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Published July 28, 2026 | Version v1

An Eight-Term Counterexample to the Special Image Conjecture in Three Pairs

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An explicit eight-term counterexample to the Special Image Conjecture in three contraction pairs. For f=tau^3(t+z)(w t^3-v y(t+y)^2) and g=z, the paper proves E(f^m)=0 and [t]E(g f^m)=(3m+1)!m! for every m>=1. Thus the minimum possible failure dimension is two or three.

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three-pair-image-counterexample.pdf

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