{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:ACJPL3TJDFZZHSBVHZXCULFNPP","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":"d3d17dea2367392419332e4645bef759c9035d1706a44ea02bfe06e95435e968","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-11-03T05:40:51Z","title_canon_sha256":"42149cda445bc0b8ba49b42e0438abb2628d8a30acd49fedf8f45ec8cf63c6dd"},"schema_version":"1.0","source":{"id":"2111.02028","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.02028","created_at":"2026-07-05T03:28:45Z"},{"alias_kind":"arxiv_version","alias_value":"2111.02028v1","created_at":"2026-07-05T03:28:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.02028","created_at":"2026-07-05T03:28:45Z"},{"alias_kind":"pith_short_12","alias_value":"ACJPL3TJDFZZ","created_at":"2026-07-05T03:28:45Z"},{"alias_kind":"pith_short_16","alias_value":"ACJPL3TJDFZZHSBV","created_at":"2026-07-05T03:28:45Z"},{"alias_kind":"pith_short_8","alias_value":"ACJPL3TJ","created_at":"2026-07-05T03:28:45Z"}],"graph_snapshots":[{"event_id":"sha256:bf76b5bf811dc0bff6b08cd6d7cfa6ec10a804be09c43c8de073f224ecf4901b","target":"graph","created_at":"2026-07-05T03:28:45Z","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/2111.02028/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, under suitable settings, we can obtain the existence and uniqueness of solutions to a class of Hessian quotient equations with Dirichlet boundary condition in Lorentz-Minkowski space $\\mathbb{R}^{n+1}_{1}$, which can be seen as a prescribed curvature problem and a continuous work of [12].","authors_text":"Jing Mao, Ya Gao, YanLing Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-11-03T05:40:51Z","title":"The Dirichlet problem for a class of Hessian quotient equations in Lorentz-Minkowski space $\\mathbb{R}^{n+1}_{1}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.02028","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":"sha256:15421117a6c473ff8b615201fc65d00f07fe511b6c82c9e74d61a94405aac331","target":"record","created_at":"2026-07-05T03:28:45Z","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":"d3d17dea2367392419332e4645bef759c9035d1706a44ea02bfe06e95435e968","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-11-03T05:40:51Z","title_canon_sha256":"42149cda445bc0b8ba49b42e0438abb2628d8a30acd49fedf8f45ec8cf63c6dd"},"schema_version":"1.0","source":{"id":"2111.02028","kind":"arxiv","version":1}},"canonical_sha256":"0092f5ee69197393c8353e6e2a2cad7bc2046405fd28f04cbd6efc406cda4a6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0092f5ee69197393c8353e6e2a2cad7bc2046405fd28f04cbd6efc406cda4a6d","first_computed_at":"2026-07-05T03:28:45.971917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:28:45.971917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m7L3jfAqpUxBti0S0oms/mxPBf0oIDszSVGi3YbRWJzaowNa6UKFOnPDMxDpnyK030Iy4LcEjY+SvzC14m2iBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:28:45.972330Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.02028","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15421117a6c473ff8b615201fc65d00f07fe511b6c82c9e74d61a94405aac331","sha256:bf76b5bf811dc0bff6b08cd6d7cfa6ec10a804be09c43c8de073f224ecf4901b"],"state_sha256":"e18be163556e2a5550db2a8d1bfef36f4152c7ffb76b84173a25cc7069d38e81"}