{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:TGIVPZV4CSHZ4M2KI6KH4COUJO","short_pith_number":"pith:TGIVPZV4","canonical_record":{"source":{"id":"2410.17515","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-10-23T02:42:13Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"a545ab3b6dc0d0489ea64373012d86cae9cb1357b83c91a9500f3b310145b01e","abstract_canon_sha256":"8e0e104a8f1d35d905cc2d4955ddbb947fbe990a7a7ae354d4315ce21612b046"},"schema_version":"1.0"},"canonical_sha256":"999157e6bc148f9e334a47947e09d44b8271d1cdd72e3931c0400a2c9112a6de","source":{"kind":"arxiv","id":"2410.17515","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.17515","created_at":"2026-07-05T09:24:23Z"},{"alias_kind":"arxiv_version","alias_value":"2410.17515v1","created_at":"2026-07-05T09:24:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.17515","created_at":"2026-07-05T09:24:23Z"},{"alias_kind":"pith_short_12","alias_value":"TGIVPZV4CSHZ","created_at":"2026-07-05T09:24:23Z"},{"alias_kind":"pith_short_16","alias_value":"TGIVPZV4CSHZ4M2K","created_at":"2026-07-05T09:24:23Z"},{"alias_kind":"pith_short_8","alias_value":"TGIVPZV4","created_at":"2026-07-05T09:24:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:TGIVPZV4CSHZ4M2KI6KH4COUJO","target":"record","payload":{"canonical_record":{"source":{"id":"2410.17515","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-10-23T02:42:13Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"a545ab3b6dc0d0489ea64373012d86cae9cb1357b83c91a9500f3b310145b01e","abstract_canon_sha256":"8e0e104a8f1d35d905cc2d4955ddbb947fbe990a7a7ae354d4315ce21612b046"},"schema_version":"1.0"},"canonical_sha256":"999157e6bc148f9e334a47947e09d44b8271d1cdd72e3931c0400a2c9112a6de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:24:23.728590Z","signature_b64":"1RXV42KUIGX7zhACpVgz+1BEDUdTGAoucTRm5pwB4vkurykEyV7py2tYKWM33XMCkbYcuAPPPuEHqy07eD8oBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"999157e6bc148f9e334a47947e09d44b8271d1cdd72e3931c0400a2c9112a6de","last_reissued_at":"2026-07-05T09:24:23.728184Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:24:23.728184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.17515","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":"2026-07-05T09:24:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7u742q+xYqfziutILsXa5jcl8dPBn5HpzniOSyM/B5304FVekzPHR16S1Mrty/H5T0y/vjFOp0AOIiLoF958CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T16:38:32.630516Z"},"content_sha256":"5b8af6f22fb1f0773d9ca2276c81a902ec50ade2957f09913437f1407de30b88","schema_version":"1.0","event_id":"sha256:5b8af6f22fb1f0773d9ca2276c81a902ec50ade2957f09913437f1407de30b88"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:TGIVPZV4CSHZ4M2KI6KH4COUJO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extremal Eigenvalues of Random Kernel Matrices with Polynomial Scaling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"David Kogan, Jiaoyang Huang, Sagnik Nandy","submitted_at":"2024-10-23T02:42:13Z","abstract_excerpt":"We study the spectral norm of random kernel matrices with polynomial scaling, where the number of samples scales polynomially with the data dimension. In this regime, Lu and Yau (2022) proved that the empirical spectral distribution converges to the additive free convolution of a semicircle law and a Marcenko-Pastur law. We demonstrate that the random kernel matrix can be decomposed into a \"bulk\" part and a low-rank part. The spectral norm of the \"bulk\" part almost surely converges to the edge of the limiting spectrum.\n  In the special case where the random kernel matrices correspond to the in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.17515","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.17515/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:24:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wwa4UFKajx+lJ/PobKJ15ZjZIIImcOsBbNp4GIH6RX0u7MsaciaFYzbjG1sfRaNfgcfhr/y99w/6enkOPgizDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T16:38:32.631608Z"},"content_sha256":"93531a21f1b439fcbe99bc8ad57c8ce2c1caf3c6696782531e41cc4ac627bafc","schema_version":"1.0","event_id":"sha256:93531a21f1b439fcbe99bc8ad57c8ce2c1caf3c6696782531e41cc4ac627bafc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TGIVPZV4CSHZ4M2KI6KH4COUJO/bundle.json","state_url":"https://pith.science/pith/TGIVPZV4CSHZ4M2KI6KH4COUJO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TGIVPZV4CSHZ4M2KI6KH4COUJO/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":"2026-08-09T16:38:32Z","links":{"resolver":"https://pith.science/pith/TGIVPZV4CSHZ4M2KI6KH4COUJO","bundle":"https://pith.science/pith/TGIVPZV4CSHZ4M2KI6KH4COUJO/bundle.json","state":"https://pith.science/pith/TGIVPZV4CSHZ4M2KI6KH4COUJO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TGIVPZV4CSHZ4M2KI6KH4COUJO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TGIVPZV4CSHZ4M2KI6KH4COUJO","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":"8e0e104a8f1d35d905cc2d4955ddbb947fbe990a7a7ae354d4315ce21612b046","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-10-23T02:42:13Z","title_canon_sha256":"a545ab3b6dc0d0489ea64373012d86cae9cb1357b83c91a9500f3b310145b01e"},"schema_version":"1.0","source":{"id":"2410.17515","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.17515","created_at":"2026-07-05T09:24:23Z"},{"alias_kind":"arxiv_version","alias_value":"2410.17515v1","created_at":"2026-07-05T09:24:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.17515","created_at":"2026-07-05T09:24:23Z"},{"alias_kind":"pith_short_12","alias_value":"TGIVPZV4CSHZ","created_at":"2026-07-05T09:24:23Z"},{"alias_kind":"pith_short_16","alias_value":"TGIVPZV4CSHZ4M2K","created_at":"2026-07-05T09:24:23Z"},{"alias_kind":"pith_short_8","alias_value":"TGIVPZV4","created_at":"2026-07-05T09:24:23Z"}],"graph_snapshots":[{"event_id":"sha256:93531a21f1b439fcbe99bc8ad57c8ce2c1caf3c6696782531e41cc4ac627bafc","target":"graph","created_at":"2026-07-05T09:24:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.17515/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the spectral norm of random kernel matrices with polynomial scaling, where the number of samples scales polynomially with the data dimension. In this regime, Lu and Yau (2022) proved that the empirical spectral distribution converges to the additive free convolution of a semicircle law and a Marcenko-Pastur law. We demonstrate that the random kernel matrix can be decomposed into a \"bulk\" part and a low-rank part. The spectral norm of the \"bulk\" part almost surely converges to the edge of the limiting spectrum.\n  In the special case where the random kernel matrices correspond to the in","authors_text":"David Kogan, Jiaoyang Huang, Sagnik Nandy","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-10-23T02:42:13Z","title":"Extremal Eigenvalues of Random Kernel Matrices with Polynomial Scaling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.17515","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":"sha256:5b8af6f22fb1f0773d9ca2276c81a902ec50ade2957f09913437f1407de30b88","target":"record","created_at":"2026-07-05T09:24:23Z","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":"8e0e104a8f1d35d905cc2d4955ddbb947fbe990a7a7ae354d4315ce21612b046","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-10-23T02:42:13Z","title_canon_sha256":"a545ab3b6dc0d0489ea64373012d86cae9cb1357b83c91a9500f3b310145b01e"},"schema_version":"1.0","source":{"id":"2410.17515","kind":"arxiv","version":1}},"canonical_sha256":"999157e6bc148f9e334a47947e09d44b8271d1cdd72e3931c0400a2c9112a6de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"999157e6bc148f9e334a47947e09d44b8271d1cdd72e3931c0400a2c9112a6de","first_computed_at":"2026-07-05T09:24:23.728184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:24:23.728184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1RXV42KUIGX7zhACpVgz+1BEDUdTGAoucTRm5pwB4vkurykEyV7py2tYKWM33XMCkbYcuAPPPuEHqy07eD8oBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:24:23.728590Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.17515","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b8af6f22fb1f0773d9ca2276c81a902ec50ade2957f09913437f1407de30b88","sha256:93531a21f1b439fcbe99bc8ad57c8ce2c1caf3c6696782531e41cc4ac627bafc"],"state_sha256":"01a809e545212987d852b22fb3f7cd1773d179d8711fe84e11c17769656df198"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q4l7ERU8pEzH6Fj5TaVle5Wt+ipWE+Osza2kHkv///V8jgV+5h1pVKcKLL31E2k/GCTGj+0/kwhioyokGor/Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T16:38:32.637939Z","bundle_sha256":"4aef2c5d582e78851847393c08aecc585fe3e6b794c143d12c5e52751b0d9d86"}}