{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:OE3XG2JGY5NMDHNLCV7M23XHLW","short_pith_number":"pith:OE3XG2JG","canonical_record":{"source":{"id":"2503.05036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-03-06T23:22:19Z","cross_cats_sorted":[],"title_canon_sha256":"310d9115c31da4d4e4d260c68d683158873554a21b7327d15327ae44533e5102","abstract_canon_sha256":"1b0722ad774ace85f39ff0799286f1a72329c2e436624fb070a8c7f6bf4a6421"},"schema_version":"1.0"},"canonical_sha256":"7137736926c75ac19dab157ecd6ee75d9fdd78c85df65861b3018dc2445d2ca6","source":{"kind":"arxiv","id":"2503.05036","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.05036","created_at":"2026-07-05T10:26:18Z"},{"alias_kind":"arxiv_version","alias_value":"2503.05036v1","created_at":"2026-07-05T10:26:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.05036","created_at":"2026-07-05T10:26:18Z"},{"alias_kind":"pith_short_12","alias_value":"OE3XG2JGY5NM","created_at":"2026-07-05T10:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"OE3XG2JGY5NMDHNL","created_at":"2026-07-05T10:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"OE3XG2JG","created_at":"2026-07-05T10:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:OE3XG2JGY5NMDHNLCV7M23XHLW","target":"record","payload":{"canonical_record":{"source":{"id":"2503.05036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-03-06T23:22:19Z","cross_cats_sorted":[],"title_canon_sha256":"310d9115c31da4d4e4d260c68d683158873554a21b7327d15327ae44533e5102","abstract_canon_sha256":"1b0722ad774ace85f39ff0799286f1a72329c2e436624fb070a8c7f6bf4a6421"},"schema_version":"1.0"},"canonical_sha256":"7137736926c75ac19dab157ecd6ee75d9fdd78c85df65861b3018dc2445d2ca6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:26:18.834370Z","signature_b64":"J7ZIM0YpJgrLh/gPF83NKs1sDmJz0kNqniXSmpFyHc74l/N32BpyaRo8vj7Z8QwoXbCCHSkaGtjwtkdc/FmqBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7137736926c75ac19dab157ecd6ee75d9fdd78c85df65861b3018dc2445d2ca6","last_reissued_at":"2026-07-05T10:26:18.833889Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:26:18.833889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.05036","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:26:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2KlaL8ZVyu6yZND5fLRpWj7g/pcLArPWJ2JqiHj89mN2DRZgNentzrd54anaYV+Anbmgu/aHsLSjYmDt2oLVAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:45:49.880222Z"},"content_sha256":"ae16bcbc573c21d9ed8608130276cddb4ac4274b4a134f7104321da678653b86","schema_version":"1.0","event_id":"sha256:ae16bcbc573c21d9ed8608130276cddb4ac4274b4a134f7104321da678653b86"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:OE3XG2JGY5NMDHNLCV7M23XHLW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$q$-numerical radius of rank-one operators and the generalized Buzano inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Du\\v{s}an Den\\v{c}i\\'c, Hranislav Stankovi\\'c, Ivan Damnjanovi\\'c, Mihailo Krsti\\'c","submitted_at":"2025-03-06T23:22:19Z","abstract_excerpt":"Here, we study the $q$-numerical radius of rank-one operators on a Hilbert space $\\mathcal{H}$. More precisely, for $q \\in [0,1]$ and $a, b \\in \\mathcal{H}$, we establish the formula \\[ \\omega_q(a \\otimes b) = \\frac{1}{2}\\left(\\|a\\|\\|b\\| + q|\\langle a, b \\rangle| + \\sqrt{1-q^2}\\sqrt{\\|a\\|^2\\|b\\|^2 - |\\langle a, b \\rangle|^2}\\right), \\] which represents a generalization of the well-known formula for the numerical radius of a rank-one operator in a Hilbert space, obtained by setting $q = 1$. As a corollary, we also derive a generalization of the classical Buzano inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.05036","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.05036/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:26:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gv8ZWgI0wgv1ZoqhauNcelXhSozTptqWn0JZm8coG4d8GPYY5joJScSTOD7dx8jk8wrcfAXC3VeGxcL+Z8rQBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:45:49.880723Z"},"content_sha256":"5f9434bad20ec57c6f00b17e7785a19c6ec4ca52531f95c48afac80ec989270b","schema_version":"1.0","event_id":"sha256:5f9434bad20ec57c6f00b17e7785a19c6ec4ca52531f95c48afac80ec989270b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OE3XG2JGY5NMDHNLCV7M23XHLW/bundle.json","state_url":"https://pith.science/pith/OE3XG2JGY5NMDHNLCV7M23XHLW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OE3XG2JGY5NMDHNLCV7M23XHLW/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":"2026-08-13T04:45:49Z","links":{"resolver":"https://pith.science/pith/OE3XG2JGY5NMDHNLCV7M23XHLW","bundle":"https://pith.science/pith/OE3XG2JGY5NMDHNLCV7M23XHLW/bundle.json","state":"https://pith.science/pith/OE3XG2JGY5NMDHNLCV7M23XHLW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OE3XG2JGY5NMDHNLCV7M23XHLW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OE3XG2JGY5NMDHNLCV7M23XHLW","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":"1b0722ad774ace85f39ff0799286f1a72329c2e436624fb070a8c7f6bf4a6421","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-03-06T23:22:19Z","title_canon_sha256":"310d9115c31da4d4e4d260c68d683158873554a21b7327d15327ae44533e5102"},"schema_version":"1.0","source":{"id":"2503.05036","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.05036","created_at":"2026-07-05T10:26:18Z"},{"alias_kind":"arxiv_version","alias_value":"2503.05036v1","created_at":"2026-07-05T10:26:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.05036","created_at":"2026-07-05T10:26:18Z"},{"alias_kind":"pith_short_12","alias_value":"OE3XG2JGY5NM","created_at":"2026-07-05T10:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"OE3XG2JGY5NMDHNL","created_at":"2026-07-05T10:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"OE3XG2JG","created_at":"2026-07-05T10:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:5f9434bad20ec57c6f00b17e7785a19c6ec4ca52531f95c48afac80ec989270b","target":"graph","created_at":"2026-07-05T10:26:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.05036/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Here, we study the $q$-numerical radius of rank-one operators on a Hilbert space $\\mathcal{H}$. More precisely, for $q \\in [0,1]$ and $a, b \\in \\mathcal{H}$, we establish the formula \\[ \\omega_q(a \\otimes b) = \\frac{1}{2}\\left(\\|a\\|\\|b\\| + q|\\langle a, b \\rangle| + \\sqrt{1-q^2}\\sqrt{\\|a\\|^2\\|b\\|^2 - |\\langle a, b \\rangle|^2}\\right), \\] which represents a generalization of the well-known formula for the numerical radius of a rank-one operator in a Hilbert space, obtained by setting $q = 1$. As a corollary, we also derive a generalization of the classical Buzano inequality.","authors_text":"Du\\v{s}an Den\\v{c}i\\'c, Hranislav Stankovi\\'c, Ivan Damnjanovi\\'c, Mihailo Krsti\\'c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-03-06T23:22:19Z","title":"$q$-numerical radius of rank-one operators and the generalized Buzano inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.05036","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:ae16bcbc573c21d9ed8608130276cddb4ac4274b4a134f7104321da678653b86","target":"record","created_at":"2026-07-05T10:26:18Z","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":"1b0722ad774ace85f39ff0799286f1a72329c2e436624fb070a8c7f6bf4a6421","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-03-06T23:22:19Z","title_canon_sha256":"310d9115c31da4d4e4d260c68d683158873554a21b7327d15327ae44533e5102"},"schema_version":"1.0","source":{"id":"2503.05036","kind":"arxiv","version":1}},"canonical_sha256":"7137736926c75ac19dab157ecd6ee75d9fdd78c85df65861b3018dc2445d2ca6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7137736926c75ac19dab157ecd6ee75d9fdd78c85df65861b3018dc2445d2ca6","first_computed_at":"2026-07-05T10:26:18.833889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:26:18.833889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J7ZIM0YpJgrLh/gPF83NKs1sDmJz0kNqniXSmpFyHc74l/N32BpyaRo8vj7Z8QwoXbCCHSkaGtjwtkdc/FmqBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:26:18.834370Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.05036","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae16bcbc573c21d9ed8608130276cddb4ac4274b4a134f7104321da678653b86","sha256:5f9434bad20ec57c6f00b17e7785a19c6ec4ca52531f95c48afac80ec989270b"],"state_sha256":"8e4ad9845e70defd2e3bc3b05f20d5aa09aff1cc9d859f9c8fbf2b5aab114465"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p5IIedtKSwuvhPK6txS11dwgMYOZk3yuC7qe1togoAcCrl49DIK2CZmwmRPSKHE7jc6U8TjsPmelhIGgYbBmDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T04:45:49.885194Z","bundle_sha256":"7751dacabee4d828b8a2ef3ffe598dacc46565dfdc9cf1b02f95ad8f8ed4b87c"}}