{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YASN4QL27SUIVMBEC6SWR6KQQM","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":"b50fceed93cb0758587dfb798418e40437735f9f89430259d4fcfda85a3abfc6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-04-12T17:46:04Z","title_canon_sha256":"a772bcb797618b8ec646f1e340d4a688a18a14e42399ad32cabeedbe6de1d484"},"schema_version":"1.0","source":{"id":"1704.03857","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03857","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03857v1","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03857","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"pith_short_12","alias_value":"YASN4QL27SUI","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YASN4QL27SUIVMBE","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YASN4QL2","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:f114aafffc67b85b1395b30afb33f877e1ba3ace3d041eaa8624c37c69ac4554","target":"graph","created_at":"2026-05-18T00:46:26Z","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 relatively polynomially convex subset $V$ of a domain $\\Omega$ has the extension property if for every polynomial $p$ there is a bounded holomorphic function $\\phi$ on $\\Omega$ that agrees with $p$ on $V$ and whose $H^\\infty$ norm on $\\Omega$ equals the sup-norm of $p$ on $V$. We show that if $\\Omega$ is either strictly convex or strongly linearly convex in ${\\mathbb C}^2$, or the ball in any dimension, then the only sets that have the extension property are retracts. If $\\Omega$ is strongly linearly convex in any dimension and $V$ has the extension property, we show that $V$ is a totally ge","authors_text":"John McCarthy, Lukasz Kosinski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-04-12T17:46:04Z","title":"Norm preserving extensions of bounded holomorphic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03857","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":"sha256:63c5e822c905af4ed7f5fa642f2ab7dd6a220b10b748e1daa92dc2e3d655697d","target":"record","created_at":"2026-05-18T00:46:26Z","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":"b50fceed93cb0758587dfb798418e40437735f9f89430259d4fcfda85a3abfc6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-04-12T17:46:04Z","title_canon_sha256":"a772bcb797618b8ec646f1e340d4a688a18a14e42399ad32cabeedbe6de1d484"},"schema_version":"1.0","source":{"id":"1704.03857","kind":"arxiv","version":1}},"canonical_sha256":"c024de417afca88ab02417a568f9508337713a2a3e643a9d1d6b27062450bdeb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c024de417afca88ab02417a568f9508337713a2a3e643a9d1d6b27062450bdeb","first_computed_at":"2026-05-18T00:46:26.701990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:26.701990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qDHv1ibjmofi5zqpYERqDqFxxshCHiCHy/w9MT01MFUBCbkqLsE2wCGiZwQ6S0bNk6zzXZXNoLVeIqoeA25IBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:26.702613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03857","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63c5e822c905af4ed7f5fa642f2ab7dd6a220b10b748e1daa92dc2e3d655697d","sha256:f114aafffc67b85b1395b30afb33f877e1ba3ace3d041eaa8624c37c69ac4554"],"state_sha256":"cfed4b20512c5ec93b25eabf3bbd388219ef161aacfe39e39b16e7e14e4fe572"}