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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.
Quantum foundations. Measurement, Born rule, interpretation Tagged papers: 81.
Measurement as Place-Crossing: Completion-Selective Adelic Projection
We propose a structural reframing of the quantum measurement problem in number-theoretic terms. By Ostrowski's theorem, the completions of $\mathbb{Q}$ consist of a single Archimedean place ($\mathbb{R}$) and countably many $p$-adic places ($\mathbb{Q}_p$); standard quantum mechanics is formulated…
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)…
Tate's Thesis as a Template for Adelic Quantum Mechanics: Local-Global Structure and the Emergence of Archimedean Artifacts
We propose that Tates 1950 thesis provides an explicit structural template for constructing adelic quantum mechanics. The Dragovich programme has realized this template for free theories; Huang, Stoica, and Zhong (2022) provide an independent proof-of-concept in CFT. We interpret the Langlands…
Functional Decoupling Framework for p-adic Hamiltonian Models of Granular Field Interactions
The reconciliation of continuous temporal evolution with discrete physical granularity remains a central challenge in theoretical physics, requiring novel mathematical approaches to model localized action within unbroken fields. This study introduces a functional decoupling framework that divides…
Mathematical Structures Underlying Physical Laws
This work addresses the foundational schism in modern physics, which arises from the perceived incompatibility between classical continuous, deterministic reality and quantum discrete, probabilistic phenomena. The Post-Quantum Synthesis (PQS) framework resolves this by asserting that the universe is…
NEW LANGUAGE FOR MATH
This report presents a fundamental reframing of Causal Set Theory (CST) within the language of category theory, establishing a relational process ontology (RPO) for fundamental physics. By recasting causal sets as small, thin categories, this framework achieves a categorical reification of…
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