{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JYZGUTCPRXE653LNX433P2FHIQ","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":"5ae5eccdd104b2c911edaf4509f910fc0950cf5cc7ad3fdf2296c11b25af1098","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-10T14:16:21Z","title_canon_sha256":"c67dd59cd83df6149cb37ec7ec4343a74d9ac234da247b6ba6de6ed5b4519ee6"},"schema_version":"1.0","source":{"id":"1709.03104","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03104","created_at":"2026-05-18T00:35:39Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03104v1","created_at":"2026-05-18T00:35:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03104","created_at":"2026-05-18T00:35:39Z"},{"alias_kind":"pith_short_12","alias_value":"JYZGUTCPRXE6","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JYZGUTCPRXE653LN","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JYZGUTCP","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:d47f764b0d60e438e89148aded8f7c1732d83d90cc4bc27125a690d6bb9f7fa9","target":"graph","created_at":"2026-05-18T00:35:39Z","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"},"paper":{"abstract_excerpt":"In this note we discuss graphs over a domain $\\Omega\\subset N^2$ in the product manifold $N^2\\times \\mathbb{R}$. Here $N^2$ is a complete Riemannian surface and $\\Omega$ has peice-wise smooth boundary. Let $\\gamma \\subset\\partial\\Omega$ be a smooth connected arc and $\\Sigma$ be a complete graph in $N^2\\times \\mathbb{R}$ over $\\Omega$. We show that if $\\Sigma$ is a minimal or translating graph, then $\\gamma$ is a geodesic in $N^2$. Moreover if $\\Sigma$ is a CMC graph, then $\\gamma$ has constant principle curvature in $N^2$. This explains the infinity value boundary condition upon domains having","authors_text":"Hengyu Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-10T14:16:21Z","title":"The boundary behavior of domains with complete translating, minimal and CMC graphs in $N^2\\times \\mathbb{R}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03104","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:d63d6d6b27cc9ca094cd72faa657f3c0df7e48ba1337b7e4bffde1c4997f3c42","target":"record","created_at":"2026-05-18T00:35:39Z","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":"5ae5eccdd104b2c911edaf4509f910fc0950cf5cc7ad3fdf2296c11b25af1098","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-10T14:16:21Z","title_canon_sha256":"c67dd59cd83df6149cb37ec7ec4343a74d9ac234da247b6ba6de6ed5b4519ee6"},"schema_version":"1.0","source":{"id":"1709.03104","kind":"arxiv","version":1}},"canonical_sha256":"4e326a4c4f8dc9eeed6dbf37b7e8a74411a033678adbcfd33048e8e88d792d9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e326a4c4f8dc9eeed6dbf37b7e8a74411a033678adbcfd33048e8e88d792d9b","first_computed_at":"2026-05-18T00:35:39.378983Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:39.378983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GK2bTGitcnTDFBYwY8dNSna7Xy/ZH/B9c3KJT53IKNhqMtU+FXQTzDhY6FgIw//iHFroea9fEbiBTOmca1n3AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:39.379513Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.03104","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d63d6d6b27cc9ca094cd72faa657f3c0df7e48ba1337b7e4bffde1c4997f3c42","sha256:d47f764b0d60e438e89148aded8f7c1732d83d90cc4bc27125a690d6bb9f7fa9"],"state_sha256":"b289e925c469456ed52ffb09a7acfefb843958340db0b56cd24ffac434d950a3"}