{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Q2HRVISSIWIV6PMWFFR7VCIGXJ","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":"c1c48b2ce5fdf873949145adc756ae15921c703d6b4ef7ed68764d4a85fcb344","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-06-25T07:33:17Z","title_canon_sha256":"9bae4f9a8bd0d6a8a2884b112a887e280bd7a10693d871f39ff4799e83cca254"},"schema_version":"1.0","source":{"id":"1306.5866","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5866","created_at":"2026-05-18T03:19:58Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5866v1","created_at":"2026-05-18T03:19:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5866","created_at":"2026-05-18T03:19:58Z"},{"alias_kind":"pith_short_12","alias_value":"Q2HRVISSIWIV","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q2HRVISSIWIV6PMW","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q2HRVISS","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:a86ea758307700fb8423d927bc029521306d957da660c73bc76ecfcf89655e86","target":"graph","created_at":"2026-05-18T03:19:58Z","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 $E$ be the union of two real intervals not containing zero. Then $L_n^r(E)$ denotes the supremum norm of that polynomial $P_n$ of degree less than or equal to $n$, which is minimal with respect to the supremum norm provided that $P_n(0)=1$. It is well known that the limit $\\kappa(E):=\\lim_{n\\to\\infty}\\sqrt[n]{L_n^r(E)}$ exists, where $\\kappa(E)$ is called the asymptotic convergence factor, since it plays a crucial role for certain iterative methods solving large-scale matrix problems. The factor $\\kappa(E)$ can be expressed with the help of Jacobi's elliptic and theta functions, where this","authors_text":"Klaus Schiefermayr","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-06-25T07:33:17Z","title":"Estimates for the asymptotic convergence factor of two intervals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5866","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":"sha256:27bef2dd35b498ff142c6f10f7bb8269b3aafdff6c6036320e55ec197ada5e9c","target":"record","created_at":"2026-05-18T03:19:58Z","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":"c1c48b2ce5fdf873949145adc756ae15921c703d6b4ef7ed68764d4a85fcb344","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-06-25T07:33:17Z","title_canon_sha256":"9bae4f9a8bd0d6a8a2884b112a887e280bd7a10693d871f39ff4799e83cca254"},"schema_version":"1.0","source":{"id":"1306.5866","kind":"arxiv","version":1}},"canonical_sha256":"868f1aa25245915f3d962963fa8906ba47054f93a5d7a02e445153cd5a611736","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"868f1aa25245915f3d962963fa8906ba47054f93a5d7a02e445153cd5a611736","first_computed_at":"2026-05-18T03:19:58.307601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:58.307601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OSYZwYhgYn5qqL3IuHCTWrFOQtiurjD6Sg/46l9DG8hl9Fs4a/KBSqpcwVmQm/wB5LpYje4nlmOHWHv6UPJHAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:58.308134Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5866","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27bef2dd35b498ff142c6f10f7bb8269b3aafdff6c6036320e55ec197ada5e9c","sha256:a86ea758307700fb8423d927bc029521306d957da660c73bc76ecfcf89655e86"],"state_sha256":"7c7053a95461b287c77730bc11b697e7340148bceeb72908fb06b007e78babc7"}