{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EJ5ORWDOC36D7UQCB3ZK6P4AW5","short_pith_number":"pith:EJ5ORWDO","canonical_record":{"source":{"id":"1711.01469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-04T17:56:05Z","cross_cats_sorted":[],"title_canon_sha256":"3031869c1aa3c7be863f85f2428b8b3c7ff63a07b0d48da5548bfeb0833cdb48","abstract_canon_sha256":"736baed9f1198e4a89bb8ad7f21ce1fc40adc31a8a5b116f108b4374649f9c66"},"schema_version":"1.0"},"canonical_sha256":"227ae8d86e16fc3fd2020ef2af3f80b7711cf42d4610e2327bb07b51b1547dc1","source":{"kind":"arxiv","id":"1711.01469","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.01469","created_at":"2026-05-18T00:31:17Z"},{"alias_kind":"arxiv_version","alias_value":"1711.01469v1","created_at":"2026-05-18T00:31:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01469","created_at":"2026-05-18T00:31:17Z"},{"alias_kind":"pith_short_12","alias_value":"EJ5ORWDOC36D","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EJ5ORWDOC36D7UQC","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EJ5ORWDO","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EJ5ORWDOC36D7UQCB3ZK6P4AW5","target":"record","payload":{"canonical_record":{"source":{"id":"1711.01469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-04T17:56:05Z","cross_cats_sorted":[],"title_canon_sha256":"3031869c1aa3c7be863f85f2428b8b3c7ff63a07b0d48da5548bfeb0833cdb48","abstract_canon_sha256":"736baed9f1198e4a89bb8ad7f21ce1fc40adc31a8a5b116f108b4374649f9c66"},"schema_version":"1.0"},"canonical_sha256":"227ae8d86e16fc3fd2020ef2af3f80b7711cf42d4610e2327bb07b51b1547dc1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:17.713258Z","signature_b64":"HAWDXtovZ9y248EGBA4MxYFmurnaOqcNaJcfq3RArR1+tDhbvFD5RxF/BhMp0qItQfkiPh3fvvROiphXSAvoCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"227ae8d86e16fc3fd2020ef2af3f80b7711cf42d4610e2327bb07b51b1547dc1","last_reissued_at":"2026-05-18T00:31:17.712759Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:17.712759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.01469","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":"2026-05-18T00:31:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VOzokno8Jmys7tW142ldzxug0785WPNkXPOA557rIAq1GlAJrf+PL2yru2Usee+f15RP3lJoQHN0WmyoctxMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:47:15.117193Z"},"content_sha256":"dd4d74017911313d8ebe2c0c85fb8e26bd67603399896817752b95e6680beeea","schema_version":"1.0","event_id":"sha256:dd4d74017911313d8ebe2c0c85fb8e26bd67603399896817752b95e6680beeea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EJ5ORWDOC36D7UQCB3ZK6P4AW5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Johnson's bijections and their application to counting simultaneous core partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hayan Nam, Jineon Baek, Myungjun Yu","submitted_at":"2017-11-04T17:56:05Z","abstract_excerpt":"Johnson recently proved Armstrong's conjecture which states that the average size of an $(a,b)$-core partition is $(a+b+1)(a-1)(b-1)/24$. He used various coordinate changes and one-to-one correspondences that are useful for counting problems about simultaneous core partitions. We give an expression for the number of $(b_1,b_2,\\cdots, b_n)$-core partitions where $\\{b_1,b_2,\\cdots,b_n\\}$ contains at least one pair of relatively prime numbers. We also evaluate the largest size of a self-conjugate $(s,s+1,s+2)$-core partition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01469","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":"2026-05-18T00:31:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PqgUd6wuWLUXEo+aCOc/ZlCcxlqOHvN6fzL7hBljf7GTkC4lrIvaMFxJ+JiNR2bPN+ARzkG4cNveogc+OTIpAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:47:15.117821Z"},"content_sha256":"66c20811898690654dd7df80eb5b95a42722c755fc4f36674964dd6a32284433","schema_version":"1.0","event_id":"sha256:66c20811898690654dd7df80eb5b95a42722c755fc4f36674964dd6a32284433"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EJ5ORWDOC36D7UQCB3ZK6P4AW5/bundle.json","state_url":"https://pith.science/pith/EJ5ORWDOC36D7UQCB3ZK6P4AW5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EJ5ORWDOC36D7UQCB3ZK6P4AW5/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":"2026-06-09T13:47:15Z","links":{"resolver":"https://pith.science/pith/EJ5ORWDOC36D7UQCB3ZK6P4AW5","bundle":"https://pith.science/pith/EJ5ORWDOC36D7UQCB3ZK6P4AW5/bundle.json","state":"https://pith.science/pith/EJ5ORWDOC36D7UQCB3ZK6P4AW5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EJ5ORWDOC36D7UQCB3ZK6P4AW5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EJ5ORWDOC36D7UQCB3ZK6P4AW5","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":"736baed9f1198e4a89bb8ad7f21ce1fc40adc31a8a5b116f108b4374649f9c66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-04T17:56:05Z","title_canon_sha256":"3031869c1aa3c7be863f85f2428b8b3c7ff63a07b0d48da5548bfeb0833cdb48"},"schema_version":"1.0","source":{"id":"1711.01469","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.01469","created_at":"2026-05-18T00:31:17Z"},{"alias_kind":"arxiv_version","alias_value":"1711.01469v1","created_at":"2026-05-18T00:31:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01469","created_at":"2026-05-18T00:31:17Z"},{"alias_kind":"pith_short_12","alias_value":"EJ5ORWDOC36D","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EJ5ORWDOC36D7UQC","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EJ5ORWDO","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:66c20811898690654dd7df80eb5b95a42722c755fc4f36674964dd6a32284433","target":"graph","created_at":"2026-05-18T00:31:17Z","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":"Johnson recently proved Armstrong's conjecture which states that the average size of an $(a,b)$-core partition is $(a+b+1)(a-1)(b-1)/24$. He used various coordinate changes and one-to-one correspondences that are useful for counting problems about simultaneous core partitions. We give an expression for the number of $(b_1,b_2,\\cdots, b_n)$-core partitions where $\\{b_1,b_2,\\cdots,b_n\\}$ contains at least one pair of relatively prime numbers. We also evaluate the largest size of a self-conjugate $(s,s+1,s+2)$-core partition.","authors_text":"Hayan Nam, Jineon Baek, Myungjun Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-04T17:56:05Z","title":"Johnson's bijections and their application to counting simultaneous core partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01469","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:dd4d74017911313d8ebe2c0c85fb8e26bd67603399896817752b95e6680beeea","target":"record","created_at":"2026-05-18T00:31:17Z","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":"736baed9f1198e4a89bb8ad7f21ce1fc40adc31a8a5b116f108b4374649f9c66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-04T17:56:05Z","title_canon_sha256":"3031869c1aa3c7be863f85f2428b8b3c7ff63a07b0d48da5548bfeb0833cdb48"},"schema_version":"1.0","source":{"id":"1711.01469","kind":"arxiv","version":1}},"canonical_sha256":"227ae8d86e16fc3fd2020ef2af3f80b7711cf42d4610e2327bb07b51b1547dc1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"227ae8d86e16fc3fd2020ef2af3f80b7711cf42d4610e2327bb07b51b1547dc1","first_computed_at":"2026-05-18T00:31:17.712759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:17.712759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HAWDXtovZ9y248EGBA4MxYFmurnaOqcNaJcfq3RArR1+tDhbvFD5RxF/BhMp0qItQfkiPh3fvvROiphXSAvoCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:17.713258Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.01469","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd4d74017911313d8ebe2c0c85fb8e26bd67603399896817752b95e6680beeea","sha256:66c20811898690654dd7df80eb5b95a42722c755fc4f36674964dd6a32284433"],"state_sha256":"b6a59ec1fc3d104390877871542771416159b02840a77ab1aa2b9a7dcd205861"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LMT4PCtCdBdPoe+G8tYITVPcnce5oBdp4yzOzGckwfcvy2rkYMT+btJqtMMQAUvhDCXbF2ZF+yViUCCfqeQ4Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T13:47:15.120345Z","bundle_sha256":"ead9f734ad283f22ab531672d7b9e35daa714f882e3f7b49ba9589ec923a2975"}}