{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:VRKPB2MOBDLJ5SXIJ3MUILL6YK","short_pith_number":"pith:VRKPB2MO","canonical_record":{"source":{"id":"nucl-th/0104033","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"nucl-th","submitted_at":"2001-04-10T10:14:27Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"ac47be268b2a0a8f092e203f6a4c6a30f07cba59c4f5e5283ea36ca17ad970ea","abstract_canon_sha256":"1faf60fec92b03a7a70865a74358b0b4aa0d63992ee7e70d8ac247cb67b6e61f"},"schema_version":"1.0"},"canonical_sha256":"ac54f0e98e08d69ecae84ed9442d7ec29a4ad5e1579bda75dcd8b8e0d17e851b","source":{"kind":"arxiv","id":"nucl-th/0104033","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nucl-th/0104033","created_at":"2026-05-18T03:42:21Z"},{"alias_kind":"arxiv_version","alias_value":"nucl-th/0104033v2","created_at":"2026-05-18T03:42:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nucl-th/0104033","created_at":"2026-05-18T03:42:21Z"},{"alias_kind":"pith_short_12","alias_value":"VRKPB2MOBDLJ","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"VRKPB2MOBDLJ5SXI","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"VRKPB2MO","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:VRKPB2MOBDLJ5SXIJ3MUILL6YK","target":"record","payload":{"canonical_record":{"source":{"id":"nucl-th/0104033","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"nucl-th","submitted_at":"2001-04-10T10:14:27Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"ac47be268b2a0a8f092e203f6a4c6a30f07cba59c4f5e5283ea36ca17ad970ea","abstract_canon_sha256":"1faf60fec92b03a7a70865a74358b0b4aa0d63992ee7e70d8ac247cb67b6e61f"},"schema_version":"1.0"},"canonical_sha256":"ac54f0e98e08d69ecae84ed9442d7ec29a4ad5e1579bda75dcd8b8e0d17e851b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:21.759864Z","signature_b64":"CkoFYi3JtJS2tHigs4/LvZ7CTDgrNXIk+RHMU+xdelOExX441er/r4+Bqh9wNR6hohBp3PejLFzNGl6se2AtBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac54f0e98e08d69ecae84ed9442d7ec29a4ad5e1579bda75dcd8b8e0d17e851b","last_reissued_at":"2026-05-18T03:42:21.759082Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:21.759082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"nucl-th/0104033","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:42:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7kyqbuR0bwUbaOEKAftjl4p0AA+JOFKAd/D+FRbTicTsKZn3rS1eOd4vsn+dU59a+bj78UIqJbV7eT2LV6xRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T13:13:38.158584Z"},"content_sha256":"563fab6a3c4361d20e39c28485cf2dd343cea2465e012687fd7eb0f4b1bee3bc","schema_version":"1.0","event_id":"sha256:563fab6a3c4361d20e39c28485cf2dd343cea2465e012687fd7eb0f4b1bee3bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:VRKPB2MOBDLJ5SXIJ3MUILL6YK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit distributions of many-particle spectra","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"nucl-th","authors_text":"Piotr Sniady","submitted_at":"2001-04-10T10:14:27Z","abstract_excerpt":"We find the limit distributions for a spectrum of a system of n particles governed by a k-body interaction. The hamiltonian of this system is modelled by a Gaussian random matrix.\n  We show that the limit distribution is a q-deformed Gaussian distribution with the deformation parameter q depending on the value of the fraction \\frac{k}{\\sqrt{n}}. The family of q-deformed Gaussian distributions include the Gaussian distribution and the semicircular law; therefore our result is a generalization of the results of Wigner, Mon and French."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nucl-th/0104033","kind":"arxiv","version":2},"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":"2026-05-18T03:42:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RCWNu15FGc+GGj0X3l4JRcyQ+LaPiFDf3gkla2kB8MUj4o3HRULU+hsjcekMicOhD80kbmuIwMiA0T4ktsc2Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T13:13:38.158958Z"},"content_sha256":"c2f8e96ad6774132d2bf6c1bef2a6b2305f8892550804fb148e02a8cf746a96e","schema_version":"1.0","event_id":"sha256:c2f8e96ad6774132d2bf6c1bef2a6b2305f8892550804fb148e02a8cf746a96e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VRKPB2MOBDLJ5SXIJ3MUILL6YK/bundle.json","state_url":"https://pith.science/pith/VRKPB2MOBDLJ5SXIJ3MUILL6YK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VRKPB2MOBDLJ5SXIJ3MUILL6YK/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":"2026-05-20T13:13:38Z","links":{"resolver":"https://pith.science/pith/VRKPB2MOBDLJ5SXIJ3MUILL6YK","bundle":"https://pith.science/pith/VRKPB2MOBDLJ5SXIJ3MUILL6YK/bundle.json","state":"https://pith.science/pith/VRKPB2MOBDLJ5SXIJ3MUILL6YK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VRKPB2MOBDLJ5SXIJ3MUILL6YK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:VRKPB2MOBDLJ5SXIJ3MUILL6YK","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":"1faf60fec92b03a7a70865a74358b0b4aa0d63992ee7e70d8ac247cb67b6e61f","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"nucl-th","submitted_at":"2001-04-10T10:14:27Z","title_canon_sha256":"ac47be268b2a0a8f092e203f6a4c6a30f07cba59c4f5e5283ea36ca17ad970ea"},"schema_version":"1.0","source":{"id":"nucl-th/0104033","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nucl-th/0104033","created_at":"2026-05-18T03:42:21Z"},{"alias_kind":"arxiv_version","alias_value":"nucl-th/0104033v2","created_at":"2026-05-18T03:42:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nucl-th/0104033","created_at":"2026-05-18T03:42:21Z"},{"alias_kind":"pith_short_12","alias_value":"VRKPB2MOBDLJ","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"VRKPB2MOBDLJ5SXI","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"VRKPB2MO","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:c2f8e96ad6774132d2bf6c1bef2a6b2305f8892550804fb148e02a8cf746a96e","target":"graph","created_at":"2026-05-18T03:42:21Z","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 find the limit distributions for a spectrum of a system of n particles governed by a k-body interaction. The hamiltonian of this system is modelled by a Gaussian random matrix.\n  We show that the limit distribution is a q-deformed Gaussian distribution with the deformation parameter q depending on the value of the fraction \\frac{k}{\\sqrt{n}}. The family of q-deformed Gaussian distributions include the Gaussian distribution and the semicircular law; therefore our result is a generalization of the results of Wigner, Mon and French.","authors_text":"Piotr Sniady","cross_cats":["math.PR"],"headline":"","license":"","primary_cat":"nucl-th","submitted_at":"2001-04-10T10:14:27Z","title":"Limit distributions of many-particle spectra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nucl-th/0104033","kind":"arxiv","version":2},"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":"sha256:563fab6a3c4361d20e39c28485cf2dd343cea2465e012687fd7eb0f4b1bee3bc","target":"record","created_at":"2026-05-18T03:42:21Z","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":"1faf60fec92b03a7a70865a74358b0b4aa0d63992ee7e70d8ac247cb67b6e61f","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"nucl-th","submitted_at":"2001-04-10T10:14:27Z","title_canon_sha256":"ac47be268b2a0a8f092e203f6a4c6a30f07cba59c4f5e5283ea36ca17ad970ea"},"schema_version":"1.0","source":{"id":"nucl-th/0104033","kind":"arxiv","version":2}},"canonical_sha256":"ac54f0e98e08d69ecae84ed9442d7ec29a4ad5e1579bda75dcd8b8e0d17e851b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac54f0e98e08d69ecae84ed9442d7ec29a4ad5e1579bda75dcd8b8e0d17e851b","first_computed_at":"2026-05-18T03:42:21.759082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:21.759082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CkoFYi3JtJS2tHigs4/LvZ7CTDgrNXIk+RHMU+xdelOExX441er/r4+Bqh9wNR6hohBp3PejLFzNGl6se2AtBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:21.759864Z","signed_message":"canonical_sha256_bytes"},"source_id":"nucl-th/0104033","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:563fab6a3c4361d20e39c28485cf2dd343cea2465e012687fd7eb0f4b1bee3bc","sha256:c2f8e96ad6774132d2bf6c1bef2a6b2305f8892550804fb148e02a8cf746a96e"],"state_sha256":"c54c03a0af8c518e5ee7ba187aeb03bf2792a42d18c7ac2e4cdc7513ae8243b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w9QybAx87uEPilP55Dhrbm/0cXD4WYHiJ2MimR1yapSkUnyJjItRQzqRK/iN9OnSjVVppfJHSSz9HZe+C1/eDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T13:13:38.160966Z","bundle_sha256":"1ea72fdb81210ca64f0bfbc791513639c7cc7f077420e0cda950e7fcd093f3a8"}}