{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:CUTWIJPSPZ3FQSMIXNTC7L2RZC","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":"3aa1f43a0a2e25fa15a0be7a442bb08e003de57019676be0e696fe7aec31d480","cross_cats_sorted":["math.AP","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2023-07-04T17:09:51Z","title_canon_sha256":"2989552229bfd39c039f1ff042c30bbb3bfdc002f4f136179aee81ca9b62b513"},"schema_version":"1.0","source":{"id":"2307.01828","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.01828","created_at":"2026-07-05T06:28:01Z"},{"alias_kind":"arxiv_version","alias_value":"2307.01828v1","created_at":"2026-07-05T06:28:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.01828","created_at":"2026-07-05T06:28:01Z"},{"alias_kind":"pith_short_12","alias_value":"CUTWIJPSPZ3F","created_at":"2026-07-05T06:28:01Z"},{"alias_kind":"pith_short_16","alias_value":"CUTWIJPSPZ3FQSMI","created_at":"2026-07-05T06:28:01Z"},{"alias_kind":"pith_short_8","alias_value":"CUTWIJPS","created_at":"2026-07-05T06:28:01Z"}],"graph_snapshots":[{"event_id":"sha256:4d5132f1ce48f8d27d310e961c5e3b40fe659209cafb77521ce0c934f6559927","target":"graph","created_at":"2026-07-05T06:28:01Z","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/2307.01828/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove that every strictly convex 3-ball with nonnegative Ricci-curvature contains at least 3 embedded free-boundary minimal 2-disks for any generic metric, and at least 2 solutions even without genericity assumption. Our approach combines ideas from mean curvature flow, min-max theory and degree theory. We also establish the existence of smooth free-boundary mean-convex foliations. In stark contrast to our prior work in the closed setting, the present result is sharp for generic metrics.","authors_text":"Daniel Ketover, Robert Haslhofer","cross_cats":["math.AP","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2023-07-04T17:09:51Z","title":"Free boundary minimal disks in convex balls"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.01828","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":"sha256:57a52e6522ba1f316248748a156dd32f758dae7db5a89bee6cc616f320245a1a","target":"record","created_at":"2026-07-05T06:28:01Z","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":"3aa1f43a0a2e25fa15a0be7a442bb08e003de57019676be0e696fe7aec31d480","cross_cats_sorted":["math.AP","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2023-07-04T17:09:51Z","title_canon_sha256":"2989552229bfd39c039f1ff042c30bbb3bfdc002f4f136179aee81ca9b62b513"},"schema_version":"1.0","source":{"id":"2307.01828","kind":"arxiv","version":1}},"canonical_sha256":"15276425f27e76584988bb662faf51c8aa96d24ba2339c3f8b183994bcdbfdd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15276425f27e76584988bb662faf51c8aa96d24ba2339c3f8b183994bcdbfdd7","first_computed_at":"2026-07-05T06:28:01.489820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:28:01.489820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"81CSJWrsagJ99C97A/ydwnAwKahUnA7rKVNaU+5QRyOYXj9ivqMbiePgpnNM+h2KnJzPud79PJZmBBA1J25fAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:28:01.490173Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.01828","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57a52e6522ba1f316248748a156dd32f758dae7db5a89bee6cc616f320245a1a","sha256:4d5132f1ce48f8d27d310e961c5e3b40fe659209cafb77521ce0c934f6559927"],"state_sha256":"036b27a90bb4c8e5db4eb651b49d80711ffae56d8e1f031fc104ad16a7957821"}