{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:MFLJP46FFLYMNXILCAAHFCMQMS","short_pith_number":"pith:MFLJP46F","canonical_record":{"source":{"id":"0911.2751","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-11-14T07:57:58Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"f1dee0ed0bf3858078eda76139cf9468a501de3d973af03280000d7df6e9c427","abstract_canon_sha256":"6d346a35986fb60a0c9e23eab71379765e4f20950b01588fee4347136e5fe31a"},"schema_version":"1.0"},"canonical_sha256":"615697f3c52af0c6dd0b100072899064a8180b4fbea8cd89771f3f25bcb0a3c7","source":{"kind":"arxiv","id":"0911.2751","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:MFLJP46FFLYMNXILCAAHFCMQMS","target":"record","payload":{"canonical_record":{"source":{"id":"0911.2751","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-11-14T07:57:58Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"f1dee0ed0bf3858078eda76139cf9468a501de3d973af03280000d7df6e9c427","abstract_canon_sha256":"6d346a35986fb60a0c9e23eab71379765e4f20950b01588fee4347136e5fe31a"},"schema_version":"1.0"},"canonical_sha256":"615697f3c52af0c6dd0b100072899064a8180b4fbea8cd89771f3f25bcb0a3c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:38.606889Z","signature_b64":"DqkyC3XBzsvGkvegYooKDP5c5LPjK6Dxat/fqyQIUtT596a9hTADS/6oQJMi4oqvH1AgrMX3PeB8rmuE56tBCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"615697f3c52af0c6dd0b100072899064a8180b4fbea8cd89771f3f25bcb0a3c7","last_reissued_at":"2026-05-18T03:59:38.606176Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:38.606176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.2751","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":"2026-05-18T03:59:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kfBscu74WKW6DfvWPH3A+0IWrmxCO/so8rq9IUQ8T55rK2hFJiDbsK5uz8YqBG/kVVSGemVsK4IfwuOidUGDCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T10:28:39.717268Z"},"content_sha256":"e3bddf102e8a0cfd7cc925a462ade70ba56b4fb59b77d7fc009a16a87f264de9","schema_version":"1.0","event_id":"sha256:e3bddf102e8a0cfd7cc925a462ade70ba56b4fb59b77d7fc009a16a87f264de9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:MFLJP46FFLYMNXILCAAHFCMQMS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reverse triangle inequality in Hilbert $C^*$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"H. Mahyar, M. Khosravi, M.S. Moslehian","submitted_at":"2009-11-14T07:57:58Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2751","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":""},"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":"2026-05-18T03:59:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g3I7onVL5O9M+f0GSU5LIy7xgPTGvrqcne6WRzou6YPAYecniQRogvStoiVQwEgtYpfdW6nfF2unygaDp5ooCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T10:28:39.717648Z"},"content_sha256":"fd81d9fb5d951d1ad1e256e29af79c1b6582e9744c710a2b4a99e07a8712372c","schema_version":"1.0","event_id":"sha256:fd81d9fb5d951d1ad1e256e29af79c1b6582e9744c710a2b4a99e07a8712372c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MFLJP46FFLYMNXILCAAHFCMQMS/bundle.json","state_url":"https://pith.science/pith/MFLJP46FFLYMNXILCAAHFCMQMS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MFLJP46FFLYMNXILCAAHFCMQMS/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":"2026-06-06T10:28:39Z","links":{"resolver":"https://pith.science/pith/MFLJP46FFLYMNXILCAAHFCMQMS","bundle":"https://pith.science/pith/MFLJP46FFLYMNXILCAAHFCMQMS/bundle.json","state":"https://pith.science/pith/MFLJP46FFLYMNXILCAAHFCMQMS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MFLJP46FFLYMNXILCAAHFCMQMS/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"10sPo6cnKXj/92lvDBl3jbvi1b5Un/J0A+9Lhdy6z3Je6PaT3ZkPX26a0G4Y3UmHvO7UREhr2DdqLwWcRyAkBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T10:28:39.719651Z","bundle_sha256":"391e91467fe309eaff76c491342424d61fd4a868d64077d6054b0ba256b3060f"}}