A Rank-One Obstruction for Odd-Primary Wood Equivalences

Let p be odd, h=(p-1)p^(r-1)m with r>=1 and m>1, and H=C_(p^r) a subgroup of the height-h Morava stabilizer. For Honda Morava E-theory over F_(p^h), put A=E^(hH). We prove that no finite p-local spectrum F satisfies A smash F equivalent to E as A-modules. More generally, if A smash F is equivalent to a nonzero finite wedge of q copies of E, then q>=2. No parity condition on the cells is required. The proof combines Ravenel's classical strict-stabilizer H^1 calculation, cyclotomic valuations, Galois base change, and an elementary modular-representation flag bound. An abstract rank-two matrix example shows the flag bound is optimal as a group-theoretic statement, without asserting a topological realization. The result concerns external finite-spectrum Wood equivalences only. Internal A-module filtrations, optimal realizable multiplicities, and the m=1,r>1 cases are not resolved; the broad source question AIM-ALGEBRAIC_GEOMETRY-0035 remains partially solved. This is an unrefereed preprint with AI assistance disclosed in ordinary prose. Classical inputs are credited; independent review, formal verification and absolute priority are not claimed.