{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Z2D7E3J4I2EA5GN67G47P7N5PT","short_pith_number":"pith:Z2D7E3J4","canonical_record":{"source":{"id":"1405.7820","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-30T10:49:27Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"7cfc183cee13cc1a139487583df05e4aa404b3c0641f21bfbe46298a753c4516","abstract_canon_sha256":"1ce798f60038c1b5d48ade666ab36076e47e9452cdc082e4971723f0cc155133"},"schema_version":"1.0"},"canonical_sha256":"ce87f26d3c46880e99bef9b9f7fdbd7cf7d9741363ddf1b5212760fdbde3972c","source":{"kind":"arxiv","id":"1405.7820","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7820","created_at":"2026-05-18T01:37:28Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7820v4","created_at":"2026-05-18T01:37:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7820","created_at":"2026-05-18T01:37:28Z"},{"alias_kind":"pith_short_12","alias_value":"Z2D7E3J4I2EA","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z2D7E3J4I2EA5GN6","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z2D7E3J4","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Z2D7E3J4I2EA5GN67G47P7N5PT","target":"record","payload":{"canonical_record":{"source":{"id":"1405.7820","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-30T10:49:27Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"7cfc183cee13cc1a139487583df05e4aa404b3c0641f21bfbe46298a753c4516","abstract_canon_sha256":"1ce798f60038c1b5d48ade666ab36076e47e9452cdc082e4971723f0cc155133"},"schema_version":"1.0"},"canonical_sha256":"ce87f26d3c46880e99bef9b9f7fdbd7cf7d9741363ddf1b5212760fdbde3972c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:28.768022Z","signature_b64":"Wu8GSWJdfhP4dsQC+bhVPRP3bz1tL/IhrJjxUWUFF4bCROI0xHOjsGk4uREJg0KkO025pUwNQclaVPSWWxOLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce87f26d3c46880e99bef9b9f7fdbd7cf7d9741363ddf1b5212760fdbde3972c","last_reissued_at":"2026-05-18T01:37:28.767453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:28.767453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.7820","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":"2026-05-18T01:37:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GnxL0sguYHG8DhC5gFbEn4espgsJ7ZVtFkx0ah8akKQ4Md+pnbUIkWQs1+F7OLfexnFsAc1JP6WIZqt1Yi87BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:09:46.484446Z"},"content_sha256":"859f566a824899c51ddbca873c3a7444f796a181d35d474344c4c9f6ef36eaa6","schema_version":"1.0","event_id":"sha256:859f566a824899c51ddbca873c3a7444f796a181d35d474344c4c9f6ef36eaa6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Z2D7E3J4I2EA5GN67G47P7N5PT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Bounds for Convergence of Expected Spectral Distributions to the Semi-Circular Law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.PR","authors_text":"A. Tikhomirov, F. G\\\"otze","submitted_at":"2014-05-30T10:49:27Z","abstract_excerpt":"Let $\\mathbf X=(X_{jk})_{j,k=1}^n$ denote a Hermitian random matrix with entries $X_{jk}$, which are independent for $1\\le j\\le k\\le n$. We consider the rate of convergence of the empirical spectral distribution function of the matrix $\\mathbf X$ to the semi-circular law assuming that ${\\mathbf E} X_{jk}=0$, ${\\mathbf E} X_{jk}^2=1$ and that $$ \\sup_{n\\ge1}\\sup_{1\\le j,k\\le n}{\\mathbf E}|X_{jk}|^4=:\\mu_4<\\infty \\quad \\text{and} \\sup_{1\\le j,k\\le n}|X_{jk}|\\le D_0n^{\\frac14}. $$ By means of a recursion argument it is shown that the Kolmogorov distance between the expected spectral distribution "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7820","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":"2026-05-18T01:37:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pkly00pBoo2W2xnMmQ2rKXiVMvDnV3omXHs5jmuvIRHrf4ovSY8Dsff6unMd4LKpZBRACQ3i65aqAveexwDtDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:09:46.484845Z"},"content_sha256":"cbb6776edeea6d4f53ccbd8dc2d6f9c8ee72029c5f77947d3c1fc676f4659b31","schema_version":"1.0","event_id":"sha256:cbb6776edeea6d4f53ccbd8dc2d6f9c8ee72029c5f77947d3c1fc676f4659b31"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z2D7E3J4I2EA5GN67G47P7N5PT/bundle.json","state_url":"https://pith.science/pith/Z2D7E3J4I2EA5GN67G47P7N5PT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z2D7E3J4I2EA5GN67G47P7N5PT/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":"2026-06-05T09:09:46Z","links":{"resolver":"https://pith.science/pith/Z2D7E3J4I2EA5GN67G47P7N5PT","bundle":"https://pith.science/pith/Z2D7E3J4I2EA5GN67G47P7N5PT/bundle.json","state":"https://pith.science/pith/Z2D7E3J4I2EA5GN67G47P7N5PT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z2D7E3J4I2EA5GN67G47P7N5PT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Z2D7E3J4I2EA5GN67G47P7N5PT","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":"1ce798f60038c1b5d48ade666ab36076e47e9452cdc082e4971723f0cc155133","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-30T10:49:27Z","title_canon_sha256":"7cfc183cee13cc1a139487583df05e4aa404b3c0641f21bfbe46298a753c4516"},"schema_version":"1.0","source":{"id":"1405.7820","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7820","created_at":"2026-05-18T01:37:28Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7820v4","created_at":"2026-05-18T01:37:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7820","created_at":"2026-05-18T01:37:28Z"},{"alias_kind":"pith_short_12","alias_value":"Z2D7E3J4I2EA","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z2D7E3J4I2EA5GN6","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z2D7E3J4","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:cbb6776edeea6d4f53ccbd8dc2d6f9c8ee72029c5f77947d3c1fc676f4659b31","target":"graph","created_at":"2026-05-18T01:37:28Z","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":"Let $\\mathbf X=(X_{jk})_{j,k=1}^n$ denote a Hermitian random matrix with entries $X_{jk}$, which are independent for $1\\le j\\le k\\le n$. We consider the rate of convergence of the empirical spectral distribution function of the matrix $\\mathbf X$ to the semi-circular law assuming that ${\\mathbf E} X_{jk}=0$, ${\\mathbf E} X_{jk}^2=1$ and that $$ \\sup_{n\\ge1}\\sup_{1\\le j,k\\le n}{\\mathbf E}|X_{jk}|^4=:\\mu_4<\\infty \\quad \\text{and} \\sup_{1\\le j,k\\le n}|X_{jk}|\\le D_0n^{\\frac14}. $$ By means of a recursion argument it is shown that the Kolmogorov distance between the expected spectral distribution ","authors_text":"A. Tikhomirov, F. G\\\"otze","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-30T10:49:27Z","title":"Optimal Bounds for Convergence of Expected Spectral Distributions to the Semi-Circular Law"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7820","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":"sha256:859f566a824899c51ddbca873c3a7444f796a181d35d474344c4c9f6ef36eaa6","target":"record","created_at":"2026-05-18T01:37:28Z","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":"1ce798f60038c1b5d48ade666ab36076e47e9452cdc082e4971723f0cc155133","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-30T10:49:27Z","title_canon_sha256":"7cfc183cee13cc1a139487583df05e4aa404b3c0641f21bfbe46298a753c4516"},"schema_version":"1.0","source":{"id":"1405.7820","kind":"arxiv","version":4}},"canonical_sha256":"ce87f26d3c46880e99bef9b9f7fdbd7cf7d9741363ddf1b5212760fdbde3972c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce87f26d3c46880e99bef9b9f7fdbd7cf7d9741363ddf1b5212760fdbde3972c","first_computed_at":"2026-05-18T01:37:28.767453Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:28.767453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wu8GSWJdfhP4dsQC+bhVPRP3bz1tL/IhrJjxUWUFF4bCROI0xHOjsGk4uREJg0KkO025pUwNQclaVPSWWxOLAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:28.768022Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.7820","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:859f566a824899c51ddbca873c3a7444f796a181d35d474344c4c9f6ef36eaa6","sha256:cbb6776edeea6d4f53ccbd8dc2d6f9c8ee72029c5f77947d3c1fc676f4659b31"],"state_sha256":"ae4c0016e2c218cf71a8456001dee44a3d36b287ae7a53505aeefa01a6c255e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j4GOz+vyILT4aLn7QhCMjjigh5dp3zrdjnGtmhuRcs9sr1O2egfoVG3rPWuT8mFXLDzuJRzEZUAARmmsfP5KAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:09:46.488096Z","bundle_sha256":"9b8e9ad52e0a96e2c1f03172c8406316e93220cd8c35529cd69443e9f208a006"}}