{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:P6L5ZDW3V3H545BXJGSFG6HHMO","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":"e13d8477a81b7e87686c3e8f0b5faeddbe5350ab9aad99e8247ee5b9ca568fb0","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-17T02:27:41Z","title_canon_sha256":"0563b1d3f9c694a72bfb7bd4631e8b3df30df71b2ae3ce92888145a20af586c3"},"schema_version":"1.0","source":{"id":"1507.04818","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04818","created_at":"2026-05-18T00:54:48Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04818v3","created_at":"2026-05-18T00:54:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04818","created_at":"2026-05-18T00:54:48Z"},{"alias_kind":"pith_short_12","alias_value":"P6L5ZDW3V3H5","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"P6L5ZDW3V3H545BX","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"P6L5ZDW3","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:79b22e1aef926319b55e67d77189f37ff7e0b4fa1acfcfeb3612bc3c028c6c14","target":"graph","created_at":"2026-05-18T00:54:48Z","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":"Motivated by classical theorems on minimal surface theory in compact hyperbolic three-manifolds, we investigate the questions of existence and deformations for least area minimal surfaces in complete noncompact hyperbolic three-manifold of finite volume. We prove any closed immersed incompressible surface can be deformed to a closed immersed least area surface within its homotopy class in any cusped hyperbolic three-manifold. Our techniques highlight how special structures of these cusped hyperbolic three-manifolds prevent any least area minimal surface going too deep into the cusped region.","authors_text":"Biao Wang, Zheng Huang","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-17T02:27:41Z","title":"Closed Minimal Surfaces in Cusped Hyperbolic Three-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04818","kind":"arxiv","version":3},"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":"sha256:21d3d2814a9121417f33437664ac5f61aafff10a776261bf173e0e3961878cab","target":"record","created_at":"2026-05-18T00:54:48Z","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":"e13d8477a81b7e87686c3e8f0b5faeddbe5350ab9aad99e8247ee5b9ca568fb0","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-17T02:27:41Z","title_canon_sha256":"0563b1d3f9c694a72bfb7bd4631e8b3df30df71b2ae3ce92888145a20af586c3"},"schema_version":"1.0","source":{"id":"1507.04818","kind":"arxiv","version":3}},"canonical_sha256":"7f97dc8edbaecfde743749a45378e7638876c6452403266b086ca6ba2e87a455","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f97dc8edbaecfde743749a45378e7638876c6452403266b086ca6ba2e87a455","first_computed_at":"2026-05-18T00:54:48.215138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:48.215138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/m35GJIootxkwSp2HZ2unpthAtY3iQFuArze6YFJBc7n7/+VNhqYN/iILli7UhkVLToAHYQ+19VbH1JnYVwvCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:48.215632Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.04818","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21d3d2814a9121417f33437664ac5f61aafff10a776261bf173e0e3961878cab","sha256:79b22e1aef926319b55e67d77189f37ff7e0b4fa1acfcfeb3612bc3c028c6c14"],"state_sha256":"50c126ac6b1f11e318133832d01686b07de5c3c97c3fe5d0ae67267a7139fd7f"}