{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZTISE2MICCGH3FLWDVDAEGSANE","short_pith_number":"pith:ZTISE2MI","canonical_record":{"source":{"id":"1804.01881","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-04-05T14:38:41Z","cross_cats_sorted":[],"title_canon_sha256":"7434323984f088f4a420c9a445abe51901f6fd2e4a7a1e84583f400766afb1ce","abstract_canon_sha256":"8628e010bf899feb90ea46bf117f3ac6b7acec15b7a6c33213b7b060905c21eb"},"schema_version":"1.0"},"canonical_sha256":"ccd1226988108c7d95761d46021a4069065955d734f83a43f51926813172d038","source":{"kind":"arxiv","id":"1804.01881","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.01881","created_at":"2026-05-18T00:19:09Z"},{"alias_kind":"arxiv_version","alias_value":"1804.01881v1","created_at":"2026-05-18T00:19:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01881","created_at":"2026-05-18T00:19:09Z"},{"alias_kind":"pith_short_12","alias_value":"ZTISE2MICCGH","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZTISE2MICCGH3FLW","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZTISE2MI","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZTISE2MICCGH3FLWDVDAEGSANE","target":"record","payload":{"canonical_record":{"source":{"id":"1804.01881","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-04-05T14:38:41Z","cross_cats_sorted":[],"title_canon_sha256":"7434323984f088f4a420c9a445abe51901f6fd2e4a7a1e84583f400766afb1ce","abstract_canon_sha256":"8628e010bf899feb90ea46bf117f3ac6b7acec15b7a6c33213b7b060905c21eb"},"schema_version":"1.0"},"canonical_sha256":"ccd1226988108c7d95761d46021a4069065955d734f83a43f51926813172d038","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:09.636168Z","signature_b64":"zzIV6xQUZYQlBdG6iXCmjYr4UF9YwxuAVrFhsiKYoNvaTrXel96d90xQE2owyDYOQhSQV9nVie8NjYIoXfFBDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccd1226988108c7d95761d46021a4069065955d734f83a43f51926813172d038","last_reissued_at":"2026-05-18T00:19:09.635629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:09.635629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.01881","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":"2026-05-18T00:19:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tmSWiwLq9DjN2OYNIYSs+IpZ+GKOvn0si7JgHrps+5s939yb7FTukMEpYOq+qCjgQfd+WYDhof0c2p9X546WAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:47:01.113131Z"},"content_sha256":"63fe6784bf7c25b431e289353667b385b2c323f808ba9d6147b55e9dee74433d","schema_version":"1.0","event_id":"sha256:63fe6784bf7c25b431e289353667b385b2c323f808ba9d6147b55e9dee74433d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZTISE2MICCGH3FLWDVDAEGSANE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ando-Hiai type inequalities for multivariate operator means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Fumio Hiai, Shuhei Wada, Yuki Seo","submitted_at":"2018-04-05T14:38:41Z","abstract_excerpt":"We present several Ando-Hiai type inequalities for $n$-variable operator means for positive invertible operators. Ando-Hiai's inequalities given here are not only of the original type but also of the complementary type and of the reverse type involving the generalized Kantorovich constant."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01881","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":"2026-05-18T00:19:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GxUdd27ydnP9t2hdDLGz+4+B6ZkG48k6cpAF4cuGpaDLVnV+Ta+5LO9X/gEeRzk/IUUgyATo+mxYkjC6R1y3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:47:01.113892Z"},"content_sha256":"7c7a1de27d9dbca9de8a33f6786b5da3eb85385fb6964e5f52a30079981340e8","schema_version":"1.0","event_id":"sha256:7c7a1de27d9dbca9de8a33f6786b5da3eb85385fb6964e5f52a30079981340e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZTISE2MICCGH3FLWDVDAEGSANE/bundle.json","state_url":"https://pith.science/pith/ZTISE2MICCGH3FLWDVDAEGSANE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZTISE2MICCGH3FLWDVDAEGSANE/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":"2026-06-10T13:47:01Z","links":{"resolver":"https://pith.science/pith/ZTISE2MICCGH3FLWDVDAEGSANE","bundle":"https://pith.science/pith/ZTISE2MICCGH3FLWDVDAEGSANE/bundle.json","state":"https://pith.science/pith/ZTISE2MICCGH3FLWDVDAEGSANE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZTISE2MICCGH3FLWDVDAEGSANE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZTISE2MICCGH3FLWDVDAEGSANE","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":"8628e010bf899feb90ea46bf117f3ac6b7acec15b7a6c33213b7b060905c21eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-04-05T14:38:41Z","title_canon_sha256":"7434323984f088f4a420c9a445abe51901f6fd2e4a7a1e84583f400766afb1ce"},"schema_version":"1.0","source":{"id":"1804.01881","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.01881","created_at":"2026-05-18T00:19:09Z"},{"alias_kind":"arxiv_version","alias_value":"1804.01881v1","created_at":"2026-05-18T00:19:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01881","created_at":"2026-05-18T00:19:09Z"},{"alias_kind":"pith_short_12","alias_value":"ZTISE2MICCGH","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZTISE2MICCGH3FLW","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZTISE2MI","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:7c7a1de27d9dbca9de8a33f6786b5da3eb85385fb6964e5f52a30079981340e8","target":"graph","created_at":"2026-05-18T00:19:09Z","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 present several Ando-Hiai type inequalities for $n$-variable operator means for positive invertible operators. Ando-Hiai's inequalities given here are not only of the original type but also of the complementary type and of the reverse type involving the generalized Kantorovich constant.","authors_text":"Fumio Hiai, Shuhei Wada, Yuki Seo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-04-05T14:38:41Z","title":"Ando-Hiai type inequalities for multivariate operator means"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01881","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":"sha256:63fe6784bf7c25b431e289353667b385b2c323f808ba9d6147b55e9dee74433d","target":"record","created_at":"2026-05-18T00:19:09Z","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":"8628e010bf899feb90ea46bf117f3ac6b7acec15b7a6c33213b7b060905c21eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-04-05T14:38:41Z","title_canon_sha256":"7434323984f088f4a420c9a445abe51901f6fd2e4a7a1e84583f400766afb1ce"},"schema_version":"1.0","source":{"id":"1804.01881","kind":"arxiv","version":1}},"canonical_sha256":"ccd1226988108c7d95761d46021a4069065955d734f83a43f51926813172d038","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccd1226988108c7d95761d46021a4069065955d734f83a43f51926813172d038","first_computed_at":"2026-05-18T00:19:09.635629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:09.635629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zzIV6xQUZYQlBdG6iXCmjYr4UF9YwxuAVrFhsiKYoNvaTrXel96d90xQE2owyDYOQhSQV9nVie8NjYIoXfFBDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:09.636168Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.01881","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63fe6784bf7c25b431e289353667b385b2c323f808ba9d6147b55e9dee74433d","sha256:7c7a1de27d9dbca9de8a33f6786b5da3eb85385fb6964e5f52a30079981340e8"],"state_sha256":"1467e35b905032e8ba1fe52692966195b7af8cae64255c0e27c76d0923bd9883"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o7vutWQqbePcNwQliynrNFXWCPaDtN6EzYyiDGoiJs3cRAFNelQ/MAuU+J90KiKYE2Rwf7OFjb07qAYP4jXRBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T13:47:01.117877Z","bundle_sha256":"5d1ea2b37d11b913ba31b272c77042bb731016a8a603bc1f378094fbc1e70df8"}}