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In the context of modular forms, we prove: given two non-CM newforms $f$ and $g$ of weight at least two, such that $a_p(f)^{n_p}=a_p(g)^{n_p}$ on a set of primes of positive upper density and for some set of natural numbers $n_p$, then $f$ and $g$ are twists of each ot"},"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":"1010.5393","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-10-26T13:40:00Z","cross_cats_sorted":[],"title_canon_sha256":"10172072dd642c652a5d4a1c6eff4911c129a64eb9f9e8d0d8aa624f77e08f9b","abstract_canon_sha256":"c2aee65ce32f6ccccd3d83253323367fe8d47d71eb467be34a3429edc03ec6c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:38.863495Z","signature_b64":"akCtD5CszAik3KqxgCfdju8BWPp+yoWV9dec6HgUgkOAWDXlYr9eEotBX30vXcAqNgHPWiI7lrj8aKAPoYgUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dded6e67a4763811d2414bc7e96a7a0d55f584ad593cf23587dbdce1ce3433f","last_reissued_at":"2026-05-18T04:38:38.862936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:38.862936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Locally potentially equivalent Galois representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"C. 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