Upon following the work of Peter Scholze

TO: Peter Scholze, now also associated with Berkeley’s Simons Collaboration on Perfection in Algebra, Geometry and Topology (directed by Martin Olsson).  Scholze’s home institution is the Max Planck Institute for Mathematics, Mathematisches Institut of the Universität Bonn in Bonn, Germany.
FM: Bruce E. Camber
RE: Your very sophisticated work… thank you, in your articles: The Oracle of Arithmetic, Nature (2016), Nature , … ‘grand unification’ theory (2021); ArXiv (35): Geometrization of the local Langlands correspondence (2021); also your homepage(s): Hausdorff, Semanitc, Google Scholar, Publications,  X: Quanta, Wikipedia; inSPIREHEP Geometrization of the local Langlands with Fargues; and YouTube: Interview with Peter Scholze, 2021; Local Langlands as Geometric Langlands on the Fargues-Fontaine Curve, July 2022 and many more.

This page URL: https://81018.com/scholze/ Also: Scholze (2022) and https://81018.com/mathematicians/

Third email:  4 May 2026

TO: Prof. Dr. Peter Scholze
FM: Bruce Camber / The 81018 Project
RE: “Wild Betti Sheaves” and continuous base-2 cosmic scaling

Dear Prof. Dr. Peter Scholze,

Your arXiv article, Wild Betti Sheaves, provides a rigorous formulation for constructing an enlargement of Betti sheaves that supports both an exponential local system on and a Fourier equivalence on all sheaves. In reading your paper, I noticed a striking mathematical and structural alignment between your continuous-filtration of spectra and the discrete-to-continuous information-theoretic scaling framework studied by the The 81018 Project. [1, 2, 3]

The project models the expansion and architecture of the universe as a continuous sequence of 202.34 base-2 notations (or doublings), spanning from the Planck scale to the current age and size of the observable universe. Below are the key structural points where your new construction in “Wild Betti Sheaves”  provides a natural language for this cosmic scaling: [1]

1. Continuity of the Scaling Section and \(S(0)\)

In Section 2 of your article, you consider the non-compact unit \(S = S(0) \in \mathcal{W}\), defined as the colimit of \(S(r)\) over \(r > 0\) once continuity is enforced at zero. [1]

  • The Scaling Parallel: The 202.34 notation model views the initial state of the universe (Planck scale) not as an isolated singularity, but as a continuous source from which all subsequent scales are “pulled” up.
  • Continuity Condition: Your completeness condition and the continuous limit exactly mirror the way local physical parameters (e.g., mass, charge, energy) are constrained to transition smoothly across the 202 discrete scale steps without producing singularities. [1]

2. Resolving the 1.754 Geometric Offset via Cohomology

A central feature of the 202.34 notation framework is the slight mathematical divergence between the expansion of space and time:

  • Mapping Planck length to the current observable edge of the universe requires exactly 204.08 doublings.
  • Mapping Planck time to the current age of the universe requires exactly 202.33 doublings.
  • This leaves a discrepancy of 1.754 steps.

In the context of your construction, this offset acts as a global cohomological obstruction. Because local geometric data cannot be glued into a perfectly flat global section across all scales, it introduces a “twisting.” This aligns with your observation that the category of coefficients of this theory behaves as a non-trivial -torsor. Cosmic expansion and dark energy emerge as the physical manifestation of this categorical twisting. [1, 2]

3. Wild Fourier Transforms as Scale Translation

Your universal solution uses a continuous kernel to establish a Fourier transform on all sheaves. [1, 2]

  • In our model, the Planck scale (Notation 1) and the Observable Universe (Notation 202) are treated as geometric and information-theoretic duals.
  • Your Fourier equivalence provides the exact functorial mechanism to explain how high-frequency quantum information at the infinitesimal level maps directly to the low-frequency, large-scale properties of the cosmos.

I believe that the continuous, \(\mathbb{R}\)-filtered approach you have developed for Betti sheaves provides the exact homological framework needed to transform this discrete, information-theoretic cosmological model into a mathematically rigorous, singularity-free continuum.

Thank you for your time and for your continuous contributions to the foundations of arithmetic geometry.

Sincerely,
Bruce

Second email: 3 April 2025

Dear Prof. Dr. Peter Scholze:

I have a radically different starting point that will accommodate your mathematics and geometries better than big bang cosmology: https://81018.com/ There is a reference to your last conference and your work and that of your colleagues at Berkeley. Those references will be duplicated in a much more playful rendering of that page (Grok’s help). It is still early in the process; do you have any words of guidance? Thanks.

Most sincerely,

Bruce

First email: August 1, 2020 at 4:51 PM

RE: “Perfectoids” and the first 64 base-2 notations from the Planck scale

Dear Prof. Dr. Peter Scholze:

Your work from November 22, 2011 has come to my attention.  Have you ever considered placing your work within a container from the Planck scale, particularly Planck Time to the current time using base-2 notation? There are 202 base-2 notations; my conjecture is that the first 64 notations are pre-quantum and provide a substantial domain for perfectoid rings and spaces. And, might spheres be added?

Thank you.

Warm regards,

Bruce

_____

__ “This is a shallow book school on deep matters about which the author speaker knows next to nothing. -R.P. Langlands”

Peter Scholze, July 2022