{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:5CGDZ6KO5MUBZGYS2V63SRKLXA","short_pith_number":"pith:5CGDZ6KO","schema_version":"1.0","canonical_sha256":"e88c3cf94eeb281c9b12d57db9454bb8265ca1a9ad163885c51dd208d59c710c","source":{"kind":"arxiv","id":"math/0312215","version":1},"attestation_state":"computed","paper":{"title":"Eigenvalue Spacing Distribution for the Ensemble of Real Symmetric Toeplitz Matrices","license":"","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Christopher Hammond, Steven J. Miller","submitted_at":"2003-12-10T17:05:12Z","abstract_excerpt":"Consider the ensemble of Real Symmetric Toeplitz Matrices, each entry iidrv from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. The limiting spectral measure (the density of normalized eigenvalues) converges weakly to a new universal distribution with unbounded support, independent of p. This distribution's moments are almost those of the Gaussian's; the deficit may be interpreted in terms of Diophantine obstructions. With a little more work, we obtain almost sure convergence. An investigation of spacings between adjacent normalized eigenvalues looks Poiss"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0312215","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2003-12-10T17:05:12Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"a95bb4b0a688b2bdd8d255af693f527c89992206cce96e754a7aed13b8bb5278","abstract_canon_sha256":"bbb06b43dbb9418aca473678914bba55edbf616b99d20dbae3d0546bbbb14182"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:55.553644Z","signature_b64":"5VNMi+yxuiHWy5tXEQP2tI25t8oiAkO+KEtYshmqDw7vPnt3ODfQfutHwi5MZCWZRk5mCANYPqmPE2o2bciDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e88c3cf94eeb281c9b12d57db9454bb8265ca1a9ad163885c51dd208d59c710c","last_reissued_at":"2026-05-18T04:35:55.553149Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:55.553149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Eigenvalue Spacing Distribution for the Ensemble of Real Symmetric Toeplitz Matrices","license":"","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Christopher Hammond, Steven J. Miller","submitted_at":"2003-12-10T17:05:12Z","abstract_excerpt":"Consider the ensemble of Real Symmetric Toeplitz Matrices, each entry iidrv from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. The limiting spectral measure (the density of normalized eigenvalues) converges weakly to a new universal distribution with unbounded support, independent of p. This distribution's moments are almost those of the Gaussian's; the deficit may be interpreted in terms of Diophantine obstructions. With a little more work, we obtain almost sure convergence. An investigation of spacings between adjacent normalized eigenvalues looks Poiss"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0312215","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0312215","created_at":"2026-05-18T04:35:55.553213+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0312215v1","created_at":"2026-05-18T04:35:55.553213+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0312215","created_at":"2026-05-18T04:35:55.553213+00:00"},{"alias_kind":"pith_short_12","alias_value":"5CGDZ6KO5MUB","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_16","alias_value":"5CGDZ6KO5MUBZGYS","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_8","alias_value":"5CGDZ6KO","created_at":"2026-05-18T12:25:51.375804+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5CGDZ6KO5MUBZGYS2V63SRKLXA","json":"https://pith.science/pith/5CGDZ6KO5MUBZGYS2V63SRKLXA.json","graph_json":"https://pith.science/api/pith-number/5CGDZ6KO5MUBZGYS2V63SRKLXA/graph.json","events_json":"https://pith.science/api/pith-number/5CGDZ6KO5MUBZGYS2V63SRKLXA/events.json","paper":"https://pith.science/paper/5CGDZ6KO"},"agent_actions":{"view_html":"https://pith.science/pith/5CGDZ6KO5MUBZGYS2V63SRKLXA","download_json":"https://pith.science/pith/5CGDZ6KO5MUBZGYS2V63SRKLXA.json","view_paper":"https://pith.science/paper/5CGDZ6KO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0312215&json=true","fetch_graph":"https://pith.science/api/pith-number/5CGDZ6KO5MUBZGYS2V63SRKLXA/graph.json","fetch_events":"https://pith.science/api/pith-number/5CGDZ6KO5MUBZGYS2V63SRKLXA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5CGDZ6KO5MUBZGYS2V63SRKLXA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5CGDZ6KO5MUBZGYS2V63SRKLXA/action/storage_attestation","attest_author":"https://pith.science/pith/5CGDZ6KO5MUBZGYS2V63SRKLXA/action/author_attestation","sign_citation":"https://pith.science/pith/5CGDZ6KO5MUBZGYS2V63SRKLXA/action/citation_signature","submit_replication":"https://pith.science/pith/5CGDZ6KO5MUBZGYS2V63SRKLXA/action/replication_record"}},"created_at":"2026-05-18T04:35:55.553213+00:00","updated_at":"2026-05-18T04:35:55.553213+00:00"}