Spiral Towers in Inverse Systems with Alternating Pairings

We study inverse systems of finite abelian groups equipped with alternating pairings taking values in Q/Z. We introduce the notion of a spiral tower, meaning a compatible inverse system of nonzero elements whose images are detected at every finite level by the pairings, while the induced inverse-limit class remains nonzero. We construct explicit algebraic models admitting spiral towers and satisfying bounded-depth detectability at every finite level. In particular, bounded-depth detectability with respect to alternating pairings does not force stabilization or triviality of the inverse limit. The results isolate a purely inverse-system obstruction to inverse-limit stabilization in duality-governed settings. No finiteness or conjectural claims are made; the results are purely structural.