{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Q2D3BMPLMY7SCRGT6CNATPAZ3D","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":"8d45928de75a6ff219c8b1132d911711587a1d4a2d83d91d69cd90465d1190d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-11T02:41:22Z","title_canon_sha256":"55ab4986b2155b963f205115ff2ccc77e41f539c0f28b7b593a60a1a44c57bbf"},"schema_version":"1.0","source":{"id":"1302.2803","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2803","created_at":"2026-05-18T03:33:50Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2803v1","created_at":"2026-05-18T03:33:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2803","created_at":"2026-05-18T03:33:50Z"},{"alias_kind":"pith_short_12","alias_value":"Q2D3BMPLMY7S","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q2D3BMPLMY7SCRGT","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q2D3BMPL","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:036c8d8c937d366d1b866c688caab766145f0f116e2c4aa249bed3c4741a6a98","target":"graph","created_at":"2026-05-18T03:33:50Z","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":"By the help of power series f we can naturally construct another power series that has as coefficients the absolute values of the coefficients of f. Utilising these functions we prove some inequalities for the spectral radius of the bounded linear operator f(T) on a complex Hilbert space and some functions of its norm. The case of two commuting operators is also investigated.","authors_text":"S.S. Dragomir","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-11T02:41:22Z","title":"Spectral Radius Inequalities for Functions of Operators Defined by Power Series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2803","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:a07673c66d7fcd1dadee0297d01ab4750c035639279c27d2a3c8e588157e5c9d","target":"record","created_at":"2026-05-18T03:33:50Z","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":"8d45928de75a6ff219c8b1132d911711587a1d4a2d83d91d69cd90465d1190d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-11T02:41:22Z","title_canon_sha256":"55ab4986b2155b963f205115ff2ccc77e41f539c0f28b7b593a60a1a44c57bbf"},"schema_version":"1.0","source":{"id":"1302.2803","kind":"arxiv","version":1}},"canonical_sha256":"8687b0b1eb663f2144d3f09a09bc19d8f7ffc1da8fab8f491513691e5fbea4c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8687b0b1eb663f2144d3f09a09bc19d8f7ffc1da8fab8f491513691e5fbea4c9","first_computed_at":"2026-05-18T03:33:50.783572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:50.783572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iQMGjbffupxP/m77LEJlTHNSFScgZW1nvFL6i7CQ3jlTzdWOPd4OkTgb0Ns/IQCNU0O5dFxtVosgb7slEgBdDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:50.784552Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.2803","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a07673c66d7fcd1dadee0297d01ab4750c035639279c27d2a3c8e588157e5c9d","sha256:036c8d8c937d366d1b866c688caab766145f0f116e2c4aa249bed3c4741a6a98"],"state_sha256":"ca0786be09bce3a02755a4b42b8def61ade7c07d77c8054bbc04a48cda5218dd"}