{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:5CGDZ6KO5MUBZGYS2V63SRKLXA","short_pith_number":"pith:5CGDZ6KO","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"},"canonical_sha256":"e88c3cf94eeb281c9b12d57db9454bb8265ca1a9ad163885c51dd208d59c710c","source":{"kind":"arxiv","id":"math/0312215","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0312215","created_at":"2026-05-18T04:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"math/0312215v1","created_at":"2026-05-18T04:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0312215","created_at":"2026-05-18T04:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"5CGDZ6KO5MUB","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"5CGDZ6KO5MUBZGYS","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"5CGDZ6KO","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:5CGDZ6KO5MUBZGYS2V63SRKLXA","target":"record","payload":{"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"},"canonical_sha256":"e88c3cf94eeb281c9b12d57db9454bb8265ca1a9ad163885c51dd208d59c710c","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"},"source_kind":"arxiv","source_id":"math/0312215","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":"2026-05-18T04:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MT9NoC6hxQXW3jaQjrPir2WNgsLgXfY4cs7QVCDNlNtL7Xd+jsI6l2E/Pn1Ap1AOPHSVgc1SCYpzQuXT5kOmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:15:01.678180Z"},"content_sha256":"4b9411ae7fe96e4e5f51c04dccdac2bac54622bf78688c63696948cc2d0c9884","schema_version":"1.0","event_id":"sha256:4b9411ae7fe96e4e5f51c04dccdac2bac54622bf78688c63696948cc2d0c9884"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:5CGDZ6KO5MUBZGYS2V63SRKLXA","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jTAgE4yphNN14+mlywSVdNUUPXNZ18oktk3vGUiEsrfL88minr96Y8QpKU9NB9BXeWvbpbJ2sdLmda+oljdsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:15:01.678893Z"},"content_sha256":"82c0a70a61048e930a5fb2d55c5e5fbc1872115bf2d707da6fd46107b4bd3810","schema_version":"1.0","event_id":"sha256:82c0a70a61048e930a5fb2d55c5e5fbc1872115bf2d707da6fd46107b4bd3810"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5CGDZ6KO5MUBZGYS2V63SRKLXA/bundle.json","state_url":"https://pith.science/pith/5CGDZ6KO5MUBZGYS2V63SRKLXA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5CGDZ6KO5MUBZGYS2V63SRKLXA/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":"2026-06-09T19:15:01Z","links":{"resolver":"https://pith.science/pith/5CGDZ6KO5MUBZGYS2V63SRKLXA","bundle":"https://pith.science/pith/5CGDZ6KO5MUBZGYS2V63SRKLXA/bundle.json","state":"https://pith.science/pith/5CGDZ6KO5MUBZGYS2V63SRKLXA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5CGDZ6KO5MUBZGYS2V63SRKLXA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:5CGDZ6KO5MUBZGYS2V63SRKLXA","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":"bbb06b43dbb9418aca473678914bba55edbf616b99d20dbae3d0546bbbb14182","cross_cats_sorted":["math.ST","stat.TH"],"license":"","primary_cat":"math.PR","submitted_at":"2003-12-10T17:05:12Z","title_canon_sha256":"a95bb4b0a688b2bdd8d255af693f527c89992206cce96e754a7aed13b8bb5278"},"schema_version":"1.0","source":{"id":"math/0312215","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0312215","created_at":"2026-05-18T04:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"math/0312215v1","created_at":"2026-05-18T04:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0312215","created_at":"2026-05-18T04:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"5CGDZ6KO5MUB","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"5CGDZ6KO5MUBZGYS","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"5CGDZ6KO","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:82c0a70a61048e930a5fb2d55c5e5fbc1872115bf2d707da6fd46107b4bd3810","target":"graph","created_at":"2026-05-18T04:35:55Z","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":"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","authors_text":"Christopher Hammond, Steven J. Miller","cross_cats":["math.ST","stat.TH"],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2003-12-10T17:05:12Z","title":"Eigenvalue Spacing Distribution for the Ensemble of Real Symmetric Toeplitz Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0312215","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":"sha256:4b9411ae7fe96e4e5f51c04dccdac2bac54622bf78688c63696948cc2d0c9884","target":"record","created_at":"2026-05-18T04:35:55Z","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":"bbb06b43dbb9418aca473678914bba55edbf616b99d20dbae3d0546bbbb14182","cross_cats_sorted":["math.ST","stat.TH"],"license":"","primary_cat":"math.PR","submitted_at":"2003-12-10T17:05:12Z","title_canon_sha256":"a95bb4b0a688b2bdd8d255af693f527c89992206cce96e754a7aed13b8bb5278"},"schema_version":"1.0","source":{"id":"math/0312215","kind":"arxiv","version":1}},"canonical_sha256":"e88c3cf94eeb281c9b12d57db9454bb8265ca1a9ad163885c51dd208d59c710c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e88c3cf94eeb281c9b12d57db9454bb8265ca1a9ad163885c51dd208d59c710c","first_computed_at":"2026-05-18T04:35:55.553149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:55.553149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5VNMi+yxuiHWy5tXEQP2tI25t8oiAkO+KEtYshmqDw7vPnt3ODfQfutHwi5MZCWZRk5mCANYPqmPE2o2bciDBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:55.553644Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0312215","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b9411ae7fe96e4e5f51c04dccdac2bac54622bf78688c63696948cc2d0c9884","sha256:82c0a70a61048e930a5fb2d55c5e5fbc1872115bf2d707da6fd46107b4bd3810"],"state_sha256":"09de22007dbe56f98d6ce3c5a8ee64dd08f8dbacab94267304fa8f6803127a99"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r1HZGlv3BbjWK9e0IIth8MTw1d1GwZgsHa7ze+iulOOgSthdcSaXwkbZ05eOdWc2ksE5sjyPFYcOSLHfA0qbDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:15:01.683516Z","bundle_sha256":"fc830a827ffe09548f89296800addfb1bc06dad0735a80def73ba2fd8d974acd"}}