I agree that definitions explanation of assumptions are required. Here's how I see principal and LBYM.
For principal [P] I'd use the starting value of the portfolio [V(0)] and multiply it by (1+r) each year, where r is the inflation rate, to account for inflation. I would not include my cash buffer in the value of the portfolio as I might have to spend that....I realize that it's a bit of a semantic decision and smacks of buckets, but it's how I think of my portfolio.
P(0) = V(0)
P(n+1) = P
*(1+r)
So basically, you are applying some arbitrary math and calling it "principal".
Nothing wrong with doing some sort of math to help you decide how much to take out -- but this formula has nothing to do with what principal actually is.
[If] the value of the portfolio has gone down [] you should do all you can to minimize the income you take out. This is when you reduce expenses, spend down the cash buffer or get a part time job.
Unfortunately, these formulas don't tell you anything concrete. Rather, they are just handwaving generalities. Again, nothing wrong with that, it's just that it's rather impossible to convert handwaving into a set of hard-and-fast concrete rules. It's when you do this step that it becomes apparent that what you thought were rules aren't actionable after all.
You realize that you can't write down the set of machanical rules that effectuate the plan. So what it ultimately comes down to is that each year to use your gut feelings to decide how much income to draw.
Also, the formulas you came up with in a flat or bull market may not work at all in a bear market -- usually because you forgot to consider those scenarios when you came up with the formula. This is the problem with withdrawal strategies that take a constant X% of your portfolio value or gains annually. Strict adherence to the rules may mean that your income varied wildly from one year to the next. Your annual income draw may get reduced by 25% - 50%, or be increased by 25%-50% depending on if the market had a big bear/bull year.
I went through all this myself a few years ago when I retired. Looked at a lot of different proposals, and discovered that many of them seem clear and obvious -- until I tried to write them down as a set of concrete rules that could be put into an Excel spreadsheet. That's when I discovered the holes.
You want to have a roughly even amount of income from your portfolio, similar to a regular paycheck. And you also don't want to exhaust your portfolio before you die.
I eventually decided that the Guyton-Klinger rules made sense --- and can be written up in Excel.