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Results for “topological” 16 papers
Primality as a Non‑Archimedean Structure Projected onto the Real Line
Primes are defined as discrete divisibility objects in the integers, yet many analytic phenomena—Riemann zeros, cryptographic protocols, and quantum‑information patterns—depend on a continuous view of number theory. The gap lies in the lack of a real‑valued functional that captures $p$‑adic…
The Exchange Phase as a Logical Scalar: R = e^(2 pi i s) from the Re-Entrant Calculus
The boson/fermion dichotomy is conventionally presented as a primitive classification of nature. Recent work established that the underlying invariant is the relation between the exchange phase of identical particles and their topological spin, R = e^{2πis}, with the dichotomy as its shadow in three…
The Universe Category: A Single Functor Encoding Quantization, Stability, and Factorization
This paper proposes a single categorical object — a functor from the divisibility category of the positive integers to the category of smooth compact manifolds — and investigates whether its image simultaneously encodes three structures that have historically been treated as separate: quantization…
The Adelic ZBW Programme: ZBW-Majorana Hypothesis, Ostrowski-QEC Synthesis, and Cross-Programme Consilience
The ZBW-Majorana hypothesis, developed across four companion papers (P1--P4), establishes that Zitterbewegung (ZBW) --- the rapid trembling motion of Dirac fermions at the Compton scale --- is a $\mathbb{Z}_2$ topological observable that distinguishes Dirac from Majorana fermions at the hardware…
Fine-Structure Constant as a Cross-Ratio: A Geometric Reframing of α
The fine-structure constant $\alpha \approx 1/137.036$ is reframed as the cross-ratio of two measurable electron length scales (classical radius $r_e$ / Compton wavelength $\lambda_C$). This reveals projective invariance in $\alpha$, connects to integer-ratio precision experiments, and integrates…
p-Adic Braid Groups on Bruhat-Tits Buildings
The standard braid group $B_n$ is defined as the fundamental group of the configuration space of $n$ distinct points in $\mathbb{R}^2$, $\pi_1(\text{Conf}_n(\mathbb{R}^2))$. This construction is inherently archimedean: it relies on the continuous topology of $\mathbb{R}^2$ to define braiding as…
Zitterbewegung as a p-Adic Observable: Ultrametric Readout and Intrinsic Topological Protection
The Zitterbewegung (ZBW) of a Dirac fermion — the rapid oscillatory motion at the Compton frequency arising from interference between positive- and negative-energy states — has resisted direct experimental observation for nearly a century. The standard interpretation attributes this to the Compton…
Base-Invariant Number-Theoretic Patterns in Fundamental Constants
This presents a systematic, first‑principles investigation of the mathematical structures that underlie fundamental constants, freed from the arbitrariness of numeral‑system representation. By focusing exclusively on properties that are independent of any choice of base we uncover striking patterns…
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…
Spectral Analysis of Anomalous Diffusion on p-Adic Fractals
The reconcilement of continuous Riemannian geometry with the discrete arithmetic of the integers remains one of the most profound challenges in mathematical physics, particularly regarding the spectral interpretation of the Riemann zeros (Berry & Keating, 1999). While standard diffusion on…
Spectral Dynamics on Bruhat-Tits Trees
The probabilistic nature of prevalent primality tests, such as Miller-Rabin, presents a fundamental limitation where certainty is achieved only asymptotically. This study proposes a deterministic alternative rooted in the non-Archimedean geometry of p-adic numbers, specifically leveraging the…
UNIFIED FIBER BUNDLE FORMALISM FOR THE HOPF FIBRATION
The history of theoretical physics is punctuated by the discovery of mathematical structures that appear with startling ubiquity across disparate scales and domains. From the simple harmonic oscillator describing both planetary orbits and quantum fields to the pervasive role of symmetry groups,…
Topological Quantization and Spectral Filtration
This paper addresses the geometric crisis in discrete computation by establishing a unified framework that synthesizes arithmetic topology, non-linear dynamics, and thermodynamic optimality. We posit that prime numbers behave as irreducible topological knots within a three-dimensional state space, a…
Prime Numbers as Universal Optimization Primitives
The scholarly understanding of prime numbers is structured around four paradigms: quantum chaos, classical optimization, algorithmic information theory, and deterministic law. However, these paradigms are marked by unresolved tensions—dynamical, hierarchical, and methodological—that have hindered a…
Biological and Engineered Computational Systems
This work establishes the categorical equivalence between biological and engineered computational systems through an explicit mathematical formalism. The central thesis posits that these seemingly disparate domains implement equivalent computational architectures, an equivalence that manifests…
Topological Origins of Number Theory
This establishes a theoretical framework wherein number-theoretic structures, particularly prime factorization, emerge as causal signatures of topological organization in quantum critical systems. We posit a foundational ontological inversion: physical reality, including particles and spacetime, is…
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