{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:R6C5SZ6GU4WSTGEYMQM6KI5WMU","short_pith_number":"pith:R6C5SZ6G","canonical_record":{"source":{"id":"1101.1923","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-10T18:44:34Z","cross_cats_sorted":[],"title_canon_sha256":"d371fa89a9789f4e0cb55580d48a9d4aaab0e4329d6a41b5bfbc6dc3dd4c05d2","abstract_canon_sha256":"5cf1adbb65be74ab0011aa6de697dc3b4ee0ad80961ae273738cddbf58b0693f"},"schema_version":"1.0"},"canonical_sha256":"8f85d967c6a72d2998986419e523b66516100822227bb112ceef738a0d2b9f85","source":{"kind":"arxiv","id":"1101.1923","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1923","created_at":"2026-05-18T03:51:58Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1923v3","created_at":"2026-05-18T03:51:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1923","created_at":"2026-05-18T03:51:58Z"},{"alias_kind":"pith_short_12","alias_value":"R6C5SZ6GU4WS","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"R6C5SZ6GU4WSTGEY","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"R6C5SZ6G","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:R6C5SZ6GU4WSTGEYMQM6KI5WMU","target":"record","payload":{"canonical_record":{"source":{"id":"1101.1923","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-10T18:44:34Z","cross_cats_sorted":[],"title_canon_sha256":"d371fa89a9789f4e0cb55580d48a9d4aaab0e4329d6a41b5bfbc6dc3dd4c05d2","abstract_canon_sha256":"5cf1adbb65be74ab0011aa6de697dc3b4ee0ad80961ae273738cddbf58b0693f"},"schema_version":"1.0"},"canonical_sha256":"8f85d967c6a72d2998986419e523b66516100822227bb112ceef738a0d2b9f85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:58.728574Z","signature_b64":"W0AnU63M2Y7V3mi5z1ockuYu0NGS+emPHTxOA+hRfbmNgsfR/uMmdgb7Gro3yt4QkIFsaBK4c/QxBD/sYw5kDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f85d967c6a72d2998986419e523b66516100822227bb112ceef738a0d2b9f85","last_reissued_at":"2026-05-18T03:51:58.727802Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:58.727802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.1923","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:51:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0eLq/TZUdJ7OaZriFmUpByQM6fz7WPOqRbn7yZ6beoLq9z3nZDm6rGcNktfOogoES4/i5aCXdz4QtdbCXk25Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:41:04.182523Z"},"content_sha256":"8a1509bb467b9d26b1f4d02944697d65d8370dfabe3da536a8e9eeacfda79e7f","schema_version":"1.0","event_id":"sha256:8a1509bb467b9d26b1f4d02944697d65d8370dfabe3da536a8e9eeacfda79e7f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:R6C5SZ6GU4WSTGEYMQM6KI5WMU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Concentration for noncommutative polynomials in random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mark W. Meckes, Stanislaw J. Szarek","submitted_at":"2011-01-10T18:44:34Z","abstract_excerpt":"We present a concentration inequality for linear functionals of noncommutative polynomials in random matrices. Our hypotheses cover most standard ensembles, including Gaussian matrices, matrices with independent uniformly bounded entries and unitary or orthogonal matrices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1923","kind":"arxiv","version":3},"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":"2026-05-18T03:51:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q08SqMsus02GfpJhsjMT+Gdk0n2dChpWt+kcrO9fLPydR6OWyfXPmoy+WEMmMG2f8SDrYrlqciaZfUsPWHowDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:41:04.182965Z"},"content_sha256":"43e75d75b992c483a4ecff80ca1a3a004ca9a06c10d41ecf25c4de21a47e2340","schema_version":"1.0","event_id":"sha256:43e75d75b992c483a4ecff80ca1a3a004ca9a06c10d41ecf25c4de21a47e2340"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R6C5SZ6GU4WSTGEYMQM6KI5WMU/bundle.json","state_url":"https://pith.science/pith/R6C5SZ6GU4WSTGEYMQM6KI5WMU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R6C5SZ6GU4WSTGEYMQM6KI5WMU/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":"2026-06-01T01:41:04Z","links":{"resolver":"https://pith.science/pith/R6C5SZ6GU4WSTGEYMQM6KI5WMU","bundle":"https://pith.science/pith/R6C5SZ6GU4WSTGEYMQM6KI5WMU/bundle.json","state":"https://pith.science/pith/R6C5SZ6GU4WSTGEYMQM6KI5WMU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R6C5SZ6GU4WSTGEYMQM6KI5WMU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:R6C5SZ6GU4WSTGEYMQM6KI5WMU","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":"5cf1adbb65be74ab0011aa6de697dc3b4ee0ad80961ae273738cddbf58b0693f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-10T18:44:34Z","title_canon_sha256":"d371fa89a9789f4e0cb55580d48a9d4aaab0e4329d6a41b5bfbc6dc3dd4c05d2"},"schema_version":"1.0","source":{"id":"1101.1923","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1923","created_at":"2026-05-18T03:51:58Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1923v3","created_at":"2026-05-18T03:51:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1923","created_at":"2026-05-18T03:51:58Z"},{"alias_kind":"pith_short_12","alias_value":"R6C5SZ6GU4WS","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"R6C5SZ6GU4WSTGEY","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"R6C5SZ6G","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:43e75d75b992c483a4ecff80ca1a3a004ca9a06c10d41ecf25c4de21a47e2340","target":"graph","created_at":"2026-05-18T03:51:58Z","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 a concentration inequality for linear functionals of noncommutative polynomials in random matrices. Our hypotheses cover most standard ensembles, including Gaussian matrices, matrices with independent uniformly bounded entries and unitary or orthogonal matrices.","authors_text":"Mark W. Meckes, Stanislaw J. Szarek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-10T18:44:34Z","title":"Concentration for noncommutative polynomials in random matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1923","kind":"arxiv","version":3},"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":"sha256:8a1509bb467b9d26b1f4d02944697d65d8370dfabe3da536a8e9eeacfda79e7f","target":"record","created_at":"2026-05-18T03:51:58Z","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":"5cf1adbb65be74ab0011aa6de697dc3b4ee0ad80961ae273738cddbf58b0693f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-10T18:44:34Z","title_canon_sha256":"d371fa89a9789f4e0cb55580d48a9d4aaab0e4329d6a41b5bfbc6dc3dd4c05d2"},"schema_version":"1.0","source":{"id":"1101.1923","kind":"arxiv","version":3}},"canonical_sha256":"8f85d967c6a72d2998986419e523b66516100822227bb112ceef738a0d2b9f85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f85d967c6a72d2998986419e523b66516100822227bb112ceef738a0d2b9f85","first_computed_at":"2026-05-18T03:51:58.727802Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:58.727802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W0AnU63M2Y7V3mi5z1ockuYu0NGS+emPHTxOA+hRfbmNgsfR/uMmdgb7Gro3yt4QkIFsaBK4c/QxBD/sYw5kDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:58.728574Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.1923","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a1509bb467b9d26b1f4d02944697d65d8370dfabe3da536a8e9eeacfda79e7f","sha256:43e75d75b992c483a4ecff80ca1a3a004ca9a06c10d41ecf25c4de21a47e2340"],"state_sha256":"5253939f072fa3bd1b535e44daff6b8f0c87ba81c91068a24858797fd8c67405"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wcs3X9L/TvwimpdBfBAmmYCCN8mabY/wDQ/BbqCrAYcgwGqSfmJ1fN6rjHg4kxkn9cqfyK45iRk7dtACJQ5/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T01:41:04.186438Z","bundle_sha256":"b5be541d901363ff9a97e37ed11cec42a0a4c91f403ef5ae4cf99d8bb630b88b"}}