{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:G7KA2YJSPYKNZYXVNYCQ46I662","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":"cb8f8abf1e690a08b1a84e8d5114739785e87292b5b549937fd56b48bae5ac1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-14T05:48:10Z","title_canon_sha256":"15866c8573d0d5e2450690ec4307d9a87780d421bf3b16cb31c9cd81c3883b5b"},"schema_version":"1.0","source":{"id":"1711.04957","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.04957","created_at":"2026-05-18T00:22:18Z"},{"alias_kind":"arxiv_version","alias_value":"1711.04957v2","created_at":"2026-05-18T00:22:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.04957","created_at":"2026-05-18T00:22:18Z"},{"alias_kind":"pith_short_12","alias_value":"G7KA2YJSPYKN","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"G7KA2YJSPYKNZYXV","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"G7KA2YJS","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:1aa4d679f6f6b194f5abb012f1bb1ad5be7a4ce25511699ba7c993da73806749","target":"graph","created_at":"2026-05-18T00:22:18Z","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"},"paper":{"abstract_excerpt":"The purpose of this paper is to present some general inequalities for operator concave functions which include some known inequalities as a particular case. Among other things, we prove that if $A\\in \\mathcal{B}\\left( \\mathcal{H} \\right)$ is a positive operator such that $mI\\le A\\le MI$ for some scalars $0<m<M$ and $\\Phi $ is a normalized positive linear map on $\\mathcal{B}\\left( \\mathcal{H} \\right)$, then \\[\\begin{aligned} {{\\left( \\frac{M+m}{2\\sqrt{Mm}} \\right)}^{r}}&\\ge {{\\left( \\frac{\\frac{1}{\\sqrt{Mm}}\\Phi \\left( A \\right)+\\sqrt{Mm}\\Phi \\left( {{A}^{-1}} \\right)}{2} \\right)}^{r}} & \\ge \\f","authors_text":"H.R. Moradi, M.E. Omidvar, S. Sheybani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-14T05:48:10Z","title":"New inequalities for operator concave functions involving positive linear maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04957","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:d50320cae03ffbabddbef7fd41daaf01dfda6403e1d3ba09c0ebe98415fdf72a","target":"record","created_at":"2026-05-18T00:22:18Z","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":"cb8f8abf1e690a08b1a84e8d5114739785e87292b5b549937fd56b48bae5ac1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-14T05:48:10Z","title_canon_sha256":"15866c8573d0d5e2450690ec4307d9a87780d421bf3b16cb31c9cd81c3883b5b"},"schema_version":"1.0","source":{"id":"1711.04957","kind":"arxiv","version":2}},"canonical_sha256":"37d40d61327e14dce2f56e050e791ef6860b479d24646ccaa536890cf4aff13f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37d40d61327e14dce2f56e050e791ef6860b479d24646ccaa536890cf4aff13f","first_computed_at":"2026-05-18T00:22:18.547385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:18.547385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fT5Grzfw5rTpAtomvJq61oSU2F1Fz0stiPZGTJCVDyOCB/kZ03jcv3tZZOAUhe+SBGOPOt6y9aK87u4VgHHGAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:18.548022Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.04957","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d50320cae03ffbabddbef7fd41daaf01dfda6403e1d3ba09c0ebe98415fdf72a","sha256:1aa4d679f6f6b194f5abb012f1bb1ad5be7a4ce25511699ba7c993da73806749"],"state_sha256":"11d63140e62f68160cdd356c0175d85b0f0e2a3d3506d8de32cd70c5e9504f88"}