{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NOJEDROHRXY7D5JQKH2X733YTF","short_pith_number":"pith:NOJEDROH","canonical_record":{"source":{"id":"1809.00412","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-02T23:55:59Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"8e04b468a3e8a16207e0cb4b0232656ced24c61ebf801b7b49e4d44feb1d76bc","abstract_canon_sha256":"0fbdd10b5aad418a8a8ec6e3a26da12d4b74e3b4d281e20a7c0920cfa496f041"},"schema_version":"1.0"},"canonical_sha256":"6b9241c5c78df1f1f53051f57fef789954b1969e04dc23b16fa1e7c02adb290d","source":{"kind":"arxiv","id":"1809.00412","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00412","created_at":"2026-05-18T00:06:35Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00412v1","created_at":"2026-05-18T00:06:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00412","created_at":"2026-05-18T00:06:35Z"},{"alias_kind":"pith_short_12","alias_value":"NOJEDROHRXY7","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NOJEDROHRXY7D5JQ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NOJEDROH","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NOJEDROHRXY7D5JQKH2X733YTF","target":"record","payload":{"canonical_record":{"source":{"id":"1809.00412","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-02T23:55:59Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"8e04b468a3e8a16207e0cb4b0232656ced24c61ebf801b7b49e4d44feb1d76bc","abstract_canon_sha256":"0fbdd10b5aad418a8a8ec6e3a26da12d4b74e3b4d281e20a7c0920cfa496f041"},"schema_version":"1.0"},"canonical_sha256":"6b9241c5c78df1f1f53051f57fef789954b1969e04dc23b16fa1e7c02adb290d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:35.285725Z","signature_b64":"ylZXCAKxuxjKEMt+Z7IEd4NAMT6F8ITJS6TEM72KxQXn/Us5Ek1ezNmRW+3taRNvIhb3uHwPZSlY9Er7aDkzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b9241c5c78df1f1f53051f57fef789954b1969e04dc23b16fa1e7c02adb290d","last_reissued_at":"2026-05-18T00:06:35.285179Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:35.285179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.00412","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":"2026-05-18T00:06:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fQwGptDQ39sUMP2SxkxnSWpfty7cPL7vrFxbd3qri9MzgAvj/V29JnfmUNIDKtyd2oeeV7mYuyqKN7VvCXrPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:07:10.820969Z"},"content_sha256":"3e341034001c490dbf3b723182e231fde8080c1a1425a41a8ec73a599e12dce0","schema_version":"1.0","event_id":"sha256:3e341034001c490dbf3b723182e231fde8080c1a1425a41a8ec73a599e12dce0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NOJEDROHRXY7D5JQKH2X733YTF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The asymptotic normality of $(s,s+1)$-cores with distinct parts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Emily Sergel, G\\'abor Tusn\\'ady, J\\'anos Koml\\'os","submitted_at":"2018-09-02T23:55:59Z","abstract_excerpt":"Simultaneous core partitions are important objects in algebraic combinatorics. Recently there has been interest in studying the distribution of sizes among all $(s,t)$-cores for coprime $s$ and $t$. Zaleski (2017) gave strong evidence that when we restrict our attention to $(s,s+1)$-cores with distinct parts, the resulting distribution is approximately normal. We prove his conjecture by applying the Combinatorial Central Limit Theorem and mixing the resulting normal distributions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00412","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":"2026-05-18T00:06:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KNZ4GaXQbqUmEP5DT13TJ9z7UtR+xo7CSggyoMOL5c5PBLSmTqKX1KpXnPrMgK7g+8fEAK/gsSRYSkjetMbzDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:07:10.821641Z"},"content_sha256":"d566f9f9313a39ccb7113876967b9ba13f16a016013d2ac3dd304642e81fb83c","schema_version":"1.0","event_id":"sha256:d566f9f9313a39ccb7113876967b9ba13f16a016013d2ac3dd304642e81fb83c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NOJEDROHRXY7D5JQKH2X733YTF/bundle.json","state_url":"https://pith.science/pith/NOJEDROHRXY7D5JQKH2X733YTF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NOJEDROHRXY7D5JQKH2X733YTF/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":"2026-06-11T15:07:10Z","links":{"resolver":"https://pith.science/pith/NOJEDROHRXY7D5JQKH2X733YTF","bundle":"https://pith.science/pith/NOJEDROHRXY7D5JQKH2X733YTF/bundle.json","state":"https://pith.science/pith/NOJEDROHRXY7D5JQKH2X733YTF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NOJEDROHRXY7D5JQKH2X733YTF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NOJEDROHRXY7D5JQKH2X733YTF","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":"0fbdd10b5aad418a8a8ec6e3a26da12d4b74e3b4d281e20a7c0920cfa496f041","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-02T23:55:59Z","title_canon_sha256":"8e04b468a3e8a16207e0cb4b0232656ced24c61ebf801b7b49e4d44feb1d76bc"},"schema_version":"1.0","source":{"id":"1809.00412","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00412","created_at":"2026-05-18T00:06:35Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00412v1","created_at":"2026-05-18T00:06:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00412","created_at":"2026-05-18T00:06:35Z"},{"alias_kind":"pith_short_12","alias_value":"NOJEDROHRXY7","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NOJEDROHRXY7D5JQ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NOJEDROH","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:d566f9f9313a39ccb7113876967b9ba13f16a016013d2ac3dd304642e81fb83c","target":"graph","created_at":"2026-05-18T00:06:35Z","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":"Simultaneous core partitions are important objects in algebraic combinatorics. Recently there has been interest in studying the distribution of sizes among all $(s,t)$-cores for coprime $s$ and $t$. Zaleski (2017) gave strong evidence that when we restrict our attention to $(s,s+1)$-cores with distinct parts, the resulting distribution is approximately normal. We prove his conjecture by applying the Combinatorial Central Limit Theorem and mixing the resulting normal distributions.","authors_text":"Emily Sergel, G\\'abor Tusn\\'ady, J\\'anos Koml\\'os","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-02T23:55:59Z","title":"The asymptotic normality of $(s,s+1)$-cores with distinct parts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00412","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":"sha256:3e341034001c490dbf3b723182e231fde8080c1a1425a41a8ec73a599e12dce0","target":"record","created_at":"2026-05-18T00:06:35Z","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":"0fbdd10b5aad418a8a8ec6e3a26da12d4b74e3b4d281e20a7c0920cfa496f041","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-02T23:55:59Z","title_canon_sha256":"8e04b468a3e8a16207e0cb4b0232656ced24c61ebf801b7b49e4d44feb1d76bc"},"schema_version":"1.0","source":{"id":"1809.00412","kind":"arxiv","version":1}},"canonical_sha256":"6b9241c5c78df1f1f53051f57fef789954b1969e04dc23b16fa1e7c02adb290d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b9241c5c78df1f1f53051f57fef789954b1969e04dc23b16fa1e7c02adb290d","first_computed_at":"2026-05-18T00:06:35.285179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:35.285179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ylZXCAKxuxjKEMt+Z7IEd4NAMT6F8ITJS6TEM72KxQXn/Us5Ek1ezNmRW+3taRNvIhb3uHwPZSlY9Er7aDkzDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:35.285725Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.00412","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e341034001c490dbf3b723182e231fde8080c1a1425a41a8ec73a599e12dce0","sha256:d566f9f9313a39ccb7113876967b9ba13f16a016013d2ac3dd304642e81fb83c"],"state_sha256":"5bb4764e7c71d04299ac7e98d2f6ddb5b77b211a9875880b5db785d4e7ecd496"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hZos4bDbk/6EHfx1CHug0ZrKSgTS621RZuz/Go40e4tT6lKrKkVgvbI02ivdhN7uTtiVSDV+ysoFE3frnlKNBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T15:07:10.825769Z","bundle_sha256":"20003b2679f841e7f1c54003db6f78c40357915fc4bf7dc64e25f9c8aff5526a"}}