{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:AWX63DRZXYZK3IUX3JYHASFR4A","short_pith_number":"pith:AWX63DRZ","canonical_record":{"source":{"id":"1712.00042","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-30T19:31:38Z","cross_cats_sorted":[],"title_canon_sha256":"7f76655f2535c89a564d40acc143847bb487b80fd1f2dd90645b3d0382635882","abstract_canon_sha256":"0d75fbc82836b455d38e547aa6cb99e7a681fea7372b7e0e8267ab5dc934464f"},"schema_version":"1.0"},"canonical_sha256":"05afed8e39be32ada297da707048b1e03b1c672421361e3b373450d60aa87ce4","source":{"kind":"arxiv","id":"1712.00042","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00042","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00042v3","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00042","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"AWX63DRZXYZK","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"AWX63DRZXYZK3IUX","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"AWX63DRZ","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:AWX63DRZXYZK3IUX3JYHASFR4A","target":"record","payload":{"canonical_record":{"source":{"id":"1712.00042","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-30T19:31:38Z","cross_cats_sorted":[],"title_canon_sha256":"7f76655f2535c89a564d40acc143847bb487b80fd1f2dd90645b3d0382635882","abstract_canon_sha256":"0d75fbc82836b455d38e547aa6cb99e7a681fea7372b7e0e8267ab5dc934464f"},"schema_version":"1.0"},"canonical_sha256":"05afed8e39be32ada297da707048b1e03b1c672421361e3b373450d60aa87ce4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:19.524844Z","signature_b64":"jMlEHjrgYEglMsUW0r9i2W21KU9WDvbWEBakt4SrM2lQvK6S3tcA2W7FLobucTrqknftNxw1sostELP6rNXBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05afed8e39be32ada297da707048b1e03b1c672421361e3b373450d60aa87ce4","last_reissued_at":"2026-05-17T23:58:19.524436Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:19.524436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.00042","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":"2026-05-17T23:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IgDxO5vD4YASErz9hhZLoBv46+oBA62yM+SwLffFanL0eATGorcecFZv772iX/K/VfWGzJO0qWRNrH7QQkt5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:49:43.503603Z"},"content_sha256":"c63b42984f05894c38937a7cabac80c45fd1c04e98ca8babf04c681682c7fdf2","schema_version":"1.0","event_id":"sha256:c63b42984f05894c38937a7cabac80c45fd1c04e98ca8babf04c681682c7fdf2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:AWX63DRZXYZK3IUX3JYHASFR4A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularization of non-normal matrices by Gaussian noise - the banded Toeplitz and twisted Toeplitz cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anirban Basak, Elliot Paquette, Ofer Zeitouni","submitted_at":"2017-11-30T19:31:38Z","abstract_excerpt":"We consider the spectrum of additive, polynomially vanishing random perturbations of deterministic matrices, as follows. Let $M_N$ be a deterministic $N\\times N$ matrix, and let $G_N$ be a complex Ginibre matrix. We consider the matrix $\\mathcal{M}_N=M_N+N^{-\\gamma}G_N$, where $\\gamma>1/2$. With $L_N$ the empirical measure of eigenvalues of $\\mathcal{M}_N$, we provide a general deterministic equivalence theorem that ties $L_N$ to the singular values of $z-M_N$, with $z\\in \\mathbb{C}$. We then compute the limit of $L_N$ when $M_N$ is an upper triangular Toeplitz matrix of finite symbol: if $M_N"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00042","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":"2026-05-17T23:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BG2+wgK3G9pHAO7BeRNA7OT1Biw0NuW9p0WoENLLA48ZAgTCc3/SCwOpiGvLYyhb3VEd2nKaIqTmrLqIv3IkBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:49:43.503959Z"},"content_sha256":"232e92e152aec598da7ca58142da6556057ae711959489428366290444e22d3f","schema_version":"1.0","event_id":"sha256:232e92e152aec598da7ca58142da6556057ae711959489428366290444e22d3f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AWX63DRZXYZK3IUX3JYHASFR4A/bundle.json","state_url":"https://pith.science/pith/AWX63DRZXYZK3IUX3JYHASFR4A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AWX63DRZXYZK3IUX3JYHASFR4A/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":"2026-05-27T20:49:43Z","links":{"resolver":"https://pith.science/pith/AWX63DRZXYZK3IUX3JYHASFR4A","bundle":"https://pith.science/pith/AWX63DRZXYZK3IUX3JYHASFR4A/bundle.json","state":"https://pith.science/pith/AWX63DRZXYZK3IUX3JYHASFR4A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AWX63DRZXYZK3IUX3JYHASFR4A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AWX63DRZXYZK3IUX3JYHASFR4A","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":"0d75fbc82836b455d38e547aa6cb99e7a681fea7372b7e0e8267ab5dc934464f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-30T19:31:38Z","title_canon_sha256":"7f76655f2535c89a564d40acc143847bb487b80fd1f2dd90645b3d0382635882"},"schema_version":"1.0","source":{"id":"1712.00042","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00042","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00042v3","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00042","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"AWX63DRZXYZK","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"AWX63DRZXYZK3IUX","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"AWX63DRZ","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:232e92e152aec598da7ca58142da6556057ae711959489428366290444e22d3f","target":"graph","created_at":"2026-05-17T23:58:19Z","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 consider the spectrum of additive, polynomially vanishing random perturbations of deterministic matrices, as follows. Let $M_N$ be a deterministic $N\\times N$ matrix, and let $G_N$ be a complex Ginibre matrix. We consider the matrix $\\mathcal{M}_N=M_N+N^{-\\gamma}G_N$, where $\\gamma>1/2$. With $L_N$ the empirical measure of eigenvalues of $\\mathcal{M}_N$, we provide a general deterministic equivalence theorem that ties $L_N$ to the singular values of $z-M_N$, with $z\\in \\mathbb{C}$. We then compute the limit of $L_N$ when $M_N$ is an upper triangular Toeplitz matrix of finite symbol: if $M_N","authors_text":"Anirban Basak, Elliot Paquette, Ofer Zeitouni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-30T19:31:38Z","title":"Regularization of non-normal matrices by Gaussian noise - the banded Toeplitz and twisted Toeplitz cases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00042","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:c63b42984f05894c38937a7cabac80c45fd1c04e98ca8babf04c681682c7fdf2","target":"record","created_at":"2026-05-17T23:58:19Z","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":"0d75fbc82836b455d38e547aa6cb99e7a681fea7372b7e0e8267ab5dc934464f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-30T19:31:38Z","title_canon_sha256":"7f76655f2535c89a564d40acc143847bb487b80fd1f2dd90645b3d0382635882"},"schema_version":"1.0","source":{"id":"1712.00042","kind":"arxiv","version":3}},"canonical_sha256":"05afed8e39be32ada297da707048b1e03b1c672421361e3b373450d60aa87ce4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05afed8e39be32ada297da707048b1e03b1c672421361e3b373450d60aa87ce4","first_computed_at":"2026-05-17T23:58:19.524436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:19.524436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jMlEHjrgYEglMsUW0r9i2W21KU9WDvbWEBakt4SrM2lQvK6S3tcA2W7FLobucTrqknftNxw1sostELP6rNXBAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:19.524844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.00042","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c63b42984f05894c38937a7cabac80c45fd1c04e98ca8babf04c681682c7fdf2","sha256:232e92e152aec598da7ca58142da6556057ae711959489428366290444e22d3f"],"state_sha256":"872f368cc5219c28ec521bb192f0b505e2aaea867a48986784b9980c7b144378"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1y0iz2+qOBRBV2T1Rd4VZ/YJGdj+F96xQT5gKJPtw+rF4WB/+cvSY4unQEaV5T0QCAyLVEjzpo/lN5nnviY0Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:49:43.506256Z","bundle_sha256":"a1f5df5a614f2ae64ef9a7e2868b8930893ffbfa2fde1560e36509d6c36f01aa"}}