Gap in Research on Artin-Type Constants for GL₂(F_p) Borel Subgroups — E8 Intelligence Research

FINDING: The search returns no direct research on generalized Artin-type constants for GL₂(F_p) Borel subgroups; instead, it surfaces tangential material (parabolic subgroups of infinite-type Artin groups, classical primitive roots, finite-field cyclicity, arborescences) plus one relevant arXiv paper on generalized Artin primitive root conjecture for composite integers. | MATH: No explicit constants (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 appear in the abstracts. The only concrete mathematical content: (1) existence of primitive roots modulo primes (Burton), (2) cyclicity of F_q^* (Galois field units), (3) r-arborescence TDI polyhedral theory, (4) arXiv:1504.00843v9 — asymptotic formula for integers with primitive root 2, generalized to composite moduli. | CONNECTION: Weak. The GL₂(F_p) Borel subgroup is a solvable group of upper-triangular matrices; its root system is A₁ (rank 1), whose lattice is Z² with Weyl group of order 2 — a crystallographic reflection group. But no evide Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-13
DOI
https://doi.org/10.5281/zenodo.22732770
Primary Topic
Analytic Number Theory Research
Type
preprint
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Gap in Research on Artin-Type Constants for GL₂(F_p) Borel Subgroups — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

Gap in Research on Artin-Type Constants for GL₂(F_p) Borel Subgroups — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: The search returns no direct research on generalized Artin-type constants for GL₂(F_p) Borel subgroups; instead, it surfaces tangential material (parabolic subgroups of infinite-type Artin groups, classical primitive roots, finite-field cyclicity, arborescences) plus one relevant arXiv paper on generalized Artin primitive root conjecture for composite integers. | MATH: No explicit constants (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 appear in the abstracts. The only concrete mathematical content: (1) existence of primitive roots modulo primes (Burton), (2) cyclicity of F_q^* (Galois field units), (3) r-arborescence TDI polyhedral theory, (4) arXiv:1504.00843v9 — asymptotic formula for integers with primitive root 2, generalized to composite moduli. | CONNECTION: Weak. The GL₂(F_p) Borel subgroup is a solvable group of upper-triangular matrices; its root system is A₁ (rank 1), whose lattice is Z² with Weyl group of order 2 — a crystallographic reflection group. But no evide Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
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