{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:TLT4HXDGMNSEK2SYBB6CIJGPBO","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":"8d187170349dd64e496afd31dc6606d53754a78433b1661a47cebcb57697ca67","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-12-10T01:43:49Z","title_canon_sha256":"771dd6bdd5aa618da2879bb0551c652d74540ccefe7c3d926bda59036b656569"},"schema_version":"1.0","source":{"id":"2012.05401","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.05401","created_at":"2026-07-05T03:03:18Z"},{"alias_kind":"arxiv_version","alias_value":"2012.05401v2","created_at":"2026-07-05T03:03:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.05401","created_at":"2026-07-05T03:03:18Z"},{"alias_kind":"pith_short_12","alias_value":"TLT4HXDGMNSE","created_at":"2026-07-05T03:03:18Z"},{"alias_kind":"pith_short_16","alias_value":"TLT4HXDGMNSEK2SY","created_at":"2026-07-05T03:03:18Z"},{"alias_kind":"pith_short_8","alias_value":"TLT4HXDG","created_at":"2026-07-05T03:03:18Z"}],"graph_snapshots":[{"event_id":"sha256:f9a79e2df2059115ec5aab5501e164aef5618f0198aa98892add767f585d21f6","target":"graph","created_at":"2026-07-05T03:03:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2012.05401/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we show that every $8$-dimensional closed Riemmanian manifold with $C^\\infty$-generic metrics admits a smooth minimal hypersurface. This generalized previous results by N. Smale and Chodosh-Liokumovich-Spolaor. Different from their local perturbation techniques, our construction is based on a global perturbation argument in and a novel geometric invariant which counts singular points with suitable weights.","authors_text":"Yangyang Li, Zhihan Wang","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-12-10T01:43:49Z","title":"Generic Regularity of Minimal Hypersurfaces in Dimension 8"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.05401","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":"sha256:889cdcdfe82b98dca0be4fcf4564777ccb839383989101ec25b410adef8278ad","target":"record","created_at":"2026-07-05T03:03:18Z","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":"8d187170349dd64e496afd31dc6606d53754a78433b1661a47cebcb57697ca67","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-12-10T01:43:49Z","title_canon_sha256":"771dd6bdd5aa618da2879bb0551c652d74540ccefe7c3d926bda59036b656569"},"schema_version":"1.0","source":{"id":"2012.05401","kind":"arxiv","version":2}},"canonical_sha256":"9ae7c3dc666364456a58087c2424cf0b888a51fa7a2b98ca29452346b716271f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ae7c3dc666364456a58087c2424cf0b888a51fa7a2b98ca29452346b716271f","first_computed_at":"2026-07-05T03:03:18.489146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:03:18.489146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sdS7hit8W7cSdT5OfDzHEELMIoM/oExedfh7CrjG164Zwmi3muNars6kmOx9VTEvsVN3xEaFJcvpA3WGI6ETBg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:03:18.489649Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.05401","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:889cdcdfe82b98dca0be4fcf4564777ccb839383989101ec25b410adef8278ad","sha256:f9a79e2df2059115ec5aab5501e164aef5618f0198aa98892add767f585d21f6"],"state_sha256":"5494d7d0bec9e7cfaf4ff910540def9ca920ef19ee22f8b569de7a94afde8b8e"}