{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:TU2XQYH5NPHXJV25VEOSFN6RRN","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":"0a2676c5bcf201d3618108cab225eb4c9c5e16e93084b8f6c414e394c65a82bd","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-11-19T17:38:33Z","title_canon_sha256":"6f38d78cc2e5297dc7d01bf93b5e23ec914713d1c8d1e258817aa4bb5773ed4e"},"schema_version":"1.0","source":{"id":"2011.09989","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.09989","created_at":"2026-07-05T04:15:40Z"},{"alias_kind":"arxiv_version","alias_value":"2011.09989v4","created_at":"2026-07-05T04:15:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.09989","created_at":"2026-07-05T04:15:40Z"},{"alias_kind":"pith_short_12","alias_value":"TU2XQYH5NPHX","created_at":"2026-07-05T04:15:40Z"},{"alias_kind":"pith_short_16","alias_value":"TU2XQYH5NPHXJV25","created_at":"2026-07-05T04:15:40Z"},{"alias_kind":"pith_short_8","alias_value":"TU2XQYH5","created_at":"2026-07-05T04:15:40Z"}],"graph_snapshots":[{"event_id":"sha256:1c50599967e0220a55749024ac98a6b53908251e0c59ee008e1621a66b9825bf","target":"graph","created_at":"2026-07-05T04:15:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2011.09989/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We classify the connection between $t$-cores and self-conjugate $t$-cores to sums of squares. To do so, we provide explicit maps between $t$-core partitions and self-conjugate $t$-core partitions of a positive integer $n$ to representations of certain numbers as sums of squares. For example, the self-conjugate $4$-core partition $\\lambda=(4,1,1,1)$ corresponds uniquely to the solution $61=6^2+5^2$. As a corollary, we completely classify the relationship between $t$-cores and Hurwitz class numbers.\n  Using these tools, we see how certain sets of representations as sums of squares naturally deco","authors_text":"Joshua Males, Zack Tripp","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-11-19T17:38:33Z","title":"Combinatorial results on $t$-cores and sums of squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.09989","kind":"arxiv","version":4},"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":"sha256:39fa10cbd64ea370c4fe55733bb4c3783be89101fe72d26ef6d8200cc8ce8d23","target":"record","created_at":"2026-07-05T04:15:40Z","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":"0a2676c5bcf201d3618108cab225eb4c9c5e16e93084b8f6c414e394c65a82bd","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-11-19T17:38:33Z","title_canon_sha256":"6f38d78cc2e5297dc7d01bf93b5e23ec914713d1c8d1e258817aa4bb5773ed4e"},"schema_version":"1.0","source":{"id":"2011.09989","kind":"arxiv","version":4}},"canonical_sha256":"9d357860fd6bcf74d75da91d22b7d18b621e69f37a780e1dc9a34ca99deebfe1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d357860fd6bcf74d75da91d22b7d18b621e69f37a780e1dc9a34ca99deebfe1","first_computed_at":"2026-07-05T04:15:40.066355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:15:40.066355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CvvMdFZpu2IlozjyUv3A82oQdz5V0rF+5mHz7YkZTXOeTGzxFqmr1LtCZkLFgef1ZKReaaTU6Z6SFgoUbhJyAw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:15:40.066871Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.09989","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39fa10cbd64ea370c4fe55733bb4c3783be89101fe72d26ef6d8200cc8ce8d23","sha256:1c50599967e0220a55749024ac98a6b53908251e0c59ee008e1621a66b9825bf"],"state_sha256":"abe9ab6b3d343bd5786d446900a9c1e866d4ddac88ffe9dcc5504266c2b00b02"}