You wrote: " The nitrogen fixing is an urban myth ". Yes, absolutely that is a dumb statement. Totally wrong. Not supported by science...even your own.
"Research Busts Legume Myth:" Trial crops showed that the legumes tested had a higher nitrogen “export” (ie. nitrogen in the crop) which offset their potential for nitrogen fixation in the soil (ie. the nitrogen left behind after the crop). Of course, the N2 fixing plants use more for themselves than they leave behind...but clearly they leave N2 behind.
So what "myth" is busted? I know no one who claims that plants that fix N2 don't also use some of that N2. My approach of growing and shredding four consecutive generations of nitrogen fixing peas works...and it absolutely is not an urban myth.
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Legumes do add nitrogen to the soil but less if you eat them " ... LOL at contradicting your own statement. This is well known by most who use this practice. More times you do it, the more total N2 is added to the soil."
Contradiction? I wrote in my first post (& you quoted)
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The nitrogen fixing is an urban myth; peas can fix nitrogen from the air, but use it themselves.
The plants have only their compost value. "
The plants at that stage would count as greens, so there WOULD be nitrogen in that.
In order to get the type of benefit you suggest you'd have to plant them solely as a cover crop.
As for your potato yields; this is personal anecdotal evidence totally akin to stating that men are not taller than women because my sister is 6 ft tall. As evidence it is worthless, & my yields, with nary a pea in sight, were far greater. Your yields were probably boosted by the chance factor of it being a good year, but if there was a macronutrient effect on yields, it would be far more likely be from higher available potassium or phosphate levels, than from nitrogen, whose main effect would be on the potato foliage.
I have shown evidence in the form of recent scientific research by the Queensland Department of Agriculture & Fisheries that supports my position.
What have you got?