{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:RGBYQD5GFPDSC2RDXMKQJ5ANDM","short_pith_number":"pith:RGBYQD5G","canonical_record":{"source":{"id":"1806.05443","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-14T10:07:30Z","cross_cats_sorted":[],"title_canon_sha256":"10f38a35d1793c4bd220b5d6d31d529d7bcd8a6b246dd9d423026f60189fbd84","abstract_canon_sha256":"d53eab7f46a4f5360d06dcdd3dfad6a8b00b879ca2eb00af177d982163ab3339"},"schema_version":"1.0"},"canonical_sha256":"8983880fa62bc7216a23bb1504f40d1b1e4f009ad9f5ca16390747e24c88155b","source":{"kind":"arxiv","id":"1806.05443","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05443","created_at":"2026-05-17T23:59:43Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05443v2","created_at":"2026-05-17T23:59:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05443","created_at":"2026-05-17T23:59:43Z"},{"alias_kind":"pith_short_12","alias_value":"RGBYQD5GFPDS","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RGBYQD5GFPDSC2RD","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RGBYQD5G","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:RGBYQD5GFPDSC2RDXMKQJ5ANDM","target":"record","payload":{"canonical_record":{"source":{"id":"1806.05443","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-14T10:07:30Z","cross_cats_sorted":[],"title_canon_sha256":"10f38a35d1793c4bd220b5d6d31d529d7bcd8a6b246dd9d423026f60189fbd84","abstract_canon_sha256":"d53eab7f46a4f5360d06dcdd3dfad6a8b00b879ca2eb00af177d982163ab3339"},"schema_version":"1.0"},"canonical_sha256":"8983880fa62bc7216a23bb1504f40d1b1e4f009ad9f5ca16390747e24c88155b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:43.591499Z","signature_b64":"eBjcAPXRY8LVpwLo14BGo0VsjDPYp+LODXrtHiCvCTul5TFR4EKgMFBvnZ/Bw0RKcs2Zj9pcKEA3BHF/VpMtDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8983880fa62bc7216a23bb1504f40d1b1e4f009ad9f5ca16390747e24c88155b","last_reissued_at":"2026-05-17T23:59:43.590959Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:43.590959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.05443","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kFLljYHSjyMU7Xa+4MiYDcYUPCxoLWDUxWEbE+DO5ZqcmaDGwV8PoJYrzuNyGCbXokwQ8h1IYhqjhRX1fac5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:21:00.176680Z"},"content_sha256":"3ff59369710b8628c3e3b569ae10d9242f0691e07f9871d76ec39e12036b4b13","schema_version":"1.0","event_id":"sha256:3ff59369710b8628c3e3b569ae10d9242f0691e07f9871d76ec39e12036b4b13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:RGBYQD5GFPDSC2RDXMKQJ5ANDM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The absolute values and support projections for a class of operator matrices involving idempotents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Shuaijie Wang, Xiaomei Cai, Yuan Li","submitted_at":"2018-06-14T10:07:30Z","abstract_excerpt":"Let $\\lambda\\in \\mathbb{R},$ $\\mu\\in \\mathbb{R}$ and $B$ be a linear bounded operator from a Hilbert space $\\mathcal{K}$ into another Hilbert space $\\mathcal{H}.$ In this paper, we consider the formulas of the absolute value $|Q_{\\lambda,\\mu}|,$ where $Q_{\\lambda,\\mu}$ with respect to the decomposition $\\mathcal{H}\\oplus\\mathcal{K}$ have the operator matrix\n  form $Q_{\\lambda,\\mu}:=\\left(\\begin{array}{cc}\\lambda I&B\\\\B^*&\\mu I\\end{array}\\right).$ Then the positive part and the support projection of $Q_{\\lambda,0}$ are obtained. Also, we characterize the symmetry $J$ such that a projection $E$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05443","kind":"arxiv","version":2},"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":"2026-05-17T23:59:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aFgiD2g0aMYhUS4QBxK9xaTTc8EIgYlRIm6tXZvRlo0fRXm/Phs+0H3PeZ0A6vi1ItAcYDYhlCgA4IZw4cg1BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:21:00.177310Z"},"content_sha256":"7b3405ba0d34fed49c2a7261dc2c9ce7d32c4e01add0a29cc8f1bc0006871e8a","schema_version":"1.0","event_id":"sha256:7b3405ba0d34fed49c2a7261dc2c9ce7d32c4e01add0a29cc8f1bc0006871e8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RGBYQD5GFPDSC2RDXMKQJ5ANDM/bundle.json","state_url":"https://pith.science/pith/RGBYQD5GFPDSC2RDXMKQJ5ANDM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RGBYQD5GFPDSC2RDXMKQJ5ANDM/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":"2026-05-31T09:21:00Z","links":{"resolver":"https://pith.science/pith/RGBYQD5GFPDSC2RDXMKQJ5ANDM","bundle":"https://pith.science/pith/RGBYQD5GFPDSC2RDXMKQJ5ANDM/bundle.json","state":"https://pith.science/pith/RGBYQD5GFPDSC2RDXMKQJ5ANDM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RGBYQD5GFPDSC2RDXMKQJ5ANDM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RGBYQD5GFPDSC2RDXMKQJ5ANDM","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":"d53eab7f46a4f5360d06dcdd3dfad6a8b00b879ca2eb00af177d982163ab3339","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-14T10:07:30Z","title_canon_sha256":"10f38a35d1793c4bd220b5d6d31d529d7bcd8a6b246dd9d423026f60189fbd84"},"schema_version":"1.0","source":{"id":"1806.05443","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05443","created_at":"2026-05-17T23:59:43Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05443v2","created_at":"2026-05-17T23:59:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05443","created_at":"2026-05-17T23:59:43Z"},{"alias_kind":"pith_short_12","alias_value":"RGBYQD5GFPDS","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RGBYQD5GFPDSC2RD","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RGBYQD5G","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:7b3405ba0d34fed49c2a7261dc2c9ce7d32c4e01add0a29cc8f1bc0006871e8a","target":"graph","created_at":"2026-05-17T23:59:43Z","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 $\\lambda\\in \\mathbb{R},$ $\\mu\\in \\mathbb{R}$ and $B$ be a linear bounded operator from a Hilbert space $\\mathcal{K}$ into another Hilbert space $\\mathcal{H}.$ In this paper, we consider the formulas of the absolute value $|Q_{\\lambda,\\mu}|,$ where $Q_{\\lambda,\\mu}$ with respect to the decomposition $\\mathcal{H}\\oplus\\mathcal{K}$ have the operator matrix\n  form $Q_{\\lambda,\\mu}:=\\left(\\begin{array}{cc}\\lambda I&B\\\\B^*&\\mu I\\end{array}\\right).$ Then the positive part and the support projection of $Q_{\\lambda,0}$ are obtained. Also, we characterize the symmetry $J$ such that a projection $E$ ","authors_text":"Shuaijie Wang, Xiaomei Cai, Yuan Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-14T10:07:30Z","title":"The absolute values and support projections for a class of operator matrices involving idempotents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05443","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":"sha256:3ff59369710b8628c3e3b569ae10d9242f0691e07f9871d76ec39e12036b4b13","target":"record","created_at":"2026-05-17T23:59:43Z","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":"d53eab7f46a4f5360d06dcdd3dfad6a8b00b879ca2eb00af177d982163ab3339","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-14T10:07:30Z","title_canon_sha256":"10f38a35d1793c4bd220b5d6d31d529d7bcd8a6b246dd9d423026f60189fbd84"},"schema_version":"1.0","source":{"id":"1806.05443","kind":"arxiv","version":2}},"canonical_sha256":"8983880fa62bc7216a23bb1504f40d1b1e4f009ad9f5ca16390747e24c88155b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8983880fa62bc7216a23bb1504f40d1b1e4f009ad9f5ca16390747e24c88155b","first_computed_at":"2026-05-17T23:59:43.590959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:43.590959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eBjcAPXRY8LVpwLo14BGo0VsjDPYp+LODXrtHiCvCTul5TFR4EKgMFBvnZ/Bw0RKcs2Zj9pcKEA3BHF/VpMtDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:43.591499Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05443","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ff59369710b8628c3e3b569ae10d9242f0691e07f9871d76ec39e12036b4b13","sha256:7b3405ba0d34fed49c2a7261dc2c9ce7d32c4e01add0a29cc8f1bc0006871e8a"],"state_sha256":"7edb79af920764e331a0cef80f48d3ef71aef0434c2d830ff964157c2810e58d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xYpreLeN9JnCs8T1DmhtcOXA55lv3oXuFANIGO8h4kMK9LVI6Pwx2MQHPxQnFvWEdV2zNcjkvMwPnNHaFDWBCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T09:21:00.180680Z","bundle_sha256":"5943943d95ce1581e4aa6d8ec2c9c8e01827cbde8579283daacde1bb19b83012"}}