Step 1: Identify the functional group present in compound \(Z\).
The given compound is an allylic alcohol because the hydroxyl group (\(-OH\)) is attached to a carbon adjacent to a carbon-carbon double bond.
Step 2: Understand isohypsic transformation.
Isohypsic transformation is a redox-neutral rearrangement in which the oxidation states of carbon atoms remain unchanged overall.
In allylic alcohols, this transformation generally converts the alcohol into a carbonyl compound through double bond migration.
Step 3: Recall the allylic alcohol isomerization pattern.
A typical allylic alcohol transformation is:
\[
\text{Allylic alcohol}
\rightarrow
\text{Aldehyde/Ketone}
\]
The carbon-carbon double bond shifts and forms a carbonyl group.
Step 4: Analyze the change in bonding.
Initially, the molecule contains one
\[
C=C
\]
double bond.
After isomerization, the alkene double bond disappears and a carbonyl bond
\[
C=O
\]
is formed.
Step 5: Count the total number of double bonds in product.
The product contains one carbonyl double bond:
\[
C=O
\]
Thus, the total number of double bonds remains
\[
1
\]
Step 6: Verify the transformation.
Since one double bond is replaced by another double bond during isomerization, the product contains exactly one double bond.
Step 7: Final conclusion.
Therefore, the number of double bonds present in the isohypsic transformation product is
\[
\boxed{1}
\]