:39Z"},{"alias_kind":"pith_short_8","alias_value":"LUOXF43Q","created_at":"2026-07-05T01:19:39Z"}],"graph_snapshots":[{"event_id":"sha256:1de4561051997b9a7a23b7ea7f5055f92aea49f230733b500c9f79bbffa208d6","target":"graph","created_at":"2026-07-05T01:19:39Z","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/2005.02639/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we study the dual Orlicz-Minkowski problem, which is a generalization of the dual Minkowski problem in convex geometry. By considering a geometric flow involving Gauss curvature and functions of normal vectors and radial vectors, we obtain a new existence result of smooth even solutions to this problem for smooth even measures.","authors_text":"Jian Lu, Li Chen, Ni Xiang, Yannan Liu","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-05-06T07:55:37Z","title":"Existence of smooth even solutions to the dual Orlicz-Minkowski problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.02639","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":"sha256:01af43a82b94d70fe6803f0b338640ceb3550b2890b9b851cac34f0167f25c9d","target":"record","created_at":"2026-07-05T01:19:39Z","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":"5349bf909d7e8599840cfb484162bea01f70495e520ff3464e173a9788e47b9f","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-05-06T07:55:37Z","title_canon_sha256":"780219a48698aca83df610e45bb3c02596fe26cca4f54acaea92c609e47fede1"},"schema_version":"1.0","source":{"id":"2005.02639","kind":"arxiv","version":2}},"canonical_sha256":"5d1d72f3704d5849c38ac0297f96c2cee1d03004f6331ea23356b69879cef0a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d1d72f3704d5849c38ac0297f96c2cee1d03004f6331ea23356b69879cef0a0","first_computed_at":"2026-07-05T01:19:39.700837Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:19:39.700837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FQ6fVB3XcLa4W91/oAFQVNsa/sPMP+H6SWHwmFpAw73sknRxGSoSgnJwL+TFRLNcHPnZ2Pjg0BqraoAtAQcnAA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:19:39.701455Z","signed_message":"canonical_sha256_bytes"},"source_id":"2005.02639","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01af43a82b94d70fe6803f0b338640ceb3550b2890b9b851cac34f0167f25c9d","sha256:1de4561051997b9a7a23b7ea7f5055f92aea49f230733b500c9f79bbffa208d6"],"state_sha256":"74f762af0d8c7bca669a2d927b4f46b0d4b81f0c837019dff20344b262a7613c"}