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611 papers from the QNFO program, filed on nine shelves by the reader each one is written for: energy per answer, error correction, physics, numbers and p-adics, logic and formalism, AI and knowledge, autonomous systems, assessments, and cross-cutting essays. Every page renders its mathematics and can be questioned in place. How a living paper works.
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Numbers & p-adics papers 6 papers
Mathematicians. Valuation theory and the p-adic and adelic programme, Bruhat-Tits trees and ultrametric geometry as mathematics, Ostrowski's theorem, numeral and radix systems, primes, arithmetic and algebraic structures, zeta and gamma functions.
Research operations. Fleets, pipelines and provenance Tagged papers: 37.
Functorial Invariance Across Presentations of the Prime Numbers, with Context-Relative Quantitative Illustrations
The prime numbers admit many simultaneous presentations: as the atomic subset of the natural numbers, as the support of the von Mangoldt function, as the zero data of the Riemann zeta function, as the output of sieve procedures, as primes inside Beatty-type sequences, and as the output of concrete…
Vertex-Anchored Geometry: Discrete Extremal Points as the Organizing Primitive of Non-Archimedean Space
Non-Archimedean (ultrametric) geometry, in which the strong triangle inequality $d(x,z) \le \max\{d(x,y),d(y,z)\}$ replaces the Euclidean one, lacks the smooth infinitesimal structure on which most physical and geometric intuition rests. We argue that in this setting the correct organizing primitive…
The Adelic Cross-Domain Program: From the Fine-Structure Constant to the Standard Model Mass Spectrum via Bruhat-Tits Trees
v3.2 corrections (2026-07-25): arithmetic errors in mass ratio triplets corrected (5 of 9 verified independently); Efimov lambda derivation replaced with honest structural correspondence; constraining literature section added per KIF-18 symmetry; semigroup density epistemological risk acknowledged;…
The Adelic Constraints Project — A Complete Account
<p></p> <p>This document is a complete, self-contained account of a research project conducted in May 2026. The project asked whether a specific piece of pure mathematics — the fact that the rational numbers can be "completed" in multiple incompatible ways, and that a single identity links all…
Comprehensive Technical Framework for Network Isomorphism
This paper investigates the structural and dynamic isomorphisms between transportation networks, neural architectures, and quantum systems. We synthesize literature from mathematical physics, transportation science, and computer science to address a critical gap regarding the lack of an integrated…
UNIFIED FIBER BUNDLE FORMALISM FOR THE HOPF FIBRATION
The history of theoretical physics is punctuated by the discovery of mathematical structures that appear with startling ubiquity across disparate scales and domains. From the simple harmonic oscillator describing both planetary orbits and quantum fields to the pervasive role of symmetry groups,…
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