{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AH2CDJOBHHOOVV7AA55PTCD5GB","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":"eae1a77b1772d0f55d693f40f469838f595dfb6773d1bf72c9593b9c743fc43e","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-06-26T18:50:33Z","title_canon_sha256":"64a011d9707f11b09107bc0e725581a36e3a7bc22e483e1701df51ba5b7efaa7"},"schema_version":"1.0","source":{"id":"1606.08888","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08888","created_at":"2026-05-18T01:11:42Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08888v1","created_at":"2026-05-18T01:11:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08888","created_at":"2026-05-18T01:11:42Z"},{"alias_kind":"pith_short_12","alias_value":"AH2CDJOBHHOO","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AH2CDJOBHHOOVV7A","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AH2CDJOB","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:f1a45c805e104d38437a09e5a5e24f4b0c0eac354064dc0f153569dd8ca4c987","target":"graph","created_at":"2026-05-18T01:11:42Z","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":"This paper generalizes the result of Elmachtoub et al to any weighted barycenter, where a transformation is considered which takes an arbitrary point of division $\\xi \\in (0,1)$ of the segments of a polygon with $n$ vertices. We then consider connecting these new points to form another polygon, and iterate this process. After considering properties of our generalized transformation matrix, a surprisingly elegant interplay of elementary complex analysis and linear algebra is used to find a closed form for our iterative process. We then specify the new limiting ellipse, $\\mathcal{E}$, which has ","authors_text":"Keller VandeBogert","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-06-26T18:50:33Z","title":"Random Polygon to Ellipse: A Generalization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08888","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:c4afdb9b65b24d44b9de6c5761916e94783013e2a4939da4c2ffcdb5097b6f42","target":"record","created_at":"2026-05-18T01:11:42Z","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":"eae1a77b1772d0f55d693f40f469838f595dfb6773d1bf72c9593b9c743fc43e","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-06-26T18:50:33Z","title_canon_sha256":"64a011d9707f11b09107bc0e725581a36e3a7bc22e483e1701df51ba5b7efaa7"},"schema_version":"1.0","source":{"id":"1606.08888","kind":"arxiv","version":1}},"canonical_sha256":"01f421a5c139dcead7e0077af9887d3079eed0bb04b89aad438e6a60ed7ca72e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01f421a5c139dcead7e0077af9887d3079eed0bb04b89aad438e6a60ed7ca72e","first_computed_at":"2026-05-18T01:11:42.139753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:42.139753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"shmhjR8t+hJHFVfVJ8VuRqGnalemPaTSNsTqY7nKLpMOkUZYrJ7v4TYeuii2IDviHPq85bWqwyyTCNBX9sZaDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:42.140114Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.08888","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4afdb9b65b24d44b9de6c5761916e94783013e2a4939da4c2ffcdb5097b6f42","sha256:f1a45c805e104d38437a09e5a5e24f4b0c0eac354064dc0f153569dd8ca4c987"],"state_sha256":"8675a1800c10d81e9de344e4f556f0fb0b358d5fe21ba559443d961d0c3dbf6b"}