讨论：当今十大物理学难题的哲学基础 Discussion: The Philosophical Basis of the Top Ten Physics Problems

Arcman

Arc Geometry I: Differential and Topological Structure of Arc Helices

弧几何学 I：弧旋的微分结构和拓扑结构

https://doi.org/10.5281/zenodo.18882067

                               
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Arcman

Arc Theory v23: Extremal CFT Uniqueness, Rademacher Regularization, and Geometric Classification of Modular Saddles

弧理论 v23：极值共形场论唯一性、拉德马赫正则化和模鞍的几何分类

https://doi.org/10.5281/zenodo.18895656

Creators: Arcman

Resource Type: Preprint / Working Paper

Description:
We analyze the uniqueness of extremal conformal field theories under modularinvariance and sparsity conditions. While the uniqueness of the partition function can be established, the general existence remains open beyond low levels. We further study the convergence of the Poincaré series representation of the partition function via Rademacher regularization. Finally, we classify non-perturbative handlebody saddles of three-dimensional AdS gravity via modular group orbits.

Notes on v23:
This manuscript explicitly addresses the analytical obstruction in the large-central-charge regime. It includes rigorous mathematical annotations on the unitarity constraints on Fourier coefficients for extremal CFTs (with $k > 3$) and details the analytical continuation ofthe regularized Niebur-Poincaré series via Kloosterman sums and modified Bessel functions.

Keywords:
Extremal Conformal Field Theory; Modular Invariance; RademacherRegularization; AdS3 Gravity; Quantum Gravity; Arc Theory; Arc Geometry.

Arcman

电弧旋流形的几何构造和运动方程

概述

本文以11章的篇幅，对电弧旋流形进行了公理化推导，建立了一个严谨的运动学演化几何框架。本文摒弃了传统的固有质量和电荷假设，将这些物理可观测量表述为涌现的几何和拓扑不变量。具体而言，它们被数学地描述为模配分函数内拓扑鞍点的全息投影和相位诱导，并受到空间边界条件的约束。索取全文

Geometric Construction and Equations of Motion for the Electric Arc-Helix Manifold

https://doi.org/10.5281/zenodo.18883200

Overview:

This paper presents an 11-chapter axiomatic derivation of the Electric Arc-Helix manifold, establishing a rigorous geometric framework for kinematic evolution. By departing from the conventional assumption of intrinsic mass and charge, this work formulates these physical observables as emergent geometric and topological invariants. Specifically, they are mathematically described as the holographic projections and phase inductions of Topological Saddles within a Modular Partition Function, subjected to constrained spatial boundary conditions. Full articleh

                               
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Arcman

Arc Geometry II: Variational Structures and Energies of Arc Helices

弧几何 II：弧螺旋的变分结构和能量

https://doi.org/10.5281/zenodo.18905574

                               
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Description:
Arc Geometry II develops the variational framework of Arc Geometry and continues
The program initiated in Arc Geometry I: Differential and Topological Structure.

Arc Geometry studies a class of spatial curves called Arc Helices, defined by a
two-frequency helical modulation. In Arc Geometry I it was shown that these curves
naturally embed in a torus and realize torus knots when the frequency ratio is rational.

The present work establishes the variational structure associated with Arc Helices.
Its main contributions include explicit formulas for curvature and torsion, the
introduction of the Arc energy functional E_arc = integral (kappa^2 + lambda tau^2) ds,
the discrete energy spectrum of closed Arc Helices indexed by torus knot type,
a small-modulation asymptotic formula, a stability criterion under perturbations,
and numerical illustrations of curvature modulation, torsion modulation, and torus-knot
realizations.