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Results for “distinction” 9 papers
Numbers & arithmetic. Primes, factorisation and arithmetic structure Tagged papers: 62.
Syntactic Token Calculus: Deriving Particle-like Normal Forms from Distinction Operations (Corrected Revision)
High-energy physics explains the observed particle spectrum through continuous quantum fields, spontaneous symmetry breaking, and a growing inventory of unobservable entities, a framework whose theoretical and experimental costs are substantial and whose falsifiability is contested. A gap remains:…
Non-Computable Reals as Projection Artifacts: A Formal Analysis of Tree‑to‑Manifold Construction of the Continuum
Continuum physics and analysis are formulated over the completed real line, yet every measurement, record, and computation is finite, and the physical role of the uncountable remainder of $\mathbb{R}$ remains unresolved. This paper develops a formal framework for the conjecture that the continuum is…
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,…
The Idempotent Core: Quantity as Broken Distinction and the Hidden Assumptions of Arithmetic and Algebra
Classical arithmetic treats the statement $1+1=2$ as a primitive truth and quantity as a fundamental concept. This paper examines the hidden premise of that statement: the two instances of the numeral $1$ must denote distinct marks. In the calculus of indications, the law of calling — idempotence…
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 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…
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