{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:USQLQBALKNPUR6YAJEH5X3J2QV","short_pith_number":"pith:USQLQBAL","canonical_record":{"source":{"id":"1710.00240","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-30T18:31:27Z","cross_cats_sorted":[],"title_canon_sha256":"c4bba1a8c1f2ad64883163a142db8b590aaf3d07e9ac8d88ac881cf9a41215cd","abstract_canon_sha256":"54b1e2472094cdee5fba428a893428675d6707a0391f85144f3762a1faf49625"},"schema_version":"1.0"},"canonical_sha256":"a4a0b8040b535f48fb00490fdbed3a855a45567fda8795cff0c38e7ddaae39d5","source":{"kind":"arxiv","id":"1710.00240","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00240","created_at":"2026-05-18T00:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00240v2","created_at":"2026-05-18T00:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00240","created_at":"2026-05-18T00:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"USQLQBALKNPU","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"USQLQBALKNPUR6YA","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"USQLQBAL","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:USQLQBALKNPUR6YAJEH5X3J2QV","target":"record","payload":{"canonical_record":{"source":{"id":"1710.00240","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-30T18:31:27Z","cross_cats_sorted":[],"title_canon_sha256":"c4bba1a8c1f2ad64883163a142db8b590aaf3d07e9ac8d88ac881cf9a41215cd","abstract_canon_sha256":"54b1e2472094cdee5fba428a893428675d6707a0391f85144f3762a1faf49625"},"schema_version":"1.0"},"canonical_sha256":"a4a0b8040b535f48fb00490fdbed3a855a45567fda8795cff0c38e7ddaae39d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:25.628867Z","signature_b64":"x91Z4VUCMpc2hMLWY7uF34lYJ31fpDIfdIZF8GOai8+1mwDD0Rrn95y3wppdD3mUVSgu0KK4dwFuM5Yc+4HNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4a0b8040b535f48fb00490fdbed3a855a45567fda8795cff0c38e7ddaae39d5","last_reissued_at":"2026-05-18T00:18:25.628200Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:25.628200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.00240","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6KhptRqAHO4eOsCvO7wHUspX35GxD7eXBJXGLC64b9ke1UXMCrTdVKYvhTRvAh0iFgbbg61B7tOrvH5BPCZfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:17:46.689975Z"},"content_sha256":"3711bf9e0485d3e66193243cea26616cb3d3370c12151c6eff1f894c846e7221","schema_version":"1.0","event_id":"sha256:3711bf9e0485d3e66193243cea26616cb3d3370c12151c6eff1f894c846e7221"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:USQLQBALKNPUR6YAJEH5X3J2QV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral distributions of periodic random matrix ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Roger Van Peski","submitted_at":"2017-09-30T18:31:27Z","abstract_excerpt":"Kolo\\u{g}lu, Kopp and Miller compute the limiting spectral distribution of a certain class of real random matrix ensembles, known as $k$-block circulant ensembles, and discover that it is exactly equal to the eigenvalue distribution of an $k \\times k$ Gaussian unitary ensemble. We give a simpler proof that under very general conditions which subsume the cases studied by Kolo\\u{g}lu-Kopp-Miller, real-symmetric ensembles with periodic diagonals always have limiting spectral distribution equal to the eigenvalue distribution of a finite Hermitian ensemble with Gaussian entries which is a `complex "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00240","kind":"arxiv","version":2},"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":"2026-05-18T00:18:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"exYf80N2CwY4RnjrhHtWUreVf5VF2eINlgb4VMkgJhRkYfp1Fa2MxvDiLPYb2zsu3B+K213Q4SpZfFHHiYxsBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:17:46.690363Z"},"content_sha256":"accc0c884aac5feb1197c11103915d4bf03da337c734cf8db983caa5a7cc2b1f","schema_version":"1.0","event_id":"sha256:accc0c884aac5feb1197c11103915d4bf03da337c734cf8db983caa5a7cc2b1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/USQLQBALKNPUR6YAJEH5X3J2QV/bundle.json","state_url":"https://pith.science/pith/USQLQBALKNPUR6YAJEH5X3J2QV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/USQLQBALKNPUR6YAJEH5X3J2QV/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":"2026-06-02T12:17:46Z","links":{"resolver":"https://pith.science/pith/USQLQBALKNPUR6YAJEH5X3J2QV","bundle":"https://pith.science/pith/USQLQBALKNPUR6YAJEH5X3J2QV/bundle.json","state":"https://pith.science/pith/USQLQBALKNPUR6YAJEH5X3J2QV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/USQLQBALKNPUR6YAJEH5X3J2QV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:USQLQBALKNPUR6YAJEH5X3J2QV","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":"54b1e2472094cdee5fba428a893428675d6707a0391f85144f3762a1faf49625","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-30T18:31:27Z","title_canon_sha256":"c4bba1a8c1f2ad64883163a142db8b590aaf3d07e9ac8d88ac881cf9a41215cd"},"schema_version":"1.0","source":{"id":"1710.00240","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00240","created_at":"2026-05-18T00:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00240v2","created_at":"2026-05-18T00:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00240","created_at":"2026-05-18T00:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"USQLQBALKNPU","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"USQLQBALKNPUR6YA","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"USQLQBAL","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:accc0c884aac5feb1197c11103915d4bf03da337c734cf8db983caa5a7cc2b1f","target":"graph","created_at":"2026-05-18T00:18:25Z","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":"Kolo\\u{g}lu, Kopp and Miller compute the limiting spectral distribution of a certain class of real random matrix ensembles, known as $k$-block circulant ensembles, and discover that it is exactly equal to the eigenvalue distribution of an $k \\times k$ Gaussian unitary ensemble. We give a simpler proof that under very general conditions which subsume the cases studied by Kolo\\u{g}lu-Kopp-Miller, real-symmetric ensembles with periodic diagonals always have limiting spectral distribution equal to the eigenvalue distribution of a finite Hermitian ensemble with Gaussian entries which is a `complex ","authors_text":"Roger Van Peski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-30T18:31:27Z","title":"Spectral distributions of periodic random matrix ensembles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00240","kind":"arxiv","version":2},"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":"sha256:3711bf9e0485d3e66193243cea26616cb3d3370c12151c6eff1f894c846e7221","target":"record","created_at":"2026-05-18T00:18:25Z","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":"54b1e2472094cdee5fba428a893428675d6707a0391f85144f3762a1faf49625","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-30T18:31:27Z","title_canon_sha256":"c4bba1a8c1f2ad64883163a142db8b590aaf3d07e9ac8d88ac881cf9a41215cd"},"schema_version":"1.0","source":{"id":"1710.00240","kind":"arxiv","version":2}},"canonical_sha256":"a4a0b8040b535f48fb00490fdbed3a855a45567fda8795cff0c38e7ddaae39d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4a0b8040b535f48fb00490fdbed3a855a45567fda8795cff0c38e7ddaae39d5","first_computed_at":"2026-05-18T00:18:25.628200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:25.628200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x91Z4VUCMpc2hMLWY7uF34lYJ31fpDIfdIZF8GOai8+1mwDD0Rrn95y3wppdD3mUVSgu0KK4dwFuM5Yc+4HNDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:25.628867Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00240","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3711bf9e0485d3e66193243cea26616cb3d3370c12151c6eff1f894c846e7221","sha256:accc0c884aac5feb1197c11103915d4bf03da337c734cf8db983caa5a7cc2b1f"],"state_sha256":"1bf85deb411a36bbb5d86592c9dc2952169eee2ac344a606558eadc12bb9fd0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PpuarXt/Hfuf6xARlG9/luy48h//NAy4Md3/Q8NtjKwSSF3oPJFwODMSCDym5nSrgWHF+Br8hwfitRsSWI80Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T12:17:46.692431Z","bundle_sha256":"4e84b5524ff9ad4845a1622f1da7a9f486b4e6a4758bcdc570c989c975c0f9de"}}