TO: Connor Malin, PhD student, University of Notre Dame, South Bend, Indiana
FM: Bruce E. Camber
RE: The stable embedding tower and operadic structures on configuration spaces.
Fourth email: 11 April 2026
RE: Infinitesimal composites, Goodwillie calculus, and the proton at Notation 65.5
Dear Connor,
I hope this finds you well. I’ve been thinking about the infinitesimal composites page you engaged with back in 2023, and a specific calculation has come up that made me want to reach out directly.
Working through the base-2 chart, the proton charge radius (0.8412 fm) lands at almost exactly Notation 65.496 — half a step between Notations 65 and 66. That half-notation position is numerically equivalent to the geometric mean of those two consecutive notations, i.e., √2 × ℓ_P × 2^65.
I’ve been exploring this with Claude (the AI), who pointed out that your work on Goodwillie calculus might offer a principled explanation: rather than the proton failing to land on a clean integer notation, it may be constitutionally a two-layer composite — a 2-excisive object in Goodwillie’s sense — whose structure requires contributions from two adjacent notation layers simultaneously. Quarks and gluons together spanning that interval.
What I’d love to know is whether you ever worked out a dictionary connecting the doubling operation in the 202-notation grid to the functor language of Goodwillie calculus — specifically what “excisive” would mean in terms of Planck-scale sphere composites. If that bridge exists, even informally, it would be the most mathematically rigorous grounding the model has yet found for why the proton sits where it does.
We are preparing an arXiv submission and this question feels like it sits right at the center of it.
With appreciation for your early engagement with this work,
Bruce
Third email: Saturday, April 29, 2023 at 10:04 AM
“…I highly recommend reading the work of Kontsevich, a famous mathematical physicist; in particular, his work, Deformation quantization of Poisson manifolds (1997), is probably more relevant to physics than these other things.”
References to Connor Malin within this website:
https://81018.com/universe-numbers/#Mail
https://81018.com/infinitesimal-composites/#History
Connor –
Do you happen to know the work of Wenxi Yao, a postdoc at Harvard? Koszul duality of quadratic operads, page 9. It is not dated, but it seems recent.
This morning I am reading the work of Pedro Tamaroff and this is what I said about you all here: https://81018.com/infinitesimnal/ composites.
-Bruce
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.
Second email: Friday, Apr 28, 2023, 6:10 AM
“The term infinitesimal composite is meant to provoke the imagery of inserting a set of elements infinitesimally close to another. This has some amount of interaction with physics in the form of quantum field theories and factorization algebras (the precise connection is through something called the little disks operad), so those would be the places to check for interaction with physics. Unfortunately, I am not so familiar with that area of math/physics, so I am likely not of much help. These objects come up in my research since it turns out that this operations of inserting points infinitesimally close helps us understand manifolds.”
– Connor Malin
Thanks, Connor. Excellent. We’re off to the races. You now have somebody who will follow all your work!
May I report your answer to my question to others? I have quite a few people around the world who are helping me sort through these conceptual frameworks.
Thanks.
Warmly,
Bruce
First email: Thu, Apr 27, 2023 at 4:59 PM (slightly updated)
Dear Connor:
You used the term, “infinitesimal composites,” in your January 2023 ArXiv article, The stable embedding tower and operadic structures on configuration space, page 4, paragraph 3. Just a few moments before discovering your article, I had concluded that it was a good description of the Planck scale geometry and the earliest dynamics within Langlands programs and strings. I thought I had invented a word, so I checked it out in a search and found eight others who had used the term.
Yours is the first reference I found within ArXiv. Might you envision your infinitesimal composites to be at or near the Planck scale?
Thanks.
Warmly,
Bruce