Taking the question as "How do we split the equity when one partner simply provides the idea while the other partner builds the software?"
In the words of Edison:
Genius is one percent inspiration, ninety-nine percent perspiration
In general it is much, much easier to come up with an idea than it is to actually implement it and make a successful business. If all one partner contributes is an "average" idea, then 50% is probably too much, particularly if it is going to take you lots of time or money to implement.
There are things that could make an idea far more valuable however. Consider the following "ideas".
If you figure out a cure for cancer we could make lots of money.
I have a formula for a drug that might cure cancer, you go test it.
I have a formula for a drug that cures cancer in the mice I tested it on.
I have a formula that cures cancer and I have a patent on it.
I have a patented formula for a drug that cures cancer and it has been approved by the FDA.
Clearly a proven, patented formula with FDA approval is worth far more than a formula that might work and which needs research and testing.
Then there is the question of implementation. There have been lots of great ideas which were simply before their time, in other words they could not be implemented with existing technology. A perfect example would be da Vinci's invention of the helicopter. In the 20th century that idea is worth megabucks, but in his day it was impossible to produce. Or consider Frank Whittle who invented and patented the jet engine. He let the patent lapse in 1935 for lack of a 5 pound renewal fee.
The bottom like is that it takes both a good idea and proper implementation to be successful. One without the other is worthless.
If you can program the idea over a weekend then the idea might be worth 50% or perhaps even more. If it is going to take you two years full time to complete a prototype then it is a quite different matter. Consider your opportunity cost, is there some other idea you could work on?
Finally the idea of a a partner who shows up for one day to provide the idea while the other slaves for months to implement it reminds me of the story of the chicken and the pig. The chicken has an idea to open a restaurant where they serve ham and eggs. As they say, "the chicken was involved while the pig was committed."
As the person who would be committed to implementing this software, what are you willing to pay for involvement?