Another approach to Riemann

Warp the problem. It is about the prime counting function, so look at that as an operation count problem, how many operations does one need to test integer N, when all integers bellow it have been tested for prime. Our guess need only be to the nearest of two integers.



So, I have a black box, I feed it an N, it tells me how many operation counts it took, minimum.  This machine minimizes rotations about the induced plane, in fact finds where there are no more rotations to test. It is marching down a decoding tree, updating paths from an arbitrary integer to the greatest prime factor, and these paths yield operation counts.

We get a graph theory, kin of on this. Atr each test of the node, the operation requires matching a modular form, likely in a remainder function. It is a spectral decomposition, really of N/[previous primes]. But counts are easier to deal with, and should be maximum on a new prime. Counts are found in the spectral space of remainders, how many digits needed to identify repeating patterns, or rather, rule out a scaled pattern from before.

So, the new prime cannot find a factor from the previous nodes, is its own modular form, and occupies part of 'round off' space below its point on the map. It is an ounounded channel, round off space grows as needed. But if we can model the black box, counting operations, as alterations in a dynamic, but growing map, then it can isolate maybe, when skew is out of bounds. Just looking for finite graphs, with loops they are good as summations and divisions.  In finite world,growing, the operation count is like a growing Avogadro's, the system adds enough primes to keep a good sphere. The optimum prime counting function should keep counts minimized. In a sense, you are looking for the largest measurable Avogadro without modular forms.

Primes make the most efficient use of the fractional digits, repeating fractions. There is no rounding function that uses less operation count, it the assumption. And wee imagine the primes are packing a circular map, a warping ot the complex plane. Each prime marks its modular form on the diameter, and the diameter expands as each new primes is found, so previous primes need add more granular marks on the diameter. As walk along the diameter is as round as the primes are dense, so we get Pi mixed in, and approximate Pi by walks through the graph that generates marks. We want to get it down to measures f graph skew, rank, relative density and variance at nodes; say something using graph properties.

Show a relationship between the number of recent primes and exess congestion in mopdular forms. Prove some delta N mus be non-prime to restore to optimum congest, and congestion is operation count.    Some unbalanced tree would be shown to exist, off the 1/2 axis, a generator terminal that is not binary. In other words, is round off spectrum monotonic as N increases.