Can I legally pursue my employer for retracting a documented verbal promotion?

Dear MEL: For the past 3 years I have worked in Operations for my employer. A couple months ago I applied for a similar role in a more technical and specialized sector of the company. I was successful and verbally offered a 10% raise. Fast-forward one month and I still had not transitioned into my new role. I was told the written offer was still going through the approval process (through our domestic headquarters). After five weeks, I was told the offer was ultimately denied and that they could offer a 5% increase. Their argument was that since my title would remain the same, this was not a promotion but rather a lateral move that did not garner a wage increase. Essentially, I was told I was lucky to get 5%. My question is, do I have any legal ground to pursue this based on the fact that there is an undeniable paper trail following the 10% increase in the initial verbal offer?