{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YZD67WYWWGOFHXFXXPV52H2RBD","short_pith_number":"pith:YZD67WYW","canonical_record":{"source":{"id":"1411.0333","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-11-02T23:14:55Z","cross_cats_sorted":[],"title_canon_sha256":"c5b8d0169814edefa9fd51596bf4416ea7f8d579b82047ea80dcf80b13e25e87","abstract_canon_sha256":"e52a7f890fbc203a1e0378df74ed6afbc30beca6ebd5f9d592fb7bc8ed4ef415"},"schema_version":"1.0"},"canonical_sha256":"c647efdb16b19c53dcb7bbebdd1f5108fc6a9706f33b686b3747cfe32e474703","source":{"kind":"arxiv","id":"1411.0333","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0333","created_at":"2026-05-18T01:42:47Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0333v4","created_at":"2026-05-18T01:42:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0333","created_at":"2026-05-18T01:42:47Z"},{"alias_kind":"pith_short_12","alias_value":"YZD67WYWWGOF","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YZD67WYWWGOFHXFX","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YZD67WYW","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YZD67WYWWGOFHXFXXPV52H2RBD","target":"record","payload":{"canonical_record":{"source":{"id":"1411.0333","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-11-02T23:14:55Z","cross_cats_sorted":[],"title_canon_sha256":"c5b8d0169814edefa9fd51596bf4416ea7f8d579b82047ea80dcf80b13e25e87","abstract_canon_sha256":"e52a7f890fbc203a1e0378df74ed6afbc30beca6ebd5f9d592fb7bc8ed4ef415"},"schema_version":"1.0"},"canonical_sha256":"c647efdb16b19c53dcb7bbebdd1f5108fc6a9706f33b686b3747cfe32e474703","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:42:47.948207Z","signature_b64":"TRVEhdEqyucjT1XhRqOGo6uJOgPchTmVTmKxC+bFWSV5rGo+MSczgG/ieJk3GJDgPAjxBBntrMil9T5ktWSMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c647efdb16b19c53dcb7bbebdd1f5108fc6a9706f33b686b3747cfe32e474703","last_reissued_at":"2026-05-18T01:42:47.947633Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:42:47.947633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.0333","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:42:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WUXzLyjsjTaaCMjuseeZT0UciX2Wdusc1euaHo87Y+pSz/TdNtAM7OzdqlzF0cyC0hCALotHxNF/P9uEpfJnCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:42:12.274021Z"},"content_sha256":"d23e27152bf175420e36c9296243fc4be92d6835fe6837aaf9410e5520a2995a","schema_version":"1.0","event_id":"sha256:d23e27152bf175420e36c9296243fc4be92d6835fe6837aaf9410e5520a2995a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YZD67WYWWGOFHXFXXPV52H2RBD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An arithmetic-geometric mean inequality for products of three matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Arie Israel, Felix Krahmer, Rachel Ward","submitted_at":"2014-11-02T23:14:55Z","abstract_excerpt":"Consider the following noncommutative arithmetic-geometric mean inequality: given positive-semidefinite matrices $\\mathbf{A}_1, \\dots, \\mathbf{A}_n$, the following holds for each integer $m \\leq n$: $$ \\frac{1}{n^m}\\sum_{j_1, j_2, \\dots, j_m = 1}^{n} ||| \\mathbf{A}_{j_1} \\mathbf{A}_{j_2} \\dots \\mathbf{A}_{j_m} ||| \\geq \\frac{(n-m)!}{n!} \\sum_{\\substack{j_1, j_2, \\dots, j_m = 1 \\\\ \\text{all distinct}}}^{n} ||| \\mathbf{A}_{j_1} \\mathbf{A}_{j_2} \\dots \\mathbf{A}_{j_m} |||,$$ where $||| \\cdot |||$ denotes a unitarily invariant norm, including the operator norm and Schatten p-norms as special cases"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0333","kind":"arxiv","version":4},"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":"2026-05-18T01:42:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wkafOMLKJ1i56yZR/y9cIIrxt2SNp8QR0vm95Dw8AmnV80E85zYN6nEYyb17cLwmkQJKE8OW/fXtGxOpxK7GDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:42:12.274369Z"},"content_sha256":"b6736b3f7b00bbbc3b239da973cf508f287de054caaac8f93423fb658a513d79","schema_version":"1.0","event_id":"sha256:b6736b3f7b00bbbc3b239da973cf508f287de054caaac8f93423fb658a513d79"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YZD67WYWWGOFHXFXXPV52H2RBD/bundle.json","state_url":"https://pith.science/pith/YZD67WYWWGOFHXFXXPV52H2RBD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YZD67WYWWGOFHXFXXPV52H2RBD/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":"2026-06-02T01:42:12Z","links":{"resolver":"https://pith.science/pith/YZD67WYWWGOFHXFXXPV52H2RBD","bundle":"https://pith.science/pith/YZD67WYWWGOFHXFXXPV52H2RBD/bundle.json","state":"https://pith.science/pith/YZD67WYWWGOFHXFXXPV52H2RBD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YZD67WYWWGOFHXFXXPV52H2RBD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YZD67WYWWGOFHXFXXPV52H2RBD","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":"e52a7f890fbc203a1e0378df74ed6afbc30beca6ebd5f9d592fb7bc8ed4ef415","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-11-02T23:14:55Z","title_canon_sha256":"c5b8d0169814edefa9fd51596bf4416ea7f8d579b82047ea80dcf80b13e25e87"},"schema_version":"1.0","source":{"id":"1411.0333","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0333","created_at":"2026-05-18T01:42:47Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0333v4","created_at":"2026-05-18T01:42:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0333","created_at":"2026-05-18T01:42:47Z"},{"alias_kind":"pith_short_12","alias_value":"YZD67WYWWGOF","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YZD67WYWWGOFHXFX","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YZD67WYW","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:b6736b3f7b00bbbc3b239da973cf508f287de054caaac8f93423fb658a513d79","target":"graph","created_at":"2026-05-18T01:42:47Z","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":"Consider the following noncommutative arithmetic-geometric mean inequality: given positive-semidefinite matrices $\\mathbf{A}_1, \\dots, \\mathbf{A}_n$, the following holds for each integer $m \\leq n$: $$ \\frac{1}{n^m}\\sum_{j_1, j_2, \\dots, j_m = 1}^{n} ||| \\mathbf{A}_{j_1} \\mathbf{A}_{j_2} \\dots \\mathbf{A}_{j_m} ||| \\geq \\frac{(n-m)!}{n!} \\sum_{\\substack{j_1, j_2, \\dots, j_m = 1 \\\\ \\text{all distinct}}}^{n} ||| \\mathbf{A}_{j_1} \\mathbf{A}_{j_2} \\dots \\mathbf{A}_{j_m} |||,$$ where $||| \\cdot |||$ denotes a unitarily invariant norm, including the operator norm and Schatten p-norms as special cases","authors_text":"Arie Israel, Felix Krahmer, Rachel Ward","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-11-02T23:14:55Z","title":"An arithmetic-geometric mean inequality for products of three matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0333","kind":"arxiv","version":4},"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:d23e27152bf175420e36c9296243fc4be92d6835fe6837aaf9410e5520a2995a","target":"record","created_at":"2026-05-18T01:42:47Z","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":"e52a7f890fbc203a1e0378df74ed6afbc30beca6ebd5f9d592fb7bc8ed4ef415","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-11-02T23:14:55Z","title_canon_sha256":"c5b8d0169814edefa9fd51596bf4416ea7f8d579b82047ea80dcf80b13e25e87"},"schema_version":"1.0","source":{"id":"1411.0333","kind":"arxiv","version":4}},"canonical_sha256":"c647efdb16b19c53dcb7bbebdd1f5108fc6a9706f33b686b3747cfe32e474703","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c647efdb16b19c53dcb7bbebdd1f5108fc6a9706f33b686b3747cfe32e474703","first_computed_at":"2026-05-18T01:42:47.947633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:42:47.947633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TRVEhdEqyucjT1XhRqOGo6uJOgPchTmVTmKxC+bFWSV5rGo+MSczgG/ieJk3GJDgPAjxBBntrMil9T5ktWSMDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:42:47.948207Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0333","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d23e27152bf175420e36c9296243fc4be92d6835fe6837aaf9410e5520a2995a","sha256:b6736b3f7b00bbbc3b239da973cf508f287de054caaac8f93423fb658a513d79"],"state_sha256":"6cb51fdf94245d70ef12d371b99f721a6f42f7b17b270e3e32895db8fcd7598f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j7I6q0yWvhRkJvJtTQkAHvxGPXIXaiHXtbBl/ZQBp3T6RqrZPCBRMk5P9tgkMNnnyKVWHFIugoKkTgTPtttADQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T01:42:12.276159Z","bundle_sha256":"6f92dcdf4e7b688023c1083d87813571c3ab5c4e9ca9d739bd49f1383f1c460d"}}