{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:INWSZ7WTVXMXOQUGIHL4EG4GWS","short_pith_number":"pith:INWSZ7WT","canonical_record":{"source":{"id":"2606.01664","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-01T04:18:29Z","cross_cats_sorted":[],"title_canon_sha256":"0515287d6a701c85f99d9ba9978993daa3f1946ee2696675a88c0cd5651328b1","abstract_canon_sha256":"f36452e883a94f2815379818ed45799c3ef9222d69a68357eb63fa157c71f2e4"},"schema_version":"1.0"},"canonical_sha256":"436d2cfed3add977428641d7c21b86b49bff07edadf49df9442708359fe77799","source":{"kind":"arxiv","id":"2606.01664","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01664","created_at":"2026-06-02T02:04:39Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01664v1","created_at":"2026-06-02T02:04:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01664","created_at":"2026-06-02T02:04:39Z"},{"alias_kind":"pith_short_12","alias_value":"INWSZ7WTVXMX","created_at":"2026-06-02T02:04:39Z"},{"alias_kind":"pith_short_16","alias_value":"INWSZ7WTVXMXOQUG","created_at":"2026-06-02T02:04:39Z"},{"alias_kind":"pith_short_8","alias_value":"INWSZ7WT","created_at":"2026-06-02T02:04:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:INWSZ7WTVXMXOQUGIHL4EG4GWS","target":"record","payload":{"canonical_record":{"source":{"id":"2606.01664","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-01T04:18:29Z","cross_cats_sorted":[],"title_canon_sha256":"0515287d6a701c85f99d9ba9978993daa3f1946ee2696675a88c0cd5651328b1","abstract_canon_sha256":"f36452e883a94f2815379818ed45799c3ef9222d69a68357eb63fa157c71f2e4"},"schema_version":"1.0"},"canonical_sha256":"436d2cfed3add977428641d7c21b86b49bff07edadf49df9442708359fe77799","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:39.558763Z","signature_b64":"/+Dw8vVehUDKG0irfWpp/45DeeyQn8bX4FQbCECTC/smaZiB0+ZZmXnCWzsf+GP3Bbrq6hKHXQD9NxJucZ2BCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"436d2cfed3add977428641d7c21b86b49bff07edadf49df9442708359fe77799","last_reissued_at":"2026-06-02T02:04:39.558422Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:39.558422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.01664","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":"2026-06-02T02:04:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ohO3k4F0NSJItPMArJBYS9uawsmSti55qSRvB2NT5Dn/dVPj9kNnEKN4rPBxZCQGZN7C5sVJT2L39UqmsDPQAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T17:24:52.531635Z"},"content_sha256":"4ef27c1fdf121e7328c83344eea6f2902ab282e79516869da640a7150edd0351","schema_version":"1.0","event_id":"sha256:4ef27c1fdf121e7328c83344eea6f2902ab282e79516869da640a7150edd0351"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:INWSZ7WTVXMXOQUGIHL4EG4GWS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Brown measure convergence for the spectrum of polynomials in Ginibre matrices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yi Han","submitted_at":"2026-06-01T04:18:29Z","abstract_excerpt":"Fix a multivariate polynomial $\\mathfrak{p}$ in $n$ non-commuting variables of arbitrary degree, and consider $n$ independent $N\\times N$ complex Ginibre matrices $X_1^N,\\cdots,X_n^N$. We prove that the empirical spectral distribution of $P^N=\\mathfrak{p}(X_1^N,\\cdots,X_n^N)$ converges as $N$ tends to infinity to the so-called Brown measure of $\\mathfrak{p}$ evaluated at free circular variables. For polynomials of degree at most 2, the convergence was proven by Cook, Guionnet, and Husson \\cite{cook2022spectrum}, and we prove that the convergence in fact holds for polynomials $\\mathfrak{p}$ of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01664","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/2606.01664/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":"2026-06-02T02:04:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A8Wtq/y1FB/9KftQ4RpaY5IW9NXB2uLAHqVZ4J89bTuox8Rplvjsr3IoYgppwjGDVyCpOTInDin85iXZh7WWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T17:24:52.532008Z"},"content_sha256":"bde4d50a33fcae32d8389dbcc7808fdd692e4693f2df2ca7c4c0c07c44b1fe72","schema_version":"1.0","event_id":"sha256:bde4d50a33fcae32d8389dbcc7808fdd692e4693f2df2ca7c4c0c07c44b1fe72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/INWSZ7WTVXMXOQUGIHL4EG4GWS/bundle.json","state_url":"https://pith.science/pith/INWSZ7WTVXMXOQUGIHL4EG4GWS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/INWSZ7WTVXMXOQUGIHL4EG4GWS/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":"2026-07-02T17:24:52Z","links":{"resolver":"https://pith.science/pith/INWSZ7WTVXMXOQUGIHL4EG4GWS","bundle":"https://pith.science/pith/INWSZ7WTVXMXOQUGIHL4EG4GWS/bundle.json","state":"https://pith.science/pith/INWSZ7WTVXMXOQUGIHL4EG4GWS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/INWSZ7WTVXMXOQUGIHL4EG4GWS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:INWSZ7WTVXMXOQUGIHL4EG4GWS","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":"f36452e883a94f2815379818ed45799c3ef9222d69a68357eb63fa157c71f2e4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-01T04:18:29Z","title_canon_sha256":"0515287d6a701c85f99d9ba9978993daa3f1946ee2696675a88c0cd5651328b1"},"schema_version":"1.0","source":{"id":"2606.01664","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01664","created_at":"2026-06-02T02:04:39Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01664v1","created_at":"2026-06-02T02:04:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01664","created_at":"2026-06-02T02:04:39Z"},{"alias_kind":"pith_short_12","alias_value":"INWSZ7WTVXMX","created_at":"2026-06-02T02:04:39Z"},{"alias_kind":"pith_short_16","alias_value":"INWSZ7WTVXMXOQUG","created_at":"2026-06-02T02:04:39Z"},{"alias_kind":"pith_short_8","alias_value":"INWSZ7WT","created_at":"2026-06-02T02:04:39Z"}],"graph_snapshots":[{"event_id":"sha256:bde4d50a33fcae32d8389dbcc7808fdd692e4693f2df2ca7c4c0c07c44b1fe72","target":"graph","created_at":"2026-06-02T02:04:39Z","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/2606.01664/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Fix a multivariate polynomial $\\mathfrak{p}$ in $n$ non-commuting variables of arbitrary degree, and consider $n$ independent $N\\times N$ complex Ginibre matrices $X_1^N,\\cdots,X_n^N$. We prove that the empirical spectral distribution of $P^N=\\mathfrak{p}(X_1^N,\\cdots,X_n^N)$ converges as $N$ tends to infinity to the so-called Brown measure of $\\mathfrak{p}$ evaluated at free circular variables. For polynomials of degree at most 2, the convergence was proven by Cook, Guionnet, and Husson \\cite{cook2022spectrum}, and we prove that the convergence in fact holds for polynomials $\\mathfrak{p}$ of ","authors_text":"Yi Han","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-01T04:18:29Z","title":"Brown measure convergence for the spectrum of polynomials in Ginibre matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01664","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":"sha256:4ef27c1fdf121e7328c83344eea6f2902ab282e79516869da640a7150edd0351","target":"record","created_at":"2026-06-02T02:04:39Z","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":"f36452e883a94f2815379818ed45799c3ef9222d69a68357eb63fa157c71f2e4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-01T04:18:29Z","title_canon_sha256":"0515287d6a701c85f99d9ba9978993daa3f1946ee2696675a88c0cd5651328b1"},"schema_version":"1.0","source":{"id":"2606.01664","kind":"arxiv","version":1}},"canonical_sha256":"436d2cfed3add977428641d7c21b86b49bff07edadf49df9442708359fe77799","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"436d2cfed3add977428641d7c21b86b49bff07edadf49df9442708359fe77799","first_computed_at":"2026-06-02T02:04:39.558422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:39.558422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/+Dw8vVehUDKG0irfWpp/45DeeyQn8bX4FQbCECTC/smaZiB0+ZZmXnCWzsf+GP3Bbrq6hKHXQD9NxJucZ2BCg==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:39.558763Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.01664","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ef27c1fdf121e7328c83344eea6f2902ab282e79516869da640a7150edd0351","sha256:bde4d50a33fcae32d8389dbcc7808fdd692e4693f2df2ca7c4c0c07c44b1fe72"],"state_sha256":"9be7f4c9a838359070065c2316c27b5b765ede9da7f38afdb2b7e335fe89e9a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KTk561sOYFO91faYnSGoU2RJsvIdTNsfO/0IRRh4WjBGxW+iEiiT09nisYZ+62z4Ukta1VZNvpJesoHtKHiHAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T17:24:52.533995Z","bundle_sha256":"29fae19042b67658ef5de1bc7963f4f73c364ba8154ecb0c54f5e8bb464237f9"}}