{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CR7WASUJ7S7WOEOLQIXTV2WY5X","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":"d31f872c21e3c13fc219fbe918458aa2b511dcc7d7b0260c2fc853bd3a13ff1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-29T14:18:25Z","title_canon_sha256":"e18a400a9a2d69d1366a297ac06b6a8f973691a4da0e68032011787d372b876e"},"schema_version":"1.0","source":{"id":"1505.08054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.08054","created_at":"2026-05-18T00:36:48Z"},{"alias_kind":"arxiv_version","alias_value":"1505.08054v1","created_at":"2026-05-18T00:36:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.08054","created_at":"2026-05-18T00:36:48Z"},{"alias_kind":"pith_short_12","alias_value":"CR7WASUJ7S7W","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CR7WASUJ7S7WOEOL","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CR7WASUJ","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:a5c91ee35158302f61f5c59a70d545b6ebe53e2aad11d478354fae48e5a1f56d","target":"graph","created_at":"2026-05-18T00:36:48Z","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 introduce a smooth quadratic conformal functional and its weighted version $$W_2=\\sum_e \\beta^2(e)\\quad W_{2,w}=\\sum_e (n_i+n_j)\\beta^2(e),$$ where $\\beta(e)$ is the extrinsic intersection angle of the circumcircles of the triangles of the mesh sharing the edge $e=(ij)$ and $n_i$ is the valence of vertex $i$. Besides minimizing the squared local conformal discrete Willmore energy $W$ this functional also minimizes local differences of the angles $\\beta$. We investigate the minimizers of this functionals for simplicial spheres and simplicial surfaces of nontrivial topology. Several remarkabl","authors_text":"Alexander I. Bobenko, Martin P. Weidner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-29T14:18:25Z","title":"On a new conformal functional for simplicial surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.08054","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:ba06a1dcdc404bdfad5cf1aa3e9176437b357bbcd6fb61879b982880cde37219","target":"record","created_at":"2026-05-18T00:36:48Z","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":"d31f872c21e3c13fc219fbe918458aa2b511dcc7d7b0260c2fc853bd3a13ff1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-29T14:18:25Z","title_canon_sha256":"e18a400a9a2d69d1366a297ac06b6a8f973691a4da0e68032011787d372b876e"},"schema_version":"1.0","source":{"id":"1505.08054","kind":"arxiv","version":1}},"canonical_sha256":"147f604a89fcbf6711cb822f3aead8edfafecf7ff166dd81cc0c33a16e28c628","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"147f604a89fcbf6711cb822f3aead8edfafecf7ff166dd81cc0c33a16e28c628","first_computed_at":"2026-05-18T00:36:48.148922Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:48.148922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+TvvY/y/kHkGrqAueVgR3pVbVfzP/RuRcgKqWrO2nAeOB7ZzhxqzevIcJLgH+F1SSbqK/p7rKXjkyYVDmsDmCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:48.149432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.08054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba06a1dcdc404bdfad5cf1aa3e9176437b357bbcd6fb61879b982880cde37219","sha256:a5c91ee35158302f61f5c59a70d545b6ebe53e2aad11d478354fae48e5a1f56d"],"state_sha256":"dafad6ab44dd766855740d2fad90502db42e5a2b6d8f18bf8be0405c8ab24d71"}