{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:YEROU4D3UD6KRAPTRWGJJA52E4","short_pith_number":"pith:YEROU4D3","canonical_record":{"source":{"id":"1805.09569","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-24T09:34:25Z","cross_cats_sorted":[],"title_canon_sha256":"220fc1feefce0bf8fe980cefb0a1521ff90c8bfb49866068dab28b1a59f9a459","abstract_canon_sha256":"75aff3d80670dd4815baef9033f2a09f57e4e56db79e1165ccc853c215d38a91"},"schema_version":"1.0"},"canonical_sha256":"c122ea707ba0fca881f38d8c9483ba27117a6dcf730d64e23a90a5556b87e403","source":{"kind":"arxiv","id":"1805.09569","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09569","created_at":"2026-05-17T23:50:07Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09569v4","created_at":"2026-05-17T23:50:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09569","created_at":"2026-05-17T23:50:07Z"},{"alias_kind":"pith_short_12","alias_value":"YEROU4D3UD6K","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YEROU4D3UD6KRAPT","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YEROU4D3","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:YEROU4D3UD6KRAPTRWGJJA52E4","target":"record","payload":{"canonical_record":{"source":{"id":"1805.09569","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-24T09:34:25Z","cross_cats_sorted":[],"title_canon_sha256":"220fc1feefce0bf8fe980cefb0a1521ff90c8bfb49866068dab28b1a59f9a459","abstract_canon_sha256":"75aff3d80670dd4815baef9033f2a09f57e4e56db79e1165ccc853c215d38a91"},"schema_version":"1.0"},"canonical_sha256":"c122ea707ba0fca881f38d8c9483ba27117a6dcf730d64e23a90a5556b87e403","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:07.278876Z","signature_b64":"CAttkjMLNiEM4Rl1D+K5vttjOfOxZlMLFJi/2C+IqxxT6AFD4MTSe7ErjmYyG3B+Qq7RFRRxtFbrxt7y9XiDBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c122ea707ba0fca881f38d8c9483ba27117a6dcf730d64e23a90a5556b87e403","last_reissued_at":"2026-05-17T23:50:07.278434Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:07.278434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.09569","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MUfoXcqQRBSe90rJw884ynHMNaNwYbrFJzdeph9mzWP9iiiO6dFaqjUfCdcum2NZKXuFJo6OcxxvzfwRd0f2Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:24:07.069308Z"},"content_sha256":"ae8f1f816ec2e53232d0ee4ffe38743d9b77983de834d55b19832e7c8c2a92ab","schema_version":"1.0","event_id":"sha256:ae8f1f816ec2e53232d0ee4ffe38743d9b77983de834d55b19832e7c8c2a92ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:YEROU4D3UD6KRAPTRWGJJA52E4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Alternative Estimate for the Numerical Radius of Hilbert Space Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"B. Moosavi, H.R. Moradi, M. Shah Hosseini","submitted_at":"2018-05-24T09:34:25Z","abstract_excerpt":"We give an alternative lower bound for the numerical radii of Hilbert space operators. As a by-product, we find conditions such that\n  \\begin{equation*} \\omega\\left(\\left[\\begin{array}{cc} 0 & R \\\\ S & 0 \\end{array}\\right]\\right)=\\frac{\\Vert R \\Vert +\\Vert S\\Vert }{2} \\end{equation*} where $R, S \\in \\mathbb{B}(\\mathcal{H})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09569","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"68LFuPhQJKnfIKTCm1FjAPLbpu470pYbg1nEEHHDCiI8SaP5lDugC6fKCGyx1nBsW1t2S2fjLODmh/K9BoSHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:24:07.069673Z"},"content_sha256":"b04135fa1b0f693d02788ff9dd2f34f480503139830124638bfd44a6caa362b1","schema_version":"1.0","event_id":"sha256:b04135fa1b0f693d02788ff9dd2f34f480503139830124638bfd44a6caa362b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YEROU4D3UD6KRAPTRWGJJA52E4/bundle.json","state_url":"https://pith.science/pith/YEROU4D3UD6KRAPTRWGJJA52E4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YEROU4D3UD6KRAPTRWGJJA52E4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T16:24:07Z","links":{"resolver":"https://pith.science/pith/YEROU4D3UD6KRAPTRWGJJA52E4","bundle":"https://pith.science/pith/YEROU4D3UD6KRAPTRWGJJA52E4/bundle.json","state":"https://pith.science/pith/YEROU4D3UD6KRAPTRWGJJA52E4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YEROU4D3UD6KRAPTRWGJJA52E4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YEROU4D3UD6KRAPTRWGJJA52E4","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":"75aff3d80670dd4815baef9033f2a09f57e4e56db79e1165ccc853c215d38a91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-24T09:34:25Z","title_canon_sha256":"220fc1feefce0bf8fe980cefb0a1521ff90c8bfb49866068dab28b1a59f9a459"},"schema_version":"1.0","source":{"id":"1805.09569","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09569","created_at":"2026-05-17T23:50:07Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09569v4","created_at":"2026-05-17T23:50:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09569","created_at":"2026-05-17T23:50:07Z"},{"alias_kind":"pith_short_12","alias_value":"YEROU4D3UD6K","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YEROU4D3UD6KRAPT","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YEROU4D3","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:b04135fa1b0f693d02788ff9dd2f34f480503139830124638bfd44a6caa362b1","target":"graph","created_at":"2026-05-17T23:50:07Z","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":"We give an alternative lower bound for the numerical radii of Hilbert space operators. As a by-product, we find conditions such that\n  \\begin{equation*} \\omega\\left(\\left[\\begin{array}{cc} 0 & R \\\\ S & 0 \\end{array}\\right]\\right)=\\frac{\\Vert R \\Vert +\\Vert S\\Vert }{2} \\end{equation*} where $R, S \\in \\mathbb{B}(\\mathcal{H})$.","authors_text":"B. Moosavi, H.R. Moradi, M. Shah Hosseini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-24T09:34:25Z","title":"An Alternative Estimate for the Numerical Radius of Hilbert Space Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09569","kind":"arxiv","version":4},"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:ae8f1f816ec2e53232d0ee4ffe38743d9b77983de834d55b19832e7c8c2a92ab","target":"record","created_at":"2026-05-17T23:50:07Z","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":"75aff3d80670dd4815baef9033f2a09f57e4e56db79e1165ccc853c215d38a91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-24T09:34:25Z","title_canon_sha256":"220fc1feefce0bf8fe980cefb0a1521ff90c8bfb49866068dab28b1a59f9a459"},"schema_version":"1.0","source":{"id":"1805.09569","kind":"arxiv","version":4}},"canonical_sha256":"c122ea707ba0fca881f38d8c9483ba27117a6dcf730d64e23a90a5556b87e403","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c122ea707ba0fca881f38d8c9483ba27117a6dcf730d64e23a90a5556b87e403","first_computed_at":"2026-05-17T23:50:07.278434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:07.278434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CAttkjMLNiEM4Rl1D+K5vttjOfOxZlMLFJi/2C+IqxxT6AFD4MTSe7ErjmYyG3B+Qq7RFRRxtFbrxt7y9XiDBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:07.278876Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.09569","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae8f1f816ec2e53232d0ee4ffe38743d9b77983de834d55b19832e7c8c2a92ab","sha256:b04135fa1b0f693d02788ff9dd2f34f480503139830124638bfd44a6caa362b1"],"state_sha256":"57859ff6e3f26baef1106c1aea672260228ad45fa0a69548878825fb776385d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5y0fwrzX3D9dTVykrZ/54ceXrMJ8jyONYDxQ8xC09UECAvf9fTQb+hGRYvZsvDXUDDH3inGHSnJYZUhTQbzoBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T16:24:07.071625Z","bundle_sha256":"50f190f1b2685ee6ef864e06bce8340274ee4a3c1c24250041a83dea26d84d62"}}