{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5DQ3KEAY5HVA5IYSBOC2ALBEYC","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":"5f29da756f140e20397883b23424c31f2b12773651414bccc178e53cc7275d08","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-24T14:53:33Z","title_canon_sha256":"38ad76afd5af9ac0ecd3be2edf29a1793b52612249ceffbc9c42aa20f9006ac1"},"schema_version":"1.0","source":{"id":"1804.09076","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09076","created_at":"2026-05-18T00:10:10Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09076v2","created_at":"2026-05-18T00:10:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09076","created_at":"2026-05-18T00:10:10Z"},{"alias_kind":"pith_short_12","alias_value":"5DQ3KEAY5HVA","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5DQ3KEAY5HVA5IYS","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5DQ3KEAY","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:c82b0876116a45e7bdadf89e186044dd6e7583e55c88ab2877651e37c378b303","target":"graph","created_at":"2026-05-18T00:10:10Z","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":"We show compactness in the locally smooth topology for certain natural families of asymptotically conical self-expanding solutions of mean curvature flow. Specifically, we show such compactness for the set of all two-dimensional self-expanders of a fixed topological type and, in all dimensions, for the set of self-expanders of low entropy and for the set of mean convex self-expanders with strictly mean convex asymptotic cones. From this we deduce that the natural projection map from the space of parameterizations of asymptotically conical self-expanders to the space of parameterizations of the","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":"2018-04-24T14:53:33Z","title":"Smooth compactness for spaces of asymptotically conical self-expanders of mean curvature flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09076","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":"sha256:59d66e92ef22cf87ae70c300a612b37339a8554640f79f0c6ae378306941cae4","target":"record","created_at":"2026-05-18T00:10:10Z","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":"5f29da756f140e20397883b23424c31f2b12773651414bccc178e53cc7275d08","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-24T14:53:33Z","title_canon_sha256":"38ad76afd5af9ac0ecd3be2edf29a1793b52612249ceffbc9c42aa20f9006ac1"},"schema_version":"1.0","source":{"id":"1804.09076","kind":"arxiv","version":2}},"canonical_sha256":"e8e1b51018e9ea0ea3120b85a02c24c0bf2e03ce21108d22f9b9040fc703a4cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8e1b51018e9ea0ea3120b85a02c24c0bf2e03ce21108d22f9b9040fc703a4cc","first_computed_at":"2026-05-18T00:10:10.292398Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:10.292398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k+NoZU7Fw2u1dAdLEc6E8V32S5pdWv1J5qk/hRp21dpizZWwDrcmCfYrVMaQOYH43rKgo8RsXO2XpXJtmd6pBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:10.292991Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.09076","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59d66e92ef22cf87ae70c300a612b37339a8554640f79f0c6ae378306941cae4","sha256:c82b0876116a45e7bdadf89e186044dd6e7583e55c88ab2877651e37c378b303"],"state_sha256":"df61032c8c2f3e64fe18f4e72888152e8544375d8e9e9c4529fe178b0243725d"}