{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:N54X5VY5IVUWSZEQZIVIPZN667","short_pith_number":"pith:N54X5VY5","canonical_record":{"source":{"id":"1408.3470","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-08-15T05:54:23Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"3f86d204d8e47153a093c135b743cbd39ccf6500a3f084e2520c6f4899747e46","abstract_canon_sha256":"f367cd8009ba7366264a8b02f4a6c29ead13b66f868e73c6b0cae3cf0341eceb"},"schema_version":"1.0"},"canonical_sha256":"6f797ed71d4569696490ca2a87e5bef7f37ab2fc154845ab147ec749d3385b1e","source":{"kind":"arxiv","id":"1408.3470","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3470","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3470v1","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3470","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"pith_short_12","alias_value":"N54X5VY5IVUW","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N54X5VY5IVUWSZEQ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N54X5VY5","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:N54X5VY5IVUWSZEQZIVIPZN667","target":"record","payload":{"canonical_record":{"source":{"id":"1408.3470","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-08-15T05:54:23Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"3f86d204d8e47153a093c135b743cbd39ccf6500a3f084e2520c6f4899747e46","abstract_canon_sha256":"f367cd8009ba7366264a8b02f4a6c29ead13b66f868e73c6b0cae3cf0341eceb"},"schema_version":"1.0"},"canonical_sha256":"6f797ed71d4569696490ca2a87e5bef7f37ab2fc154845ab147ec749d3385b1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:05.810533Z","signature_b64":"rHVnCF2asjI0ZXCKdMqq2XJgzPzpumQUNFaZbhipcR/F7TeAtPMYu0OLiDOW2P9oZOGsDcg+UT7W/wpPaetEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f797ed71d4569696490ca2a87e5bef7f37ab2fc154845ab147ec749d3385b1e","last_reissued_at":"2026-05-18T02:45:05.809861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:05.809861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.3470","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":"2026-05-18T02:45:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qsFDXZqc28NHlbhzRRqcPrJlNxPgfffg3gz77tIU17jwW/syp1cHEZHfdufqqSDm9gp8Xri7aHS2JhQGmg9ZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:38:59.972385Z"},"content_sha256":"9d12188e89182d2eb84a321b08a969e774c4c3127317ffb5a79e0cd04bae9d68","schema_version":"1.0","event_id":"sha256:9d12188e89182d2eb84a321b08a969e774c4c3127317ffb5a79e0cd04bae9d68"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:N54X5VY5IVUWSZEQZIVIPZN667","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efron-Stein Inequalities for Random Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Daniel Paulin, Joel A. Tropp, Lester Mackey","submitted_at":"2014-08-15T05:54:23Z","abstract_excerpt":"This paper establishes new concentration inequalities for random matrices constructed from independent random variables. These results are analogous with the generalized Efron-Stein inequalities developed by Boucheron et al. The proofs rely on the method of exchangeable pairs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3470","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":"2026-05-18T02:45:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SY3YOjdOQ3sk80PgLoxlCMebEeh3CzDoRM/N5I3A18ElJf9ohkwXw6ztjBQGM6FheBAbjkkmFCf3LGrgfa1cAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:38:59.973004Z"},"content_sha256":"f2b05fab26a0dee6a242311ad97ba9243d61b4444c97c47cba5f7e40e27666da","schema_version":"1.0","event_id":"sha256:f2b05fab26a0dee6a242311ad97ba9243d61b4444c97c47cba5f7e40e27666da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N54X5VY5IVUWSZEQZIVIPZN667/bundle.json","state_url":"https://pith.science/pith/N54X5VY5IVUWSZEQZIVIPZN667/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N54X5VY5IVUWSZEQZIVIPZN667/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":"2026-06-09T06:38:59Z","links":{"resolver":"https://pith.science/pith/N54X5VY5IVUWSZEQZIVIPZN667","bundle":"https://pith.science/pith/N54X5VY5IVUWSZEQZIVIPZN667/bundle.json","state":"https://pith.science/pith/N54X5VY5IVUWSZEQZIVIPZN667/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N54X5VY5IVUWSZEQZIVIPZN667/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:N54X5VY5IVUWSZEQZIVIPZN667","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":"f367cd8009ba7366264a8b02f4a6c29ead13b66f868e73c6b0cae3cf0341eceb","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-08-15T05:54:23Z","title_canon_sha256":"3f86d204d8e47153a093c135b743cbd39ccf6500a3f084e2520c6f4899747e46"},"schema_version":"1.0","source":{"id":"1408.3470","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3470","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3470v1","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3470","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"pith_short_12","alias_value":"N54X5VY5IVUW","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N54X5VY5IVUWSZEQ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N54X5VY5","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:f2b05fab26a0dee6a242311ad97ba9243d61b4444c97c47cba5f7e40e27666da","target":"graph","created_at":"2026-05-18T02:45:05Z","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":"This paper establishes new concentration inequalities for random matrices constructed from independent random variables. These results are analogous with the generalized Efron-Stein inequalities developed by Boucheron et al. The proofs rely on the method of exchangeable pairs.","authors_text":"Daniel Paulin, Joel A. Tropp, Lester Mackey","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-08-15T05:54:23Z","title":"Efron-Stein Inequalities for Random Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3470","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":"sha256:9d12188e89182d2eb84a321b08a969e774c4c3127317ffb5a79e0cd04bae9d68","target":"record","created_at":"2026-05-18T02:45:05Z","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":"f367cd8009ba7366264a8b02f4a6c29ead13b66f868e73c6b0cae3cf0341eceb","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-08-15T05:54:23Z","title_canon_sha256":"3f86d204d8e47153a093c135b743cbd39ccf6500a3f084e2520c6f4899747e46"},"schema_version":"1.0","source":{"id":"1408.3470","kind":"arxiv","version":1}},"canonical_sha256":"6f797ed71d4569696490ca2a87e5bef7f37ab2fc154845ab147ec749d3385b1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f797ed71d4569696490ca2a87e5bef7f37ab2fc154845ab147ec749d3385b1e","first_computed_at":"2026-05-18T02:45:05.809861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:05.809861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rHVnCF2asjI0ZXCKdMqq2XJgzPzpumQUNFaZbhipcR/F7TeAtPMYu0OLiDOW2P9oZOGsDcg+UT7W/wpPaetEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:05.810533Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.3470","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d12188e89182d2eb84a321b08a969e774c4c3127317ffb5a79e0cd04bae9d68","sha256:f2b05fab26a0dee6a242311ad97ba9243d61b4444c97c47cba5f7e40e27666da"],"state_sha256":"bad72e519d7f6fd4484494e2caa20b0d220e2ee66567634337151e8cddc30c6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZzSoxI9qSPMa5oyxtS4du2BMTtLZUABJl+WzFPIWw1T9YCtCchh3E478qWDLRpV4IVQMGJOcz6NrMmDROlN/CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:38:59.978054Z","bundle_sha256":"881e99956dada0e892a0ed8aab5dd66569ae85d8c725ed33bceaed0a4aedee67"}}