{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FKEV6KB4ZHSFGPSC5GNXRLU6IL","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":"61eea62d8f281b174a34944f084e76dec37044a6d38766433ed69bf4b7a976e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-15T13:40:01Z","title_canon_sha256":"79e60084847680f544f6a8605d017cf5b9e16f2a26f5cd81f273d1e937db2c81"},"schema_version":"1.0","source":{"id":"1108.2992","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2992","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2992v1","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2992","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"pith_short_12","alias_value":"FKEV6KB4ZHSF","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FKEV6KB4ZHSFGPSC","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FKEV6KB4","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:daa00287432831d3b3c583d5d5c9fe0af12b82a92da2a7ae62352d578769321d","target":"graph","created_at":"2026-05-18T04:15:28Z","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":"Let $X\\subset\\A^{2r}$ be a real curve embedded into an even-dimensional affine space. In the main result of this paper, we characterise when the r-th secant variety to $X$ is an irreducible component of the algebraic boundary of the convex hull of the real points $X(\\R)$ of $X$. This fact is then applied to 4-dimensional SO(2)-orbitopes and to the so called Barvinok-Novik orbitopes to study when they are basic closed as semi-algebraic sets. In the case of 4-dimensional SO(2)-orbitopes, we find all irreducible components of their algebraic boundary.","authors_text":"Rainer Sinn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-15T13:40:01Z","title":"The Algebraic Boundary of SO(2)-Orbitopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2992","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:e4e7413f38cf0d5246c6219769ca44ca1e28af2331aee8c8cd10d2cc524fab5f","target":"record","created_at":"2026-05-18T04:15:28Z","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":"61eea62d8f281b174a34944f084e76dec37044a6d38766433ed69bf4b7a976e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-15T13:40:01Z","title_canon_sha256":"79e60084847680f544f6a8605d017cf5b9e16f2a26f5cd81f273d1e937db2c81"},"schema_version":"1.0","source":{"id":"1108.2992","kind":"arxiv","version":1}},"canonical_sha256":"2a895f283cc9e4533e42e99b78ae9e42dbb161c5357ac1397736ea68a834c8d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a895f283cc9e4533e42e99b78ae9e42dbb161c5357ac1397736ea68a834c8d5","first_computed_at":"2026-05-18T04:15:28.874591Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:28.874591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HYcmYYfG1rFKpwyLJnLAiG3RvqJLhyMGdbKmQtXRBYg5/7vnM43/HQ1w2rF7zKtq5mVf8CL6WT0c3kBv4aI/BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:28.875231Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2992","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4e7413f38cf0d5246c6219769ca44ca1e28af2331aee8c8cd10d2cc524fab5f","sha256:daa00287432831d3b3c583d5d5c9fe0af12b82a92da2a7ae62352d578769321d"],"state_sha256":"5153ec39bc0d1be921ec2c439048813c3c69b7bf9d07ec699d676feb1cd4a94d"}