{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RJDGSQSKVXUE6MDX3ZX4GTNFFB","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":"816eb036fe468746366a1f2964b4e1533ded5651a8438adf7b232b4a8e50754d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-03-13T14:27:46Z","title_canon_sha256":"130368b78361a5d0bedf58834ae3b0fa18eb5aaf90b837a0a43816e8421c368e"},"schema_version":"1.0","source":{"id":"1603.04030","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04030","created_at":"2026-05-18T01:08:18Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04030v2","created_at":"2026-05-18T01:08:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04030","created_at":"2026-05-18T01:08:18Z"},{"alias_kind":"pith_short_12","alias_value":"RJDGSQSKVXUE","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RJDGSQSKVXUE6MDX","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RJDGSQSK","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:c32718ada5d31130434fcb2d8ef3dbdc82c0f9fdba92983d4342f94fcaca3b1e","target":"graph","created_at":"2026-05-18T01:08:18Z","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":"A set $V$ in a domain $U$ in $\\mathbb{C}^n$ has the {\\em norm-preserving extension property} if every bounded holomorphic function on $V$ has a holomorphic extension to $U$ with the same supremum norm. We prove that an algebraic subset of the {\\em symmetrized bidisc} \\[ G := \\{(z+w,zw):|z|<1, |w| < 1 \\} \\] has the norm-preserving extension property if and only if it is either a singleton, $G$ itself, a complex geodesic of $G$, or the union of the set $\\{(2z,z^2): |z|<1\\}$ and a complex geodesic of degree $1$ in $G$. We also prove that the complex geodesics in $G$ coincide with the nontrivial h","authors_text":"Jim Agler, Nicholas Young, Zinaida Lykova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-03-13T14:27:46Z","title":"Geodesics, retracts, and the norm-preserving extension property in the symmetrized bidisc"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04030","kind":"arxiv","version":2},"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:f22b06273366101847c74fcc543ca8d0ade135d388f946f11e31073eaa05d36e","target":"record","created_at":"2026-05-18T01:08:18Z","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":"816eb036fe468746366a1f2964b4e1533ded5651a8438adf7b232b4a8e50754d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-03-13T14:27:46Z","title_canon_sha256":"130368b78361a5d0bedf58834ae3b0fa18eb5aaf90b837a0a43816e8421c368e"},"schema_version":"1.0","source":{"id":"1603.04030","kind":"arxiv","version":2}},"canonical_sha256":"8a4669424aade84f3077de6fc34da5284f5e8e51e87f3509e9f7763dd00b57fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a4669424aade84f3077de6fc34da5284f5e8e51e87f3509e9f7763dd00b57fd","first_computed_at":"2026-05-18T01:08:18.172449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:18.172449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uUcmEhib1IpFiB+9AIr3WANeUn5OnePELXKy5Xk/kIBIlZhNS1o+8LjsB0LsLF75ZelDJDm/5pdpZ2fB2prvAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:18.173065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04030","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f22b06273366101847c74fcc543ca8d0ade135d388f946f11e31073eaa05d36e","sha256:c32718ada5d31130434fcb2d8ef3dbdc82c0f9fdba92983d4342f94fcaca3b1e"],"state_sha256":"1b5e367a2709cae171e2b8323c69222931555195a40590753edd3f758e7fd440"}