There doesn't need to some mathematical proof or nobel prize winning study, because... well, the proof is in the pudding if you look at athletes.
Most people are not doing the basics, but by doing some form of exercise often and consistently. Eat a nutritious meal, don't binge on junk food and sleep well. People love to complicate and over engineer the situation by diving into everything 100% when they have a 'I'm going to lose weight' mindset. Weight loss takes a while and you might need to be a little hungry at times to lose weight.
Just don't expect exercise to be the one reason you will lose weight, the largest reason will be your diet. As the old saying goes, you can't outrun a poor diet.