{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OH6ZE7XWDPZTGMQLUTQGMTMO2F","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":"60b91dcbb6883e765402b89c65e2e96ecfd8f2a0cbcb5c1ccb5c3889b1a77e8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-26T04:15:37Z","title_canon_sha256":"6dbb4ccd5e01752beebce2788b2e5f7fa5fba300af76e8cb59d5dce12f1fa8aa"},"schema_version":"1.0","source":{"id":"1610.08162","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08162","created_at":"2026-05-18T00:46:51Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08162v2","created_at":"2026-05-18T00:46:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08162","created_at":"2026-05-18T00:46:51Z"},{"alias_kind":"pith_short_12","alias_value":"OH6ZE7XWDPZT","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OH6ZE7XWDPZTGMQL","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OH6ZE7XW","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:032293b2ae3d9ff1b1b365360525cad8db29e44a5d487a6cde0fa07b584da0dd","target":"graph","created_at":"2026-05-18T00:46:51Z","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":"Lawson-Osserman constructed three types of non-parametric minimal cones of high codimensions based on Hopf maps between spheres, which correspond to Lipschitz but non-differentiable solutions to the minimal surface equations, thereby making sharp contrast to the regularity theorem for minimal graphs of codimension 1. In this paper, we develop the constructions in a more general scheme. Once a mapping f between unit spheres is composited of a harmonic Riemannian submersion and a homothetic (i.e., up to a constant factor, isometric) minimal immersion, certain twisted graph of f can yield a non-p","authors_text":"Ling Yang, Xiaowei Xu, Yongsheng Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-26T04:15:37Z","title":"On Lawson-Osserman Constructions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08162","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:ab94d858fefe55cabde5315f3cced7df666f2fb1d8c47c34b8c9d995fc299e9f","target":"record","created_at":"2026-05-18T00:46:51Z","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":"60b91dcbb6883e765402b89c65e2e96ecfd8f2a0cbcb5c1ccb5c3889b1a77e8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-26T04:15:37Z","title_canon_sha256":"6dbb4ccd5e01752beebce2788b2e5f7fa5fba300af76e8cb59d5dce12f1fa8aa"},"schema_version":"1.0","source":{"id":"1610.08162","kind":"arxiv","version":2}},"canonical_sha256":"71fd927ef61bf333320ba4e0664d8ed17d421e89f739c9772745a356941755da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71fd927ef61bf333320ba4e0664d8ed17d421e89f739c9772745a356941755da","first_computed_at":"2026-05-18T00:46:51.591110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:51.591110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ombxDfxaNN0pE+JT5WNswsfDCIMNT2lX1HJozVtz1S21wwfUJgNMXUQOUWYkU0P6gd3rKF09aFqFQo/mbbVPAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:51.591728Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08162","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab94d858fefe55cabde5315f3cced7df666f2fb1d8c47c34b8c9d995fc299e9f","sha256:032293b2ae3d9ff1b1b365360525cad8db29e44a5d487a6cde0fa07b584da0dd"],"state_sha256":"651b77f6ab48afc7bf78cc125ea17ce107029bfb54e6448c3b354c29dd868855"}