{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PNGAMBECH4NX7O5MFSXLJXCCKP","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":"d19b6912ca771df0cbb4359516072aa910b568721903536c8d4939f45842e92e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-09T14:54:49Z","title_canon_sha256":"9c95201dc254f6765c7f3be2d9e2bfbebbd7aeeaead8dea583dceed2023889a9"},"schema_version":"1.0","source":{"id":"1608.02823","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02823","created_at":"2026-05-18T01:09:33Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02823v1","created_at":"2026-05-18T01:09:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02823","created_at":"2026-05-18T01:09:33Z"},{"alias_kind":"pith_short_12","alias_value":"PNGAMBECH4NX","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PNGAMBECH4NX7O5M","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PNGAMBEC","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:4f0c1165e962387bce35be4c014fc9f0f973f0fdbf8203f9fd7ef0de77064a44","target":"graph","created_at":"2026-05-18T01:09:33Z","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 every $g\\in\\mathbb{N}_0$ and $\\epsilon>0$, we construct a smooth genus $g$ surface embedded into the unit ball with area $8\\pi$ and Willmore energy smaller than $8\\pi + \\epsilon$. From this we deduce that a minimising sequence for Willmore's energy in the class of genus $g$ surfaces embedded in the unit ball with area $8\\pi$ converges to a doubly covered sphere for all $g\\in\\mathbb{N}_0$. We obtain the same result for certain Canham-Helfrich energies with $\\chi_K\\leq 0$ without genus constraint and show that Canham-Helfrich energies with $\\chi_K>0$ are not bounded from below in the class o","authors_text":"Stephan Wojtowytsch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-09T14:54:49Z","title":"Helfrich's Energy and Constrained Minimisation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02823","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:c9bf0fe84c391167b209a9797fb3b2244520f71aaf2b35cf5b95ab10cbc97fbe","target":"record","created_at":"2026-05-18T01:09:33Z","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":"d19b6912ca771df0cbb4359516072aa910b568721903536c8d4939f45842e92e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-09T14:54:49Z","title_canon_sha256":"9c95201dc254f6765c7f3be2d9e2bfbebbd7aeeaead8dea583dceed2023889a9"},"schema_version":"1.0","source":{"id":"1608.02823","kind":"arxiv","version":1}},"canonical_sha256":"7b4c0604823f1b7fbbac2caeb4dc4253c5ffcd46080f9c91685dadacdaf8e4fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b4c0604823f1b7fbbac2caeb4dc4253c5ffcd46080f9c91685dadacdaf8e4fb","first_computed_at":"2026-05-18T01:09:33.609936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:33.609936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zlqaKOFlF5ZjaLQnJmdtULR+1MhCueatjCdwEslzoMx0Pt+7n7obPAB2CuH8I6M8rrcnQMzCGjFsKxafa54xAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:33.610331Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.02823","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9bf0fe84c391167b209a9797fb3b2244520f71aaf2b35cf5b95ab10cbc97fbe","sha256:4f0c1165e962387bce35be4c014fc9f0f973f0fdbf8203f9fd7ef0de77064a44"],"state_sha256":"2443fdcfe0dc6d43b5eda5262dd3fc25a79951db888f0c698224abd978ae29b9"}