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Results for “distinction” 9 papers
Valuation theory. Valuations, Ostrowski's theorem, completions Tagged papers: 79.
Distinction, Number, and the Empirical Filter: The Pre-Arithmetic Research Framework
Several research lines in mathematical physics begin from identities between arithmetic objects and partition functions, or between hierarchical structure and ultrametric geometry, and ask whether any physical system realizes the resulting structure. Each such line must answer the same two…
The Distinction-Based Ultrametric: A Hierarchy Distance Without Primes, and the Statistical Test of Arithmetic Structure in Physical Spectra
Quantum mechanics is written in one completion of the rational numbers, the real line, though Ostrowski's theorem gives one completion for every prime. A line of work reads physical structure through those other places, but its empirical tests of prime-specific geometry in physical systems have…
Invariant Structural Value: Fundamental Constants and Formulas as Invariant Relations
We develop the thesis that the fundamental constants and formulas of physics encode invariant relations rather than unit-dependent magnitudes. Measurable physics is characterized as the invariant quotient of a larger non-measurable mathematical structure modulo redundancy groups: units, coordinates,…
Prime Valuation Depth: Multiplication as Branching, the Calculus of Indications, and the Structural No-Cloning Reading
This paper develops a structural reading of the p-adic valuation as a measure of depth along a prime branch of the integer factorization tree, rather than a measure of size. The reading, grounded in Ostrowski's classification of absolute values on the rationals, is proposed as a bridge between the…
The Consilience Framework: From Valuation Theory to the Void — A Cross-Domain Synthesis
This memo synthesizes two deep-dive conversations on valuation theory and foundational mathematics into a unified framework. We trace the complete hierarchy from the void (unmarked state) through the calculus of distinctions (Laws of Form), ZFC set theory, and Ostrowski's theorem, arriving at a…
The History and Future of Measurement Stratigraphy, Number Theory, and Valuation Theory
[We propose a unified framework — the Stratigraphy of Measurement — that reinterprets the history of number systems as a sequence of expanding distinction operations. Each era adds a new enclosure: marking ($\\mathbb{N}$), comparing ratios ($\\mathbb{Q}$), convergent sequences ($\\mathbb{R}$_comp),…
The p-Adic Temperley-Lieb Parameter: Cyclotomic Units, Markov Traces, and the p-Adic Jones Polynomial
In Phase 1, we defined the p-adic braid group $B_n(\mathbb{Q}_p)$ on the Bruhat-Tits tree $\mathcal{T}_p$ and showed it satisfies the standard braid relations. Here we complete the connection to the Temperley-Lieb algebra and the Jones polynomial at non-archimedean places. The TL algebra parameter…
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…
Principia Ontologica
Human understanding operates through representational models rather than direct reality apprehension. Alfred Korzybski famously articulated this principle, noting that abstractions derived from perception necessarily differ from their source. Cognitive frameworks function as biological…
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