{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UYMDT6WEIH6EOMXQMYTPBH2CSD","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":"4ae4fbdf48b78a4161373a9803c3cb0707ae2eef49ee291095a0ef0e8e465ded","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-25T14:01:50Z","title_canon_sha256":"f55f0fabcbf6d0bc67926e7cbf4e2f375993de93ce511dad2e243dbbc0faf23b"},"schema_version":"1.0","source":{"id":"1709.08495","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08495","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08495v2","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08495","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"UYMDT6WEIH6E","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UYMDT6WEIH6EOMXQ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UYMDT6WE","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:ea8a3076b20c0262dab711e4d029f09746972da283fc5fb174eaad635c8fbe65","target":"graph","created_at":"2026-05-18T00:03:24Z","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":"We construct a sequence of compact, oriented, embedded, two-dimensional surfaces of genus one into Euclidean 3-space with prescribed, almost constant, mean curvature of the form $H(X)=1+{A}{|X|^{-\\gamma}}$ for $|X|$ large, when $A<0$ and $\\gamma\\in(0,2)$. Such surfaces are close to sections of unduloids with small necksize, folded along circumferences centered at the origin and with larger and larger radii. The construction involves a deep study of the corresponding Jacobi operators, an application of the Lyapunov-Schmidt reduction method and some variational argument.","authors_text":"Monica Musso, Paolo Caldiroli","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-25T14:01:50Z","title":"Embedded tori with prescribed mean curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08495","kind":"arxiv","version":2},"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":"sha256:437af58d575998a65fd88719f285a4fa1e6a61a9f7eeb77761f2b8a9e92ff0f9","target":"record","created_at":"2026-05-18T00:03:24Z","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":"4ae4fbdf48b78a4161373a9803c3cb0707ae2eef49ee291095a0ef0e8e465ded","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-25T14:01:50Z","title_canon_sha256":"f55f0fabcbf6d0bc67926e7cbf4e2f375993de93ce511dad2e243dbbc0faf23b"},"schema_version":"1.0","source":{"id":"1709.08495","kind":"arxiv","version":2}},"canonical_sha256":"a61839fac441fc4732f06626f09f4290d8bfdd7d1c9f76a8459ac7baeb25bc96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a61839fac441fc4732f06626f09f4290d8bfdd7d1c9f76a8459ac7baeb25bc96","first_computed_at":"2026-05-18T00:03:24.950682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:24.950682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0RN0qu0rOzXURzbGL1MZjTOLiNvufPfj5xG4cSYeco8UBRswsS7ht4LDOaXfJJCOCdXzvuNf1T6YlFIfOw7eDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:24.951126Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.08495","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:437af58d575998a65fd88719f285a4fa1e6a61a9f7eeb77761f2b8a9e92ff0f9","sha256:ea8a3076b20c0262dab711e4d029f09746972da283fc5fb174eaad635c8fbe65"],"state_sha256":"d8052837e279e4bedc8660d927c7f57e35c4402fea48ad3c8398e90fdd1e49e0"}