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We also obtain exact formulas for the number of self-conjugate t-core partitions for \"small\" t via explicit computations with modular forms. For instance, self-conjugate 9-core partitions are related to counting points on elliptic curves over \\Q with conductor dividing 108, and self-conjugate 6-core partitions are related to the representations of integers congruent to 11 mod 24 by 3X^2 + 32Y^2 + 96Z^2, a f"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.0158","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-29T22:35:31Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"6c7a43984d2154589df2273f8acc15e02376c99add124b523b7e67f63407c2aa","abstract_canon_sha256":"504afd84d3da5b4a25ccd3d2eb29c458a923e0da122712df63dfec7c9791eb9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:23.785287Z","signature_b64":"4kHREZOGmODqkg7aQOrjeyhmbRgqcAGrp8IaOMOofn8JsfzEoP98kS0RclUZl9Y9hc2vti/vvizZY3QzDuZPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e30b4754b21f16f5d0ae0a2b139e0249faf18f47eccb4a52978dd02e23a505d6","last_reissued_at":"2026-05-18T02:57:23.784768Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:23.784768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-conjugate core partitions and modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Levent Alpoge","submitted_at":"2013-06-29T22:35:31Z","abstract_excerpt":"A recent paper by Hanusa and Nath states many conjectures in the study of self-conjugate core partitions. 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