{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:MFLJP46FFLYMNXILCAAHFCMQMS","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":"6d346a35986fb60a0c9e23eab71379765e4f20950b01588fee4347136e5fe31a","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-11-14T07:57:58Z","title_canon_sha256":"f1dee0ed0bf3858078eda76139cf9468a501de3d973af03280000d7df6e9c427"},"schema_version":"1.0","source":{"id":"0911.2751","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.2751","created_at":"2026-05-18T03:59:38Z"},{"alias_kind":"arxiv_version","alias_value":"0911.2751v1","created_at":"2026-05-18T03:59:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.2751","created_at":"2026-05-18T03:59:38Z"},{"alias_kind":"pith_short_12","alias_value":"MFLJP46FFLYM","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"MFLJP46FFLYMNXIL","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"MFLJP46F","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:fd81d9fb5d951d1ad1e256e29af79c1b6582e9744c710a2b4a99e07a8712372c","target":"graph","created_at":"2026-05-18T03:59:38Z","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 prove several versions of reverse triangle inequality in Hilbert $C^*$-modules. We show that if $e_1, ..., e_m$ are vectors in a Hilbert module ${\\mathfrak X}$ over a $C^*$-algebra ${\\mathfrak A}$ with unit 1 such that $<e_i,e_j>=0 (1\\leq i\\neq j \\leq m)$ and $\\|e_i\\|=1 (1\\leq i\\leq m)$, and also $r_k,\\rho_k\\in\\Bbb{R} (1\\leq k\\leq m)$ and $x_1, ..., x_n\\in {\\mathfrak X}$ satisfy $$0\\leq r_k^2 \\|x_j\\|\\leq {Re}< r_ke_k,x_j> ,\\quad0\\leq \\rho_k^2 \\|x_j\\| \\leq {Im}< \\rho_ke_k,x_j> ,$$ then [\\sum_{k=1}^m(r_k^2+\\rho_k^2)]^{{1/2}}\\sum_{j=1}^n \\|x_j\\|\\leq\\|\\sum_{j=1}^nx_j\\|, and the equality holds i","authors_text":"H. Mahyar, M. Khosravi, M.S. Moslehian","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-11-14T07:57:58Z","title":"Reverse triangle inequality in Hilbert $C^*$-modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2751","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:e3bddf102e8a0cfd7cc925a462ade70ba56b4fb59b77d7fc009a16a87f264de9","target":"record","created_at":"2026-05-18T03:59:38Z","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":"6d346a35986fb60a0c9e23eab71379765e4f20950b01588fee4347136e5fe31a","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-11-14T07:57:58Z","title_canon_sha256":"f1dee0ed0bf3858078eda76139cf9468a501de3d973af03280000d7df6e9c427"},"schema_version":"1.0","source":{"id":"0911.2751","kind":"arxiv","version":1}},"canonical_sha256":"615697f3c52af0c6dd0b100072899064a8180b4fbea8cd89771f3f25bcb0a3c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"615697f3c52af0c6dd0b100072899064a8180b4fbea8cd89771f3f25bcb0a3c7","first_computed_at":"2026-05-18T03:59:38.606176Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:38.606176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DqkyC3XBzsvGkvegYooKDP5c5LPjK6Dxat/fqyQIUtT596a9hTADS/6oQJMi4oqvH1AgrMX3PeB8rmuE56tBCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:38.606889Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.2751","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3bddf102e8a0cfd7cc925a462ade70ba56b4fb59b77d7fc009a16a87f264de9","sha256:fd81d9fb5d951d1ad1e256e29af79c1b6582e9744c710a2b4a99e07a8712372c"],"state_sha256":"a74ae5cfcd1b4c1d6094f7bfc0883c748b7fd25f80919e4a0277a6a4b985e1ad"}