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Results for “foundations” 10 papers
Valuation theory. Valuations, Ostrowski's theorem, completions Tagged papers: 79.
Completion-Invariance of Physical Ontology: The Rational Base Field in Quantum Foundations
We propose and formalize a principle of completion-invariance for physical ontology: since all recorded measurement outcomes are rational numbers, the archimedean completion $\mathbb{R}$ and the non-archimedean completions $\mathbb{Q}_p$ of the rational base field $\mathbb{Q}$ are equally…
Completeness Senses and the Levi-Civita Field: Ordered Non-Archimedean Number Systems Beyond Ostrowski's Classification
Ostrowski's theorem classifies every nontrivial rank-1 absolute value on the rationals: the Archimedean absolute value and, for each prime p, a p-adic absolute value. Their completions are the real numbers and the p-adic fields. This classification is often read as closing the question of what a…
Five Objections, One Standard: An Evidence-Graded Adjudication of a Critique of Post-Quantum Synthesis
A five-point red-team critique of the Post-Quantum Synthesis (PQS) research program was examined point by point against the primary sources it targets and the external literature it invokes. Each objection was graded against a symmetric evidence standard: the objection's own factual premises were…
Valuation Without R: A Category-Theoretic Foundation for Finite Measurement
Measurement in physics is always finite and approximate — yet its mathematical foundations are embedded in the Archimedean continuum of real numbers and the cumulative hierarchy of set theory. We invert this dependency: the act of measurement is axiomatized as a graded distinguishability map…
ODR Thesis: The Compton Count as the Only Primitive
The Ontological Distribution of Reality (ODR) framework identifies a particle with its Compton count \(N_C = m/m_P \in \mathbb{Q}^+\), a dimensionless rational number whose prime factorization assigns it a fixed vertex on the Bruhat–Tits tree. This paper synthesises five research questions into a…
ODR Thesis: The Compton Count as the Only Primitive — A Five-Question Synthesis
The Ontological Distribution of Reality (ODR) framework identifies a particle with its Compton count \(N_C = m/m_P \in \mathbb{Q}^+\), a dimensionless rational number whose prime factorization assigns it a fixed vertex on the Bruhat–Tits tree. This paper synthesises five research questions into a…
Counterfactual Physics: What If p-Adic Methods Had Won?
The p-adic approach to physics was nearly mainstream. Vladimirov and Volovich developed p-adic quantum mechanics in the 1980s. Freund and Witten connected p-adic string amplitudes to the adelic product formula in 1987. Dragovich extended p-adic methods to cosmology and the Standard Model. Yet by…
REIFICATION AND NON-ARCHIMEDEAN FOUNDATIONS IN THEORETICAL PHYSICS
This synthesis examines the persistent difficulties in contemporary theoretical physics through the lens of the Copernican diagnostic: the proliferation of unobservable entities (virtual particles, dark matter, the inflaton, etc.) signals not that nature is complex but that the descriptive framework…
Static Architecture of Reality
URL: https://papers.qnfo.org/papers/static-architecture-of-reality/ Date: 2026-03-21 Version: 1.0.1 Human consciousness presents a world in constant flux. From the rotation of planets to the decay of particles, every measurement confirms a dynamic universe. This experience of temporal flow is so…
Hydrodynamic Stability Hypothesis
This work identifies a “chronological fallacy” at the heart of quantum foundations: the axiomatization of quantum mechanics by von Neumann (1932) predated the rigorous formulation of classical probability by Kolmogorov (1933), creating an artificial schism between physics and statistics. To resolve…
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