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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.
Information theory. Entropy, capacity and coding bounds Tagged papers: 34.
Quantum Statistics from the Adelic Product Formula: The Squarefree Origin of the Fermi-Dirac/Bose-Einstein Distinction
The Bose-Einstein and Fermi-Dirac occupation distributions are read as the maximum-entropy solutions of one lattice with two multiplicity rules: the unrestricted integer lattice (Dirichlet series the Riemann zeta function) and the squarefree restriction (a ratio of two zeta values). The paper…
The Self-Referential Scalar Family: e, the Half-Turn, and the Unification of Information Theory, Statistics, Thermodynamics, and QND Measurement in the Adelic Picture
The p-adic maximum-entropy distribution of Adelic Shannon Theory is exactly the Bose-Einstein occupation distribution at fugacity 1/p, i.e. at inverse temperature ln p at the p-adic place; the squarefree restriction of the integers is its Fermi-Dirac counterpart, with occupation probability 1/(p+1)…
Adelic Rate-Distortion Theory: The p-Adic Distortion Measure and the Adelic Information-Rate Function
The Adelic Shannon Theory [1] generalised channel capacity to the adele ring $\mathbb{A}_{\mathbb{Q}}$. The companion bridge paper [2] established that the entropic number $(x, S)$ from Measurement Stratigraphy [3] is precisely the adelic information vector…
Adelic Entropic Numbers: When the Adelic Information Vector Becomes the Entropic Number
Two papers, written independently on the same day, converge on the same structure from opposite directions. Adelic Shannon Theory [1] generalises Shannon information theory to the adele ring $\mathbb{A}_{\mathbb{Q}}$, defining the *adelic information vector…
Adelic Shannon Theory: From Problem Statement to Constructive Foundations
Standard Shannon theory — channel capacity, entropy, source coding, and the Gaussian noise model — is archimedean: it measures information in bits over $\mathbb{R}$. The Adelic Physics Programme's central claim — $\mathbb{Q}$, not $\mathbb{R}$, is the physically accessible base field — suggests that…
Projective Geometric Frameworks for Semantic Structures
Current critical literature often dismisses Large Language Models (LLMs) as statistical parrots operating via mere stochastic approximation, yet their capacity for cross-lingual zero-shot inference suggests the internalization of deep, invariant topological rules. This study establishes that…
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