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

特别是当代，数学对象不是点、线、面，而是“结构生成律”。

Especially in contemporary times, the object of mathematics is not points, lines, or planes, but the "law of structural generation".

Arcman

Arc Geometry I: Differential and Topological Structure of Arc Helices

弧几何学 I：弧螺旋的微分结构和拓扑结构

[url=https://zenodo.org/records/18869377]https://zenodo.org/records/18869377[/url]

                               
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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.

Arcman

更多研究资料：

https://www.researchgate.net/profile/Frank-Meng-10

Arcman

当代数学物理的理论与技术骨架支撑之一是黎曼几何。而黎曼几何严格意义上是欧氏几何体系的深度延续与扩展，逻辑本质仍旧停留在“点”空间的概念中。

Arcman

《 e-Arc-Helix》Volume 0, I, II, III, IV, in total 5/set, has been published on Amazon and IngramSpark.

《电弧旋》第 0、1、2、3、4卷，共5册/套，已在亚马逊和IngramSpark上发售。

Arcman

“虚无” = everything，如同白光是所有光那样。一切“实相”皆如常，源于斯归于斯，此亦世间“无常相”。

你的想法变了，你的宇宙必将随之改变。你“没”了想法就是自性回“空”。

有鉴于人类认知的极限边界是表观，即现象。因此，形式决定存在。
你用什么“样子”理解世界，你的“眼光”就定义了怎样的世界，包括虚幻不实，但非虚无自恒。

虚无自在，变幻无穷。虚无仅一，宇宙各异。
你的宇宙感受决定你从同一个自然虚无生产出何种宇宙。这就是弧学认识论的底构逻辑。


“Nothingness” = everything. just as white light contains all light. All manifest realities run their natural course: from it they arise, and to it they return. This, too, is the world’s form of impermanence.

When your thoughts change, your universe changes with them. When thought falls away, your intrinsic nature returns to Emptiness.

Human cognition can reach no further than appearances—that is, phenomena. Therefore, Form determines existence.
The “form” through which you understand the world determines the world your way of seeing brings forth. This includes what may be illusory or unreal—but not self-abiding Nothingness itself.

Nothingness is self-existent, yet infinitely mutable. Nothingness is one; universes are many and distinct.
Your felt sense of the universe determines what kind of universe you bring forth from the same natural Nothingness. This is the underlying logic of Arc Theory epistemology.