{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:26L7KM2DO2H3ZHL57RYCT4VRQN","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":"e1eb5f77dacb121bbb641496acf5d3ef6e008c16adaa596ca31b79b8370801df","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-25T08:01:33Z","title_canon_sha256":"070d956a7981d533226bcb70bdedcbb955d416d7deb5ec8942f7a19398aa4266"},"schema_version":"1.0","source":{"id":"1710.09714","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.09714","created_at":"2026-05-18T00:31:56Z"},{"alias_kind":"arxiv_version","alias_value":"1710.09714v1","created_at":"2026-05-18T00:31:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09714","created_at":"2026-05-18T00:31:56Z"},{"alias_kind":"pith_short_12","alias_value":"26L7KM2DO2H3","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"26L7KM2DO2H3ZHL5","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"26L7KM2D","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:3d5277e2123807dafb9bd6e9045cbbdc7febcbd280514603f053532c36f01f39","target":"graph","created_at":"2026-05-18T00:31:56Z","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"},"paper":{"abstract_excerpt":"This paper focuses on the problem of prescribing mean curvature on the unit ball. Assume that $f$, which is allowed to change sign, satisfies Morse index counting or certain kind of symmetry condition. By using a negative gradient flow method, we then prove that $f$ can be realized as the boundary mean curvature of some conformal metric.","authors_text":"Hong Zhang","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-25T08:01:33Z","title":"Prescribing sign-changing mean curvature candidates on the n+1-dimensional unit ball"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09714","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:f639292e4dfd7612d8afd9e9333d25a64d77576f02240163432710df7da7a040","target":"record","created_at":"2026-05-18T00:31:56Z","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":"e1eb5f77dacb121bbb641496acf5d3ef6e008c16adaa596ca31b79b8370801df","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-25T08:01:33Z","title_canon_sha256":"070d956a7981d533226bcb70bdedcbb955d416d7deb5ec8942f7a19398aa4266"},"schema_version":"1.0","source":{"id":"1710.09714","kind":"arxiv","version":1}},"canonical_sha256":"d797f53343768fbc9d7dfc7029f2b1837e0b6e1f67bd8a98240e50e6fbaf198d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d797f53343768fbc9d7dfc7029f2b1837e0b6e1f67bd8a98240e50e6fbaf198d","first_computed_at":"2026-05-18T00:31:56.592459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:56.592459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/fFutC6taDP/n4LYvpW4569zeci7xoW27zISH/306KpdfbZxCv/ccZ1rPJVhBXs1JcgfxQRJnhX+s8OYwqp/Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:56.592850Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.09714","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f639292e4dfd7612d8afd9e9333d25a64d77576f02240163432710df7da7a040","sha256:3d5277e2123807dafb9bd6e9045cbbdc7febcbd280514603f053532c36f01f39"],"state_sha256":"413096b483cce88ead09ad6ad1ecfa14315c5c92d45b52fa460aedb01254489f"}