The words, asymptotic freedom, hold keys to the finite-infinite relation.

This document was started in March 2023. It is in process.

History. Big O notation… Asymptotic analysis, Asymptotic freedom. Calculating backgrounds with Frank Wilczek (On the Origin of Mass, 2003)

Asymptotic Freedom Wins A Nobel Prize. That earliest work, the foundations for that prize, first appeared in Physical Review Letters, Vol. 30, Issue 26 (1973). Works by David Gross and Frank Wilczek were published, Ultraviolet Behavior of Non-Abelian Gauge Theories and Asymptotically Free Gauge Theories (Phys. Rev. D 8, 3633 – Published 15 November 1973). Independent work by David Politzer was published as Reliable Perturbative Results for Strong Interactions? (Phys. Rev. Lett. 30, 1346 (1973). The net-net was their discovery of what was called, “asymptotic freedom.” That has become a key part of the definition of strong interactions, i.e., how the beta function describes a coupling constant. This interaction changes with energy and, contrary to general belief, it could be be negative value.

“This means that the interaction strength can decrease with increasing energy, making quarks ‘asymptotically free‘ at high energies.” –CERN: https://cerncourier.com/a/asymptotic-freedom-wins-nobel/

“The famous beta function, which underlies asymptotic freedom, where g is the coupling constant, Nc is the number of colours (three in QCD) and NF is the number of quarks (six in the Standard Model)” – Royal Swedish Academy of Sciences

Asymptotics became a study on its own. Today it is taught to everyone!

The key distinction that can only be made within the 202 base-2 notations from the Planck Time to this very moment (an encapsulation of all time) is where the limiting factor either hits the Planck Wall and is finite, or it passes through the Planck Wall within the continuity-symmetry-harmony equations of the sphere and is infinite. Much more to come…

See: Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards (1) a particular value or (2) infinity. Big O is a member of a family of notations invented by Paul Bachmann,[1] Edmund Landau,[2] and others, collectively called Bachmann–Landau notation or asymptotic notation. The letter O was chosen by Bachmann to stand for Ordnung, meaning the order of approximation.

https://en.wikipedia.org/wiki/Asymptotic_analysis

My apologies to Steve Goldman: This page has a ways to go. You’ll notice the link to WhyU?‘s work on asymptotic.