{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U52OEKBWFBZZEBRKK4KMCNSQFF","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":"6b8fa9720428e87ecee9c024ac743cd5ba83202d56660b835b61ef48a58370aa","cross_cats_sorted":["math.AP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-05T14:39:39Z","title_canon_sha256":"06888a365e91ea0fffa3c62af8126ee67a48eab982d7edfad97022146bf34aef"},"schema_version":"1.0","source":{"id":"1802.01423","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.01423","created_at":"2026-07-05T02:10:36Z"},{"alias_kind":"arxiv_version","alias_value":"1802.01423v3","created_at":"2026-07-05T02:10:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01423","created_at":"2026-07-05T02:10:36Z"},{"alias_kind":"pith_short_12","alias_value":"U52OEKBWFBZZ","created_at":"2026-07-05T02:10:36Z"},{"alias_kind":"pith_short_16","alias_value":"U52OEKBWFBZZEBRK","created_at":"2026-07-05T02:10:36Z"},{"alias_kind":"pith_short_8","alias_value":"U52OEKBW","created_at":"2026-07-05T02:10:36Z"}],"graph_snapshots":[{"event_id":"sha256:ad3dcad8f98d5eca4b973dc4dfcb42aa35270e00d6e198f4e73cbb03a57bd8aa","target":"graph","created_at":"2026-07-05T02:10:36Z","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/1802.01423/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"On the one hand, we prove that the Clifford torus in $\\mathbb{C}^2$ is unstable for Lagrangian mean curvature flow under arbitrarily small Hamiltonian perturbations, even though it is Hamiltonian $F$-stable and locally area minimising under Hamiltonian variations. On the other hand, we show that the Clifford torus is rigid: it is locally unique as a self-shrinker for mean curvature flow, despite having infinitesimal deformations which do not arise from rigid motions. The proofs rely on analysing higher order phenomena: specifically, showing that the Clifford torus is not a local entropy minimi","authors_text":"Christopher G. Evans, Felix Schulze, Jason D. Lotay","cross_cats":["math.AP","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-05T14:39:39Z","title":"Remarks on the self-shrinking Clifford torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01423","kind":"arxiv","version":3},"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":"sha256:6a6e58ae49a7df4f18a7da24e74e847d6337f427817bcdbb53f0692f0fb64583","target":"record","created_at":"2026-07-05T02:10:36Z","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":"6b8fa9720428e87ecee9c024ac743cd5ba83202d56660b835b61ef48a58370aa","cross_cats_sorted":["math.AP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-05T14:39:39Z","title_canon_sha256":"06888a365e91ea0fffa3c62af8126ee67a48eab982d7edfad97022146bf34aef"},"schema_version":"1.0","source":{"id":"1802.01423","kind":"arxiv","version":3}},"canonical_sha256":"a774e22836287392062a5714c13650295720383278e93a288e0c1769f031f167","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a774e22836287392062a5714c13650295720383278e93a288e0c1769f031f167","first_computed_at":"2026-07-05T02:10:36.068414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:10:36.068414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Re4Ry+VlMQZYPChbrPv94QpXy6dWCa2ZzSB5SpZ8rWndd7zn3syKzIrXJEgGMYM2dtfGuSnLn/I8b+PsrArTAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:10:36.068896Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.01423","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a6e58ae49a7df4f18a7da24e74e847d6337f427817bcdbb53f0692f0fb64583","sha256:ad3dcad8f98d5eca4b973dc4dfcb42aa35270e00d6e198f4e73cbb03a57bd8aa"],"state_sha256":"d6212a15d0ff360dfeee4bdce0a30c2084bb711fa213c17eb6daa53573a7fdc5"}