{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OUHO27CGGCV2FBGPRAKTAQBSPW","short_pith_number":"pith:OUHO27CG","canonical_record":{"source":{"id":"1308.0572","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-02T18:26:31Z","cross_cats_sorted":[],"title_canon_sha256":"e7c5ae8f876c71d8ae1e75c99e81b2a655831892b748b6185834f8058a2f36e9","abstract_canon_sha256":"5601971f7e9f3dab2514239f9274403fa2ab22785cfed8862bf372f2385abb2d"},"schema_version":"1.0"},"canonical_sha256":"750eed7c4630aba284cf88153040327da8b4d27e66689b841b02934e7d4656f0","source":{"kind":"arxiv","id":"1308.0572","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0572","created_at":"2026-05-18T02:53:41Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0572v2","created_at":"2026-05-18T02:53:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0572","created_at":"2026-05-18T02:53:41Z"},{"alias_kind":"pith_short_12","alias_value":"OUHO27CGGCV2","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OUHO27CGGCV2FBGP","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OUHO27CG","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OUHO27CGGCV2FBGPRAKTAQBSPW","target":"record","payload":{"canonical_record":{"source":{"id":"1308.0572","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-02T18:26:31Z","cross_cats_sorted":[],"title_canon_sha256":"e7c5ae8f876c71d8ae1e75c99e81b2a655831892b748b6185834f8058a2f36e9","abstract_canon_sha256":"5601971f7e9f3dab2514239f9274403fa2ab22785cfed8862bf372f2385abb2d"},"schema_version":"1.0"},"canonical_sha256":"750eed7c4630aba284cf88153040327da8b4d27e66689b841b02934e7d4656f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:41.265237Z","signature_b64":"tlWfLAfka+0HJURb4emt6TsbCAZwLD96CVkK0kTEyky4DXkGsOLFEfFCZcRkL1xcm+ikeagoroMbdlXwADMKAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"750eed7c4630aba284cf88153040327da8b4d27e66689b841b02934e7d4656f0","last_reissued_at":"2026-05-18T02:53:41.264716Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:41.264716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.0572","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":"2026-05-18T02:53:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZZT8RuOzCbXksje1llJdERNKCqMNlLYVCr49nuasjwmnMx4Nlo401kBhvOkL4pfdFFfxgHUdXQ8O7IaPNt4DCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T22:09:37.873697Z"},"content_sha256":"b4e74644387b27f197ae41d2906a8b2d1b1347e0beba8afe457f41345952c223","schema_version":"1.0","event_id":"sha256:b4e74644387b27f197ae41d2906a8b2d1b1347e0beba8afe457f41345952c223"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OUHO27CGGCV2FBGPRAKTAQBSPW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Results and conjectures on simultaneous core partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brant C. Jones, Christopher R. H. Hanusa, Drew Armstrong","submitted_at":"2013-08-02T18:26:31Z","abstract_excerpt":"An n-core partition is an integer partition whose Young diagram contains no hook lengths equal to n. We consider partitions that are simultaneously a-core and b-core for two relatively prime integers a and b. These are related to abacus diagrams and the combinatorics of the affine symmetric group (type A). We observe that self-conjugate simultaneous core partitions correspond to the combinatorics of type C, and use abacus diagrams to unite the discussion of these two sets of objects.\n  In particular, we prove that (2n)- and (2mn+1)-core partitions correspond naturally to dominant alcoves in th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0572","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":"2026-05-18T02:53:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nzcF17Q23O++B/4IuE/SgYlvATNMo2pcE5B5v/fMGvEiRc+J/ZYGD6tYo/of/i3epVSQbV/Fki/TRsXMXPF1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T22:09:37.874436Z"},"content_sha256":"5a66ad1f40e4ac32aa983736f997ffd208e8bb436ada539d7e04af086f46606c","schema_version":"1.0","event_id":"sha256:5a66ad1f40e4ac32aa983736f997ffd208e8bb436ada539d7e04af086f46606c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OUHO27CGGCV2FBGPRAKTAQBSPW/bundle.json","state_url":"https://pith.science/pith/OUHO27CGGCV2FBGPRAKTAQBSPW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OUHO27CGGCV2FBGPRAKTAQBSPW/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":"2026-06-09T22:09:37Z","links":{"resolver":"https://pith.science/pith/OUHO27CGGCV2FBGPRAKTAQBSPW","bundle":"https://pith.science/pith/OUHO27CGGCV2FBGPRAKTAQBSPW/bundle.json","state":"https://pith.science/pith/OUHO27CGGCV2FBGPRAKTAQBSPW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OUHO27CGGCV2FBGPRAKTAQBSPW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OUHO27CGGCV2FBGPRAKTAQBSPW","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":"5601971f7e9f3dab2514239f9274403fa2ab22785cfed8862bf372f2385abb2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-02T18:26:31Z","title_canon_sha256":"e7c5ae8f876c71d8ae1e75c99e81b2a655831892b748b6185834f8058a2f36e9"},"schema_version":"1.0","source":{"id":"1308.0572","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0572","created_at":"2026-05-18T02:53:41Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0572v2","created_at":"2026-05-18T02:53:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0572","created_at":"2026-05-18T02:53:41Z"},{"alias_kind":"pith_short_12","alias_value":"OUHO27CGGCV2","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OUHO27CGGCV2FBGP","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OUHO27CG","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:5a66ad1f40e4ac32aa983736f997ffd208e8bb436ada539d7e04af086f46606c","target":"graph","created_at":"2026-05-18T02:53:41Z","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":"An n-core partition is an integer partition whose Young diagram contains no hook lengths equal to n. We consider partitions that are simultaneously a-core and b-core for two relatively prime integers a and b. These are related to abacus diagrams and the combinatorics of the affine symmetric group (type A). We observe that self-conjugate simultaneous core partitions correspond to the combinatorics of type C, and use abacus diagrams to unite the discussion of these two sets of objects.\n  In particular, we prove that (2n)- and (2mn+1)-core partitions correspond naturally to dominant alcoves in th","authors_text":"Brant C. Jones, Christopher R. H. Hanusa, Drew Armstrong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-02T18:26:31Z","title":"Results and conjectures on simultaneous core partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0572","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:b4e74644387b27f197ae41d2906a8b2d1b1347e0beba8afe457f41345952c223","target":"record","created_at":"2026-05-18T02:53:41Z","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":"5601971f7e9f3dab2514239f9274403fa2ab22785cfed8862bf372f2385abb2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-02T18:26:31Z","title_canon_sha256":"e7c5ae8f876c71d8ae1e75c99e81b2a655831892b748b6185834f8058a2f36e9"},"schema_version":"1.0","source":{"id":"1308.0572","kind":"arxiv","version":2}},"canonical_sha256":"750eed7c4630aba284cf88153040327da8b4d27e66689b841b02934e7d4656f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"750eed7c4630aba284cf88153040327da8b4d27e66689b841b02934e7d4656f0","first_computed_at":"2026-05-18T02:53:41.264716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:41.264716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tlWfLAfka+0HJURb4emt6TsbCAZwLD96CVkK0kTEyky4DXkGsOLFEfFCZcRkL1xcm+ikeagoroMbdlXwADMKAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:41.265237Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0572","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4e74644387b27f197ae41d2906a8b2d1b1347e0beba8afe457f41345952c223","sha256:5a66ad1f40e4ac32aa983736f997ffd208e8bb436ada539d7e04af086f46606c"],"state_sha256":"5d014377cb56fe37b888ce9e9656e5e8dc5ac4af755e6b4350a9af3eb72f3bcb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fP8OInW070sKwgwNrIvmAexWl9BJlTBY1ZpZlifSqvTaNomCYdWrSqgCb1/79/L96VGesXyykgP/QN4hyiq4DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T22:09:37.878081Z","bundle_sha256":"ef4c907928f56354891ec2fb447edb74e72bf6a46394772882e91f04fcd2d27e"}}