{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:BLCLGRHO7WSW3OP3HBVPANIF77","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":"948dbafb206bf74a7a52398fb7b85795c10d1268f40e0d5a7763ff8de37bcd00","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math-ph","math.MP"],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2001-04-04T20:48:11Z","title_canon_sha256":"26b0ba9ed8a2a3897ff8498887021c3da07ad4405b57b4d1d65ae41241fdaca0"},"schema_version":"1.0","source":{"id":"cond-mat/0104072","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0104072","created_at":"2026-05-18T01:40:07Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0104072v1","created_at":"2026-05-18T01:40:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0104072","created_at":"2026-05-18T01:40:07Z"},{"alias_kind":"pith_short_12","alias_value":"BLCLGRHO7WSW","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"BLCLGRHO7WSW3OP3","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"BLCLGRHO","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:393a2b7cd3f0db7013ca09a3c41d88eb64f6f8f2af304486c8d9d15035616615","target":"graph","created_at":"2026-05-18T01:40:07Z","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":"Recently, an analytic method was developed to study in the large $N$ limit non-hermitean random matrices that are drawn from a large class of circularly symmetric non-Gaussian probability distributions, thus extending the existing Gaussian non-hermitean literature. One obtains an explicit algebraic equation for the integrated density of eigenvalues from which the Green's function and averaged density of eigenvalues could be calculated in a simple manner. Thus, that formalism may be thought of as the non-hermitean analog of the method due to Br\\'ezin, Itzykson, Parisi and Zuber for analyzing he","authors_text":"A. Zee, Joshua Feinberg, R. Scalettar","cross_cats":["cond-mat.stat-mech","hep-th","math-ph","math.MP"],"headline":"","license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2001-04-04T20:48:11Z","title":"\"Single Ring Theorem\" and the Disk-Annulus Phase Transition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0104072","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:bafc2b9f1ef38c6020ecc8474f65d862f47fb4b76c864efbccbe838a9e238172","target":"record","created_at":"2026-05-18T01:40:07Z","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":"948dbafb206bf74a7a52398fb7b85795c10d1268f40e0d5a7763ff8de37bcd00","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math-ph","math.MP"],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2001-04-04T20:48:11Z","title_canon_sha256":"26b0ba9ed8a2a3897ff8498887021c3da07ad4405b57b4d1d65ae41241fdaca0"},"schema_version":"1.0","source":{"id":"cond-mat/0104072","kind":"arxiv","version":1}},"canonical_sha256":"0ac4b344eefda56db9fb386af03505ffc0aa024ab7b9985e32768e2dbe5a5c10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ac4b344eefda56db9fb386af03505ffc0aa024ab7b9985e32768e2dbe5a5c10","first_computed_at":"2026-05-18T01:40:07.443755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:07.443755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aoybXDXbRd06KYTKcnjMIpVEHrh6QsvF5gzB5L0DybhF2GW9o4zi3qZqHyXNGw5l94Vh/4u3RjCerLbpjprOAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:07.444463Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0104072","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bafc2b9f1ef38c6020ecc8474f65d862f47fb4b76c864efbccbe838a9e238172","sha256:393a2b7cd3f0db7013ca09a3c41d88eb64f6f8f2af304486c8d9d15035616615"],"state_sha256":"90f0c323cc94055cbe3db437e1ba30a800c447a3cb23b3975ae4993ca046000d"}