{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4NYBSMHQTCQCTX2XXISLZYAB2P","short_pith_number":"pith:4NYBSMHQ","canonical_record":{"source":{"id":"1608.02262","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-07T20:15:46Z","cross_cats_sorted":[],"title_canon_sha256":"9819a13eec4b0e83d5aa3af9000c93ae6f5f3c6e0f73e1919b443f4fda59559f","abstract_canon_sha256":"55a85bb691775cda93b3ea7340219a23b2b24a80b226bb319f12af47e32435ce"},"schema_version":"1.0"},"canonical_sha256":"e3701930f098a029df57ba24bce001d3d51f0d1be8fbe5076599b6f1441c09de","source":{"kind":"arxiv","id":"1608.02262","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02262","created_at":"2026-05-18T00:57:04Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02262v2","created_at":"2026-05-18T00:57:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02262","created_at":"2026-05-18T00:57:04Z"},{"alias_kind":"pith_short_12","alias_value":"4NYBSMHQTCQC","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4NYBSMHQTCQCTX2X","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4NYBSMHQ","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4NYBSMHQTCQCTX2XXISLZYAB2P","target":"record","payload":{"canonical_record":{"source":{"id":"1608.02262","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-07T20:15:46Z","cross_cats_sorted":[],"title_canon_sha256":"9819a13eec4b0e83d5aa3af9000c93ae6f5f3c6e0f73e1919b443f4fda59559f","abstract_canon_sha256":"55a85bb691775cda93b3ea7340219a23b2b24a80b226bb319f12af47e32435ce"},"schema_version":"1.0"},"canonical_sha256":"e3701930f098a029df57ba24bce001d3d51f0d1be8fbe5076599b6f1441c09de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:04.154647Z","signature_b64":"RjwaBVIq9U+GA1TdmxGq+i4Z9ui5wyImJmVtokep9voAdAQyJ9h58slcCAbE6o8JxtxC1qeedHGSrVTmSc/eBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3701930f098a029df57ba24bce001d3d51f0d1be8fbe5076599b6f1441c09de","last_reissued_at":"2026-05-18T00:57:04.154123Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:04.154123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.02262","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":"2026-05-18T00:57:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PQ4UeukbD0A2UIQpMQe+IDgauM8QcqPnyzlWvaMOH/594o//pLq4PfiWDcFQ+FJR5VWlxZ4UWqB6T0DGC8RbBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T04:17:16.239401Z"},"content_sha256":"340876b926ca00820c1f1a1f59080edacf09e243bcc1f483cdec43568ea701fa","schema_version":"1.0","event_id":"sha256:340876b926ca00820c1f1a1f59080edacf09e243bcc1f483cdec43568ea701fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4NYBSMHQTCQCTX2XXISLZYAB2P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit expressions for the moments of the size of an (s,s+1)-core partition with distinct parts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anthony Zaleski","submitted_at":"2016-08-07T20:15:46Z","abstract_excerpt":"For fixed s, the size of an (s, s+1)-core partition with distinct parts can be seen as a random variable X_s. Using computer-assisted methods, we derive formulas for the expectation, variance, and higher moments of X_s. Our results give good evidence that X_s is asymptotically normal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02262","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":"2026-05-18T00:57:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hHDEN5KWFVV1WKORODGs9pvyz3NOcUzRJIMkk0nnYogU2nCJ99sYoiGgGMjzVLrfMjXXC+ssFH+rezN41GykBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T04:17:16.239997Z"},"content_sha256":"b42a661070c3f735f26db104296a25e9279c0c1ea4613d3c86cdb9a77f91aa12","schema_version":"1.0","event_id":"sha256:b42a661070c3f735f26db104296a25e9279c0c1ea4613d3c86cdb9a77f91aa12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4NYBSMHQTCQCTX2XXISLZYAB2P/bundle.json","state_url":"https://pith.science/pith/4NYBSMHQTCQCTX2XXISLZYAB2P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4NYBSMHQTCQCTX2XXISLZYAB2P/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":"2026-06-08T04:17:16Z","links":{"resolver":"https://pith.science/pith/4NYBSMHQTCQCTX2XXISLZYAB2P","bundle":"https://pith.science/pith/4NYBSMHQTCQCTX2XXISLZYAB2P/bundle.json","state":"https://pith.science/pith/4NYBSMHQTCQCTX2XXISLZYAB2P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4NYBSMHQTCQCTX2XXISLZYAB2P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4NYBSMHQTCQCTX2XXISLZYAB2P","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":"55a85bb691775cda93b3ea7340219a23b2b24a80b226bb319f12af47e32435ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-07T20:15:46Z","title_canon_sha256":"9819a13eec4b0e83d5aa3af9000c93ae6f5f3c6e0f73e1919b443f4fda59559f"},"schema_version":"1.0","source":{"id":"1608.02262","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02262","created_at":"2026-05-18T00:57:04Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02262v2","created_at":"2026-05-18T00:57:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02262","created_at":"2026-05-18T00:57:04Z"},{"alias_kind":"pith_short_12","alias_value":"4NYBSMHQTCQC","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4NYBSMHQTCQCTX2X","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4NYBSMHQ","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:b42a661070c3f735f26db104296a25e9279c0c1ea4613d3c86cdb9a77f91aa12","target":"graph","created_at":"2026-05-18T00:57:04Z","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":"For fixed s, the size of an (s, s+1)-core partition with distinct parts can be seen as a random variable X_s. Using computer-assisted methods, we derive formulas for the expectation, variance, and higher moments of X_s. Our results give good evidence that X_s is asymptotically normal.","authors_text":"Anthony Zaleski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-07T20:15:46Z","title":"Explicit expressions for the moments of the size of an (s,s+1)-core partition with distinct parts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02262","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":"sha256:340876b926ca00820c1f1a1f59080edacf09e243bcc1f483cdec43568ea701fa","target":"record","created_at":"2026-05-18T00:57:04Z","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":"55a85bb691775cda93b3ea7340219a23b2b24a80b226bb319f12af47e32435ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-07T20:15:46Z","title_canon_sha256":"9819a13eec4b0e83d5aa3af9000c93ae6f5f3c6e0f73e1919b443f4fda59559f"},"schema_version":"1.0","source":{"id":"1608.02262","kind":"arxiv","version":2}},"canonical_sha256":"e3701930f098a029df57ba24bce001d3d51f0d1be8fbe5076599b6f1441c09de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3701930f098a029df57ba24bce001d3d51f0d1be8fbe5076599b6f1441c09de","first_computed_at":"2026-05-18T00:57:04.154123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:04.154123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RjwaBVIq9U+GA1TdmxGq+i4Z9ui5wyImJmVtokep9voAdAQyJ9h58slcCAbE6o8JxtxC1qeedHGSrVTmSc/eBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:04.154647Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.02262","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:340876b926ca00820c1f1a1f59080edacf09e243bcc1f483cdec43568ea701fa","sha256:b42a661070c3f735f26db104296a25e9279c0c1ea4613d3c86cdb9a77f91aa12"],"state_sha256":"87e05578ea9c028680d7369635ae7643eb408821d1d28fec9b68bfc8794c714d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8IO4cb3fUjUhOueyBYUX/rVvv6CbMaTDhjB6mAo/R0K7bv9eLQjqYg/NBTU2Rp6Pxxo+PIGpYY94w5Kt+Xy8Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T04:17:16.244592Z","bundle_sha256":"88812f2d07fe9ca0f61423d27294fed2fed602b59734ef4ac05468adbd6b3048"}}