{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6HDWNU3JN3ELU7MJJ3K3PEYUOR","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":"d844fbd11a9b8e773b92078cc709090463d0ee23c8249e6383cfb8eb73990f61","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-29T08:14:46Z","title_canon_sha256":"dc58176046dced898cec48490803ca50b644c75c21d8d0efc77e394e7303c4bc"},"schema_version":"1.0","source":{"id":"1708.08633","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.08633","created_at":"2026-05-17T23:54:56Z"},{"alias_kind":"arxiv_version","alias_value":"1708.08633v2","created_at":"2026-05-17T23:54:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08633","created_at":"2026-05-17T23:54:56Z"},{"alias_kind":"pith_short_12","alias_value":"6HDWNU3JN3EL","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6HDWNU3JN3ELU7MJ","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6HDWNU3J","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:3e8162a559a3e0df3c6e2697ad322f8be387ab916ee23735f6878970a2681f6c","target":"graph","created_at":"2026-05-17T23:54:56Z","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":"Crouzeix and Palencia recently showed that the numerical range of a Hilbert-space operator is a $(1+\\sqrt2)$-spectral set for the operator. One of the principal ingredients of their proof can be formulated as an abstract functional-analysis lemma. We give a new short proof of the lemma and show that, in the context of this lemma, the constant $(1+\\sqrt2)$ is sharp.","authors_text":"Felix Schwenninger, Thomas Ransford","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-29T08:14:46Z","title":"Remarks on the Crouzeix-Palencia proof that the numerical range is a $(1+\\sqrt2)$-spectral set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08633","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":"sha256:819688f92d9296c1772ad917b0648819b0a5f79dc96a83a9eba20a0ad5aea5b9","target":"record","created_at":"2026-05-17T23:54:56Z","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":"d844fbd11a9b8e773b92078cc709090463d0ee23c8249e6383cfb8eb73990f61","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-29T08:14:46Z","title_canon_sha256":"dc58176046dced898cec48490803ca50b644c75c21d8d0efc77e394e7303c4bc"},"schema_version":"1.0","source":{"id":"1708.08633","kind":"arxiv","version":2}},"canonical_sha256":"f1c766d3696ec8ba7d894ed5b79314745d2f19b9b4ec6d1698c5fe981b647263","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1c766d3696ec8ba7d894ed5b79314745d2f19b9b4ec6d1698c5fe981b647263","first_computed_at":"2026-05-17T23:54:56.708180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:56.708180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"chBNJBNqnjdaETs+WYEOekkxBXJBcPmX5jbmEmzxm0xip1y8HtdNVivYe1XKRnVdOKaYHU2SDWztAIQRJK74CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:56.708637Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.08633","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:819688f92d9296c1772ad917b0648819b0a5f79dc96a83a9eba20a0ad5aea5b9","sha256:3e8162a559a3e0df3c6e2697ad322f8be387ab916ee23735f6878970a2681f6c"],"state_sha256":"82b78277f3f7dc1c7de775ccd09d44af1c4a0b5269ec343b038c41aa7daca841"}