Mechanism of a cyclization reaction - why does an enol ether form?
@Carbenoid: A year has passed since you requested a mechanism from @Mithoron. The statutes of limitation have run out. Your comment about why not do an aldol condensation (in base) is well taken. But the question was what is the structure of compound A.  I have no problem with the dienol ether 5 (aka A) in spite of many people's aversion to forming 8-membered rings.
Full stereochemistry of structure 1 could have been informative but not essential. I will forgo the mechanism of the acid-catalyzed aldol condensation and defer to @ringo's contribution. The bold bonds in structure 2 form a rigid framework so that the degrees of freedom are minimized in the formation of the hemiketal 3. Effectively, the cyclization is that of a much smaller ring. This ring closure is mechanistically more sound than the SN2 displacement with an enol particularly one with an (E)-geometry when at least the (Z)-geometry would be required. The red arrows terminate with dienolether 5. Aqueous acid and microscopic reversibility via the blue arrows return dienolether 5 to structure 2. In fact, structures 2 and 3 may well be in equilibrium with each other.