{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HM6QEKGNMMPO4FWUYERTKWGUHE","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":"b7607540e4d82a3067c97dc61271768260d879233bffd6f586b797ab993ab741","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-25T15:13:16Z","title_canon_sha256":"fd507629696f441c9ac26bf3c5406bd744d6bf70fbc4b4d776e4ff614fab0c2a"},"schema_version":"1.0","source":{"id":"1807.09654","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.09654","created_at":"2026-05-18T00:09:50Z"},{"alias_kind":"arxiv_version","alias_value":"1807.09654v1","created_at":"2026-05-18T00:09:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09654","created_at":"2026-05-18T00:09:50Z"},{"alias_kind":"pith_short_12","alias_value":"HM6QEKGNMMPO","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HM6QEKGNMMPO4FWU","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HM6QEKGN","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:80f7f71806d536f6dfcbb0cb3878eca5e060c129caaef4206e1784b932d2934b","target":"graph","created_at":"2026-05-18T00:09:50Z","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 simply connected homogeneous three-manifold with isometry group of dimension $4$, and let $\\Sigma$ be any compact surface of genus zero immersed in $M$ whose mean, extrinsic and Gauss curvatures satisfy a smooth elliptic relation $\\Phi(H,K_e,K)=0$. In this paper we prove that $\\Sigma$ is a sphere of revolution, provided that the unique inextendible rotational surface $S$ in $M$ that satisfies this equation and touches its rotation axis orthogonally has bounded second fundamental form. In particular, we prove that: (i) any elliptic Weingarten sphere immersed in $\\mathbb{H}^2\\times ","authors_text":"Jose A. Galvez, Pablo Mira","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-25T15:13:16Z","title":"Rotational symmetry of Weingarten spheres in homogeneous three-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09654","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":"sha256:940d172f55b2e3e013df5dcc59569d2e47cf4613c54095440fdfdda66d3eb937","target":"record","created_at":"2026-05-18T00:09:50Z","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":"b7607540e4d82a3067c97dc61271768260d879233bffd6f586b797ab993ab741","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-25T15:13:16Z","title_canon_sha256":"fd507629696f441c9ac26bf3c5406bd744d6bf70fbc4b4d776e4ff614fab0c2a"},"schema_version":"1.0","source":{"id":"1807.09654","kind":"arxiv","version":1}},"canonical_sha256":"3b3d0228cd631eee16d4c1233558d4392953c7606d9aae9ae00e323532daf679","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b3d0228cd631eee16d4c1233558d4392953c7606d9aae9ae00e323532daf679","first_computed_at":"2026-05-18T00:09:50.691174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:50.691174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0FI3FvwdvDjkmtpMq+7lPvGqcpqVobNsD0TZonU5HdIhk92X793SLbTtmwEu73yHIbgPOpmjTuB/X+X7tQtoDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:50.691862Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.09654","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:940d172f55b2e3e013df5dcc59569d2e47cf4613c54095440fdfdda66d3eb937","sha256:80f7f71806d536f6dfcbb0cb3878eca5e060c129caaef4206e1784b932d2934b"],"state_sha256":"56ee1e9d3ee9eefdafe9cf3f5e4db664a34e9e9795d82700d40c1b5efa14062a"}