Write out the mechanism (using correct curved arrow notation) for the acid-catalyzed, cis-trans isomerization of maleic acid (into fumaric acid)

If the electrophilic addition reaction of maleic acid with HCl had gone to completion what would be the structure of the addition product(s). Be sure to take into account any stereochemical consequences of the reaction.

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The acid-catalyzed, cis-trans isomerization of maleic acid into fumaric acid involves the redistribution of the double bonds within the molecule. The reaction proceeds through the following steps:

Step 1: Protonation of Maleic Acid
In the presence of an acid catalyst, maleic acid is protonated to form a more reactive intermediate. The curved arrow notation for this step is:

O H+
//\ ||
C O => C-OH
\\ / ||
C==O O-

Step 2: Intramolecular Proton Transfer
The protonated maleic acid undergoes an intramolecular proton transfer, where the proton is transferred from the hydroxyl group to the adjacent carbon atom, resulting in the formation of a carbocation intermediate. The curved arrow notation for this step is:

O OH
//\ ||
C-OH => C H+
\\ / ||
C==O O-

Step 3: Double Bond Migration
The carbocation intermediate rearranges through a migration of the double bond from the initial position to the adjacent carbon atom. The curved arrow notation for this step is:

OH O
|| //
H+-C => C-OH
|| \\ /
O- C==C
||
O-

Step 4: Deprotonation
Finally, the deprotonation of the rearranged carbocation results in the formation of fumaric acid. The curved arrow notation for this step is:

O OH
//\ ||
C-OH => C==C
\\ ||
O- O-

Therefore, the acid-catalyzed, cis-trans isomerization of maleic acid results in the formation of fumaric acid.

Now, regarding the electrophilic addition reaction of maleic acid with HCl, if it had gone to completion, it would have formed an addition product called cis-1,2-dichlorosuccinic acid. However, this product would not have the same stereochemical consequences as the isomerization reaction. The electrophilic addition reaction would result in the formation of a saturated molecule, with the chlorine atoms added across the double bond, while the isomerization reaction results in the redistribution of the double bonds while maintaining the unsaturation.