{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HXFEWFDCQ7TJBSVQNEONGWPLPK","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":"0fad820f593a7004e069d2aba9e56f4755d75f9a9fb3b7f405298e4efd2b30d7","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-08T14:55:11Z","title_canon_sha256":"bfd4368a961ac9a967329f3dbb5506b44207074dfa520bb0803d5e81f0a67b29"},"schema_version":"1.0","source":{"id":"1504.01996","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01996","created_at":"2026-05-18T00:49:52Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01996v2","created_at":"2026-05-18T00:49:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01996","created_at":"2026-05-18T00:49:52Z"},{"alias_kind":"pith_short_12","alias_value":"HXFEWFDCQ7TJ","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HXFEWFDCQ7TJBSVQ","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HXFEWFDC","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:74b95ca786a04b0f5ff630bccf410f2776d8797ca1ba8ef486459c4d95332544","target":"graph","created_at":"2026-05-18T00:49:52Z","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":"For any asymptotically conical self-shrinker with entropy less than or equal to that of a cylinder we show that the link of the asymptotic cone must separate the unit sphere into exactly two connected components, both diffeomorphic to the self-shrinker. Combining this with recent work of Brendle, we conclude that the round sphere uniquely minimizes the entropy among all non-flat two-dimensional self-shrinkers. This confirms a conjecture of Colding-Ilmanen-Minicozzi-White in dimension two.","authors_text":"Jacob Bernstein, Lu Wang","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-08T14:55:11Z","title":"A Topological Property of Asymptotically Conical Self-Shrinkers of Small Entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01996","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":"sha256:2d6eb0503d6095f2826ab147f711f9885eec40bed2c24d5d36630a6e4c01d557","target":"record","created_at":"2026-05-18T00:49:52Z","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":"0fad820f593a7004e069d2aba9e56f4755d75f9a9fb3b7f405298e4efd2b30d7","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-08T14:55:11Z","title_canon_sha256":"bfd4368a961ac9a967329f3dbb5506b44207074dfa520bb0803d5e81f0a67b29"},"schema_version":"1.0","source":{"id":"1504.01996","kind":"arxiv","version":2}},"canonical_sha256":"3dca4b146287e690cab0691cd359eb7ab3ff0b9b60a87bd4111b9d3e8f8e7600","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3dca4b146287e690cab0691cd359eb7ab3ff0b9b60a87bd4111b9d3e8f8e7600","first_computed_at":"2026-05-18T00:49:52.708878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:52.708878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cg06m1TXhZVIbxcyWLgHmpDAxeDx48Y9NBrc/4F6r86AF4dGhxuodJKR67gJLWREG26RS1x0m5cThiH5KwTOCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:52.709563Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01996","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d6eb0503d6095f2826ab147f711f9885eec40bed2c24d5d36630a6e4c01d557","sha256:74b95ca786a04b0f5ff630bccf410f2776d8797ca1ba8ef486459c4d95332544"],"state_sha256":"1062700150e4bc6dc2928fcc7815a0b89259ab0eb519f4a944ca8b7f74db962f"}