Update: The 2nd mash was reduced down to 5.5 cups. 5 cups where collected. Half a cup was added back to reduce to a viscosity to something similar to Liquid malt extract. The 1/2 cup proved to reduce down to approximately 1/4 cup similar enough to a Liquid malt extract to be considered a success in producing Liquid malt extract. The sweetness and viscosity on taste and examination where consistent with a liquid malt extract. With the fluid in the pot lowered down to a smaller level it became more difficult to control temperature to prevent fear of any scorching of sugars or congeners. Taste did not reveal any evidence of scorching. Flavor was highly sweet like malt extract with a bitter off flavor I attribute to a cereal like taste and a slight hint of smokiness, not over powering, relieving the fear of over extraction of the heavy peated malt congeners. Any over extraction is within the cereal note flavor category that could produce an off flavor in a final product. I had another person sample it and it was described as "honey". This person is unfamiliar with brewing and Malt extracts.
A little math I've worked out that is the most fascinating: Considering that a half reduction of 5.5 cups would yield 2.75 cups of Liquid malt extract as a final measurement of reclaimed sugars. I have no way of testing whether this amount can truly be considered a malt extract based on sugar content beyond taste and viscosity. This measurement is converted over to 22 fluid ounces. a pound of liquid malt extract is approximately 9.5-10.6oz determined here:
https://www.homebrewtalk.com/forum/threads/how-much-volume-is-1-pound-of-extract.375047/
This would equal around 2 pounds of liquid malt extract recovered from the spent grain. Financially, that's a savings of about $6.50 if the liquid malt extract where purchased from my home brewing supply. to get the equivalent pounds of grain, 2lbs was divided by .75 to give 2.66 pounds of grain at approximately $7.50 local prices. Here's where it gets interesting, 2.66 is 33.25% of 8 lbs of the original grain bill, giving an inefficiency of 33.25% in my brewing process. this math seems to add up to the taste test of greater than 20%. But 33.25% puts 66% of the grains potential in the 1st mash if I have reached 100% efficiency. 33% is half of 66% and thus half beer if not condensed. I find that amazing the crude science and math has added up to the second run yielding exactly half or half beer. Thus the term half beer.
Extrapolating this home brewers such as myself are missing out on 2 gallons for every 4 gallon run. That's about a buy 2 get 1 free proposition on grain bills for me with 4 gallon run capacities. By either reducing the second wort down from 4 gallons to 2 gallons and running an additional 2 gallon separate fermentation of whole beer, running 4 gallons of half beer, or reducing the second wort down to liquid malt extract and using it as an addition to the next brews 2nd wort to fortify the next batches half beer into a whole beer.
The final 5 cups of diluted liquid malt extract where chilled off to temp. then added to the 1st worts fermentation to fortify it's ABV. This has several issues. 1: I lack equipment such as gravity meters to test sugar gravity or final ABV of the finished beer or any way to test the brix of the product LME against a control LME. This is an experimental recipe I have done this with so I have no way to compare it to a control batch for off flavor beyond is it drinkable? But this preliminary poke in the dark seems promising based on the crude science and sketchy math for both beer brewing,commercial malt extraction and increased efficiency of grain distilleries since the math seems to scale with production levels. I`m not sure if this is not economically viable in large productions comparing to the time, cost and space of spent grain extractions vs. costs of large scale grain purchases.
I think that's all I've got besides a final taste test of drinkable undrinkable which provides very little value considering it's a random test recipe. But will probably continue to do this on my next two runs to save up enough 2nd wort LME to compare that to an unadulterated 1st wort whole beer control.