{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:N5V3YY6CLMHKXBEJQNBOKVRQW7","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":"9044786a4666491d15907a5a2a62a592eb9b0f7fc5048a18fb25fc0bd4a219ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-17T06:24:33Z","title_canon_sha256":"57ea5eaf7703259df821e1016d6d8748266fa3904158e7ea27358923f48e1539"},"schema_version":"1.0","source":{"id":"1805.06613","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06613","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06613v1","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06613","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"N5V3YY6CLMHK","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"N5V3YY6CLMHKXBEJ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"N5V3YY6C","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:e8255a891ad421dddfc83551f7475389d4e8537c94cb1ca5ee3fda3e418b5496","target":"graph","created_at":"2026-05-18T00:15:43Z","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":"The main goal of this article is to present new types of inequalities refining and reversing inequalities of the harmonic mean of scalars and matrices. Furthermore, implementing the spectral decomposition of positive matrices, we present a new type of inequalities treating certain harmonic matrix perturbation.","authors_text":"Mohammad Sababheh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-17T06:24:33Z","title":"On the matrix harmonic mean"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06613","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":"sha256:93c37685f4687be2656f40a1ab407fb2229e301f0485c856b0fc21b8407b05ef","target":"record","created_at":"2026-05-18T00:15:43Z","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":"9044786a4666491d15907a5a2a62a592eb9b0f7fc5048a18fb25fc0bd4a219ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-17T06:24:33Z","title_canon_sha256":"57ea5eaf7703259df821e1016d6d8748266fa3904158e7ea27358923f48e1539"},"schema_version":"1.0","source":{"id":"1805.06613","kind":"arxiv","version":1}},"canonical_sha256":"6f6bbc63c25b0eab84898342e55630b7dd896f3befc6d31162e9db66d0a5c7c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f6bbc63c25b0eab84898342e55630b7dd896f3befc6d31162e9db66d0a5c7c4","first_computed_at":"2026-05-18T00:15:43.907846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:43.907846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LqTuXO7KgqSUbF7D3d9/FjGzvg8ZRQxclI2kFr6hCOQc/bnBqvd/jJR+e54KSisqb5GG7593GQG54OQJBoPiBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:43.908298Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.06613","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93c37685f4687be2656f40a1ab407fb2229e301f0485c856b0fc21b8407b05ef","sha256:e8255a891ad421dddfc83551f7475389d4e8537c94cb1ca5ee3fda3e418b5496"],"state_sha256":"07b8d788ddb4b843c282c983afbdd40221e3ff70fc652742f7ba2a25cf5a68eb"}