Page 3 of Sessions 2,3,4, and 5(Residue Applied to 2-D strings

Now that we learned what is meant by Real residue, I will apply this concept to metaphorical vibrating circles, which represent two-dimensional strings. Take two circles. One has a small radius while the other has a large radius. The two circles are initially parallel to each other and are not touching. The two circles are actually thin hoops. The two circles propagate. These are not merely duplicated. In one of such an array, the pattern of small circle placewise differentiation and large circle placewise differentiation converges to a discrete symmetry. In another array as above, the pattern of small circle placewise differentiation to large circle placewise differentiation never converges to a discrete symmetry. You might say, "Well, if it's a pattern, then it is discrete." Not necessarily. If the pattern is anharmonic or if it is long enough, it may form sub-symmetries that diverge as the "pattern" ends its phenomenal discharge. By "ends its phenomenal discharge", I mean that the circles would stop moving around, and the pattern of all of the places that the circles were at would have a limitation. Such an erratic pattern has zero Weyl-Invariance, since invariance means that it doesn't change, and something that is erratic changes the eigenbasis of symmetry that would otherwise exist. If an eigenbasis of encodement due to discharged wave homotopy diverges in terms of wave commutation, while the divergent wave commutation (not divergent wave generation, which would do just the opposite), causing these waves to keep iterating in a string-like fashion that may be of different transversal, spin-orbital, and/or radial placements respectively, exists due to the same substringular operation, then the associated superstrings will always be within the same general locus of tori sector. Such waves that diverge during ultimon flow obey an odd function of wave residue in-between instantons, and thus bear an Imaginary Residue. Once the associated waves, along with the differentiating path operands that the "odd" waves propagate along, act upon the other correlative waves that have diverged from the initial said waves, the waves as a unit are then back into iteration mode, and thus bear residue that is said to be Real. Then their residue may be taken from the strings in a method I will later show, in order that norm conditions among substringular phenomena may have equilibrium. Imaginary residue that's already delineated stays within a general relative locus per iteration in spite of the fact that Imaginary residue is residue that is produced during ultimon flow, and ultimon flow is in-between instantons, and Imaginary residue causes Cassimer Invariant modes via certain motion of Planck phenomena related phenomena that I will describe in later courses.