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"As I understand it the crux of the minus-sign problem is finding a physical way to determine, sample and use both Positive and Negative probability distributions [please correct me if this is wrong]"
Not wrong so much as not complete. It's more than a computational problem designed to give numerical simulators headaches. It appears to be a fundamental barrier to progress in condensed matter physics. It's plain awful.
"Using my work [www.youtube.com/tetryonics] you CAN solve for this problem by using Charge geometries. Negative and Positive charge geometries result from the non-neutral component bosons of any charge [equilateral] geometry. The Bosons [odd number] components form a transverse quantum level and the Photon geometries [even numbers]form a longitudinal probabilistic geometry."
Okay ... without evaluating your video let me say this: you need to appreciate the goldmine you might be sitting on top of. If you're right, and you can get someone to mathematize your geometry, you may have managed to put strongly-interacting chiral fermions on the lattice and bosonize them for Monte Carlo simulation, and in addition (by disproving Troyer-Wiese) proven P=NP. That last could be worth a million dollars (US) from the Clay Mathematics Institute. Seriously.