Maximum entropic extent theory

Quanta magazine on polynomial complexity: 

They still haven’t solved Hilbert’s 13th problem and probably aren’t even close, Farb admitted. But they have unearthed mathematical strategies that had practically disappeared, and they have explored connections between the problem and a variety of fields including complex analysis, topology, number theory, representation theory and algebraic geometry. In doing so, they’ve made inroads of their own, especially in connecting polynomials to geometry and narrowing the field of possible answers to Hilbert’s question. Their work also suggests a way to classify polynomials using metrics of complexity — analogous to the complexity classes associated with the unsolved P vs. NP problem.

They will end up with relative prime theory and show that a seventh degree polynomial needs a Markov 4-Tuple, rather than a 3-Tuple.  We reach an Avogadro limits in any dimension, Shannon defined is as the maximum entropy, for 3D systems. But it should extend up to n-Tuples. 

That is why they got the number theory pro involved, he needs to develop relative prime theory. And relative prime theory warps into topology. Classic theory of everything.

The seventh order polynomial needs three continued fractions and the round off errors spread about a Torus, so surface to volume has increases. The key is Shannon and his maximum entropic extent. Expanded as a series of lwas for increasing dimensions, it tells us how many relative primes we need.

Hurwitz rational approximation gets extended.  Hilbert was looking at the actual computation of a Taylor series, noting that it is an extending series of fraction approximation, all of which r Otherwise, the round off errors along the way cannot distinguish between two zero crossings of the polynomial require arithmetic counts that can only be inb=crease by adding a retaative prime at some point.

There should be a stopping point at 6 which then needs another prime, then 24 then 120. They rise fast, and are related to combinatorials of the Markov axes under the generalized Markov condition to arbitrary N-tuples.

Haven;t read it yet, but will.