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Results for “topological” 6 papers
Numbers & arithmetic. Primes, factorisation and arithmetic structure Tagged papers: 62.
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…
Critical Values on a Non-Uniform Number Line: Bifurcation Markers, Normalization Dependence, and the Conjectured Specialness of Physical Constants
We examine the conjecture that the real number line, as a model of physical state space, is misleadingly uniform: that certain parameter values act as topological phase boundaries rather than smooth increments, and that fundamental constants such as the fine-structure constant $\alpha \approx 1/137$…
Quantitative Bulk–Boundary Correspondence for Anyon Condensation: Two Computable Indices with Explicit Arithmetic
When a $(2+1)$-dimensional topologically ordered phase terminates at a boundary where a subset of anyons condenses, the boundary becomes gapped, and the bulk–boundary correspondence acquires sharp quantitative content: which boundary phenomena are forced by the bulk condensation data, and which…
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…
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…
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