{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:RBEWWV632FLQGYEO4J6ZBHF4TC","short_pith_number":"pith:RBEWWV63","canonical_record":{"source":{"id":"1411.0339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-03T00:22:55Z","cross_cats_sorted":[],"title_canon_sha256":"bae5207f35377c683537c5cd6d308509aec50dc429c9eda7b1774f0d2ac67e07","abstract_canon_sha256":"f3acba796956f5d77fe13e9b344e108ec171019215382bca19923f75a037e5f2"},"schema_version":"1.0"},"canonical_sha256":"88496b57dbd15703608ee27d909cbc98b2ef64bafecda19b134f9533d12efd47","source":{"kind":"arxiv","id":"1411.0339","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0339","created_at":"2026-05-18T02:38:51Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0339v1","created_at":"2026-05-18T02:38:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0339","created_at":"2026-05-18T02:38:51Z"},{"alias_kind":"pith_short_12","alias_value":"RBEWWV632FLQ","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RBEWWV632FLQGYEO","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RBEWWV63","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:RBEWWV632FLQGYEO4J6ZBHF4TC","target":"record","payload":{"canonical_record":{"source":{"id":"1411.0339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-03T00:22:55Z","cross_cats_sorted":[],"title_canon_sha256":"bae5207f35377c683537c5cd6d308509aec50dc429c9eda7b1774f0d2ac67e07","abstract_canon_sha256":"f3acba796956f5d77fe13e9b344e108ec171019215382bca19923f75a037e5f2"},"schema_version":"1.0"},"canonical_sha256":"88496b57dbd15703608ee27d909cbc98b2ef64bafecda19b134f9533d12efd47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:51.972025Z","signature_b64":"uS3A4c+VkL9O99dz1EnBAWdFAXKpNuw7TAyXg/T8kqb+GV/R0b+hsd1Uou87WpTKZaV/GIl6cB7BV5m5m6jsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88496b57dbd15703608ee27d909cbc98b2ef64bafecda19b134f9533d12efd47","last_reissued_at":"2026-05-18T02:38:51.971242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:51.971242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.0339","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":"2026-05-18T02:38:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ivkRKLAT7A8HVqmBilxpHi0pLADFaV2uDWSd0N9o7u0eeLXGFkYQFGy9b/PADYakzmnP3xGN+oPeKf2I3bwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:08:07.721497Z"},"content_sha256":"340d0905a63d4e425401b1d1f366e6c7ab883580e511811167833b3c5e8f42ec","schema_version":"1.0","event_id":"sha256:340d0905a63d4e425401b1d1f366e6c7ab883580e511811167833b3c5e8f42ec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:RBEWWV632FLQGYEO4J6ZBHF4TC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetry in maximal $(s-1,s+1)$ cores","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Rishi Nath","submitted_at":"2014-11-03T00:22:55Z","abstract_excerpt":"We explain a \"curious symmetry\" for maximal $(s-1,s+1)$-core partitions first observed by T. Amdeberhan and E. Leven. Specifically, using the $s$-abacus, we show such partitions have empty $s$-core and that their $s$-quotient is comprised of 2-cores. This imposes strong conditions on the partition structure, and implies both the Amdeberhan-Leven result and additional symmetry. We also find a more general family that exhibits these symmetries."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0339","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":"2026-05-18T02:38:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Cv8TKuIMnPIHel8AK9Js3kZzXZCstp2hD5TEUskJf45A3cZbgEv1pqmh3+IaKnFkU1IMjtt65l1e8qnsYewCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:08:07.721834Z"},"content_sha256":"5820e5dad5d22021a0afd28b99211932a9ce33ec18023533a48566df5b5738bf","schema_version":"1.0","event_id":"sha256:5820e5dad5d22021a0afd28b99211932a9ce33ec18023533a48566df5b5738bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RBEWWV632FLQGYEO4J6ZBHF4TC/bundle.json","state_url":"https://pith.science/pith/RBEWWV632FLQGYEO4J6ZBHF4TC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RBEWWV632FLQGYEO4J6ZBHF4TC/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":"2026-06-25T20:08:07Z","links":{"resolver":"https://pith.science/pith/RBEWWV632FLQGYEO4J6ZBHF4TC","bundle":"https://pith.science/pith/RBEWWV632FLQGYEO4J6ZBHF4TC/bundle.json","state":"https://pith.science/pith/RBEWWV632FLQGYEO4J6ZBHF4TC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RBEWWV632FLQGYEO4J6ZBHF4TC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RBEWWV632FLQGYEO4J6ZBHF4TC","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":"f3acba796956f5d77fe13e9b344e108ec171019215382bca19923f75a037e5f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-03T00:22:55Z","title_canon_sha256":"bae5207f35377c683537c5cd6d308509aec50dc429c9eda7b1774f0d2ac67e07"},"schema_version":"1.0","source":{"id":"1411.0339","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0339","created_at":"2026-05-18T02:38:51Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0339v1","created_at":"2026-05-18T02:38:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0339","created_at":"2026-05-18T02:38:51Z"},{"alias_kind":"pith_short_12","alias_value":"RBEWWV632FLQ","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RBEWWV632FLQGYEO","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RBEWWV63","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:5820e5dad5d22021a0afd28b99211932a9ce33ec18023533a48566df5b5738bf","target":"graph","created_at":"2026-05-18T02:38:51Z","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 explain a \"curious symmetry\" for maximal $(s-1,s+1)$-core partitions first observed by T. Amdeberhan and E. Leven. Specifically, using the $s$-abacus, we show such partitions have empty $s$-core and that their $s$-quotient is comprised of 2-cores. This imposes strong conditions on the partition structure, and implies both the Amdeberhan-Leven result and additional symmetry. We also find a more general family that exhibits these symmetries.","authors_text":"Rishi Nath","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-03T00:22:55Z","title":"Symmetry in maximal $(s-1,s+1)$ cores"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0339","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":"sha256:340d0905a63d4e425401b1d1f366e6c7ab883580e511811167833b3c5e8f42ec","target":"record","created_at":"2026-05-18T02:38:51Z","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":"f3acba796956f5d77fe13e9b344e108ec171019215382bca19923f75a037e5f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-03T00:22:55Z","title_canon_sha256":"bae5207f35377c683537c5cd6d308509aec50dc429c9eda7b1774f0d2ac67e07"},"schema_version":"1.0","source":{"id":"1411.0339","kind":"arxiv","version":1}},"canonical_sha256":"88496b57dbd15703608ee27d909cbc98b2ef64bafecda19b134f9533d12efd47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88496b57dbd15703608ee27d909cbc98b2ef64bafecda19b134f9533d12efd47","first_computed_at":"2026-05-18T02:38:51.971242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:51.971242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uS3A4c+VkL9O99dz1EnBAWdFAXKpNuw7TAyXg/T8kqb+GV/R0b+hsd1Uou87WpTKZaV/GIl6cB7BV5m5m6jsDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:51.972025Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0339","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:340d0905a63d4e425401b1d1f366e6c7ab883580e511811167833b3c5e8f42ec","sha256:5820e5dad5d22021a0afd28b99211932a9ce33ec18023533a48566df5b5738bf"],"state_sha256":"046c60a29461188bf330b90e21b3f7ffbf369dddb427ecbb81487add0a00dee8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G5/cqYoDxPoFtMSlM44xE/Lr9OkVcQBvhoqOT1hi5ojQ+uandZ8Ozpf54qB8QnLsuuiSK9ISOkb1HDwWsf8cCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T20:08:07.726243Z","bundle_sha256":"e120e6e315efb817ff0207b8e546df510bab60e79538f220c9d211a1036ac024"}}