Key Questions:
•  Are infinitesimal composites on the grid?
• Are infinitesimal composites part of the mathematical formulations within Langland Programs?
Are these on the grid?
•  Are infinitesimal composites part of the constructions of string and M-theory?
Would these be on that same grid?
•  Are infinitesimal composites part of the key relations defined within SSM, LQG, CST, CDT, SUSY and all our hypothetical particles (of every and any kind)?
Are these also part of the grid?
Answers: Yes, yes, yes, and yes. We envision that there are infinitesimal composites for every hypothetical particle and each in different combinations engages the mathematics of Langlands, strings, SSM, LQG, CST, CDT, SUSY and all our field theories.

A little history. In December 2011 we uncovered the 202 notations by going from our classroom objects of a tetrahedron and its embedded octahedron (and four smaller tetrahedrons), smaller and smaller until we were in the range of the Planck base units. We used those units as our first measurement of a space-time moment and assumed one infinitesimal sphere. per unit of Planck Time and Planck Length. We multiplied the Planck base units by 2; and in 202 notations we were at the age and approximate size of the universe.

In 1927 Lemaître had assumed a primeval atom. An infinitesimal sphere seems more generic and does not impute the history of the atom, but the much longer and more dynamic history of the mathematical constant, pi (π), and its sphere.

In 2013, in an attempt to grasp the nature of the first 64 notations of the 202 base-2 notations that encapsulate the universe and creates an ordered set of data, those first notations were grouped in bundles of ten units each. The first units were about form, the second group, 11-20, were about geometric structures or Ousia. The third group, 21-30 were about qualities, the fourth group about relations, and the fifth group about systems. Learning how the finite-infinite relation is in some manner defined by continuity-symmetry-harmony, the three primary facets of pi (π), created a dynamic bridge between all notations.

Composite particle. The definition within Wikipedia for composite particles prompted more research. It was not definitive enough. Upon discovering, Elementary Particle Theory of Composite Particles, Steven Weinberg, Phys. Rev. 130, 776 – published 15 April 1963, it seemed to be a better foundation than “…depending on the energy contained by the quarks, the quarks of a proton vibrate, and this gives a proton a size larger than the actual size of the three quarks combined” (within Wikipedia).

Infinitesimal Composites. The components are geometric, numeric, dimensional, computational, and dynamic and carry at least trace characteristics of continuity, symmetry and harmony…

History: On Friday, April 28, 2023 at 6 AM nine pages came up in a search of “infinitesimal composites.” Our first use of the term was posted on April 27, 2023. The first reference that I spotted in ArXiv, The stable embedding tower and operadic structures on configuration spaces (Nov. 2022) was written by Connor Malin, a doctoral candidate at Notre Dame University. I sent him a note asking, “Might you envision your infinitesimal composites to be at or near the Planck scale?” He had introduced Poincare-Koszul operads. Then I discovered the work of Wenxi Yao (Chicago, Harvard) who wrote Koszul duality of quadratic operads (2022-2023) and on page 9 introduces the concept of infinitesimal composites. Pedro Tamaroff of the Institut für Mathematik, Humboldt-Universität zu Berlin, wrote Algebraic operads, Koszul duality and Gröbner bases: an introduction (2020-2021) and on page 89 defines two types of infinitesimal composites. In 2012 landmark work, Algebraic Operads, Jean-Louis Loday and Bruno Vallette also use the term, infinitesimal composite, extensively. In 2011 Patrick Hilger and Norbert Poncin in their work, Lectures on Algebraic Operads (page 71ff), wrote what appears to be the earliest reference to an infinitesimal composite.

Also, upon the recommendation of Connor Malin, the work of Maxim Kontsevich is also being studied.

Much more to come…

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