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Motivated by the holographic swampland program, we study possible bounds on the coefficients $\\alpha_i$. For $\\alpha_0$, the weak gravity conjecture motivates the CFT charge convexity conjecture, which requires the bound $\\alpha_0\\leq 0$. Using the moduli space EFT we prove this bound for the $\\textit{projected}$ $\\Delta_{\\min}(Q)$, obtained by fixing a single char"},"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":"2607.28726","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-07-30T18:00:02Z","cross_cats_sorted":[],"title_canon_sha256":"8d1e298e8a57ac34196e97ddffd363e9b24437232cf716d02a1282cda454c664","abstract_canon_sha256":"e9ddb814f53caa2e3d14f82446d833555cf1a40b387f92a7465384281e00bf07"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-03T00:12:28.882526Z","signature_b64":"uGR8NfZG1vKmPRvQeHQ2EiAuYLCnXzYV7GUKZ85Us7H3NWn4T6LCp9PHcZwpFb2YFvPBsEcUcUdC4+iGNVVXCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2a7aa3005e73e420921ad4e3a0dd9429c04fc8cb2ef1d604f52c736f805bfd8","last_reissued_at":"2026-08-03T00:12:28.880180Z","signature_status":"signed_v1","first_computed_at":"2026-08-03T00:12:28.880180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towers of Operators in CFTs and Convexity Bounds at Large Charge","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Adar Sharon, Fedor K. 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