{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YBSIAYDLOLCVOIYZD2POJ5DK5A","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":"af6bbd54c4b6c94b4b044bc6209dfaa13461ff2a8cc092355aabfd8e20eec932","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-05T15:29:35Z","title_canon_sha256":"d0c95d3d7fa90230c7f84ec118d0ba015b46060bd8e2074838f2e58929a9f5f9"},"schema_version":"1.0","source":{"id":"1403.1160","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1160","created_at":"2026-05-18T02:57:00Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1160v1","created_at":"2026-05-18T02:57:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1160","created_at":"2026-05-18T02:57:00Z"},{"alias_kind":"pith_short_12","alias_value":"YBSIAYDLOLCV","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YBSIAYDLOLCVOIYZ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YBSIAYDL","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:2dcc6415150994917f86753d3117fad5e4b4ea2097bb260f87646d43da630048","target":"graph","created_at":"2026-05-18T02:57:00Z","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":"Let $M$ be a Hadamard manifold with curvature bounded above by a negative constant $-\\alpha$, satisfying the \"strict convexity condition\", and assume that $M$ admits a \"helicoidal\" one-parameter subgroup $G$ of isometries of $M$. Then, given a compact topological $G-$shaped hypersurface $\\Gamma$ in the asymptotic boundary of $M,$ and $|H|<\\sqrt{\\alpha}$, we prove the existence of a complete properly embedded hypersurface whose mean curvature is equal to $H$ and whose asymptotic boundary is $\\Gamma$. We are able, this way, to extend a previous theorem of B.Guan and J.Spruck on the hyperbolic sp","authors_text":"Jaime Ripoll, Jean-Baptiste Casteras","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-05T15:29:35Z","title":"On the asymptotic Plateau's problem for CMC hypersurfaces on rank 1 symmetric spaces of noncompact type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1160","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":"sha256:4268feff68d888739c6827c7259933a0f5568805e05ea36887fee5f36edba598","target":"record","created_at":"2026-05-18T02:57:00Z","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":"af6bbd54c4b6c94b4b044bc6209dfaa13461ff2a8cc092355aabfd8e20eec932","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-05T15:29:35Z","title_canon_sha256":"d0c95d3d7fa90230c7f84ec118d0ba015b46060bd8e2074838f2e58929a9f5f9"},"schema_version":"1.0","source":{"id":"1403.1160","kind":"arxiv","version":1}},"canonical_sha256":"c06480606b72c55723191e9ee4f46ae8181d1a15e6512c1249734ccfefd4de62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c06480606b72c55723191e9ee4f46ae8181d1a15e6512c1249734ccfefd4de62","first_computed_at":"2026-05-18T02:57:00.519418Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:00.519418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mhLPQVfvgF++YQqoeCP381KY4Ap7TqH+Z5eyW0IBTiCRm8ui6oCYqUv7upsxVDbrFFoZX89b23LeWrk0y1CyCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:00.519853Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.1160","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4268feff68d888739c6827c7259933a0f5568805e05ea36887fee5f36edba598","sha256:2dcc6415150994917f86753d3117fad5e4b4ea2097bb260f87646d43da630048"],"state_sha256":"18a5a4103f6881ff672b7a6a680c50c669f264ef7050b4c278ecf1d99bd5f5c7"}