Gravity as a Macroscopic Response of Manifold Tension in Arc Geometry

Arcman

重力作为弧几何中流形张力的宏观响应

Gravity as a Macroscopic Response of Manifold Tension in Arc Geometry

https://doi.org/10.5281/zenodo.19305498

Version-ready description

This record presents a structurally explicit academic formulation of the manifold-tension program in arc geometry. The purpose of the present release is to state the conceptual architecture of arc theory in a form suitable for rational communication with established mathematical and theoretical-physics language, while preserving the distinct internal content of the framework.

Overview

The manuscript proposes that gravitational, weak, and electromagnetic responses may be interpreted as sectoral manifestations of a common manifold-tension substrate, organized in arc-geometric terms. The construction is built from two structurally related bases, called the energy base and the mass base, together with a 2+1 projection principle. Within this setting, a 4:12 partition of a total temporal count 16 yields a baseline ratio

χw=14,\chi_{\mathrm{w}} = \frac{1}{4},χw​=41​,

which is interpreted as a geometric electroweak reference value rather than as a complete derivation of the renormalization-scheme and scale-dependent weak mixing angle of standard quantum field theory.

What this version contains

This version presents the manifold-tension interpretation in a more rigorous academic format by explicitly separating:

• structural postulates
• projection rules
• response ansätze
• toy models
• interpretive claims
  

The paper includes:

• a structural formulation of dual sectoral bases (energy base and mass base);
• a projection rule leading to the 4:12 partition;
• a logarithmically normalized operator-overlap ansatz for a gravitational response modulus;
• a boundary-confinement toy model in which discrete geometric mass scales arise from localized Dirichlet conditions;
• a section on interpretive scope, present limitations, and falsification criteria.
  

Academic positioning

This work is not intended as a polemical rejection of established science. Rather, it is an attempt to present the arc-geometric program in a form consistent with high-standard mathematical and theoretical-physics exposition. In particular:

• the 4:12 split is presented as the output of a projection rule, not as the unconstrained minimizer of the auxiliary reference functional;
• the gravitational overlap formula is stated as an ansatz for a response modulus, not as a completed operator-theoretic derivation of Newton’s constant;
• the mass-emergence construction is stated as a toy boundary-confinement model, not as a full spectral theory of matter.
  

The intention is therefore to make the current status of the manifold-tension program explicit, discussable, and open to scrutiny.

Current status of claims

The present release should be read as a geometric research program rather than as a finalized replacement for established field-theoretic or gravitational frameworks. Its main contribution lies in clarifying the mathematical status of its components and in formulating the resulting relations in a way that allows critical examination and future development.

Citation note

If citing this work, please cite the specific Zenodo version DOI corresponding to the version you used. Zenodo also provides a concept DOI covering all versions of the record.

Version note

This release supersedes earlier versions by providing:

• a stricter separation between definitions, assumptions, propositions, and interpretive remarks;
• a more disciplined academic tone;
• an explicitly delimited statement of limitations and falsification criteria.
  

Key word:

• Arc Geometry
• Manifold Tension
• Gravitational Response
• Sectoral Decomposition
• Energy Base
• Mass Base
• 2+1 Projection Principle
• Electroweak Baseline
• Operator Overlap Ansatz
• Boundary Confinement
• Geometric Mass Scale
• Mathematical Physics
  

版本描述
本文给出弧几何中“流形张力”方案的一种结构化学术表述，目的是在不与传统科学对抗的前提下，以严格、克制且可讨论的数学物理语言，呈现弧理论的独特思想内涵。文稿将引力、弱作用与电磁响应解释为同一几何基底上的不同扇区显现，并以两个结构相关的基底——能量基底与质量基底——以及一个 2+1 投影原则来组织这一框架。在该设定下，总时间计数 16 的 4:12 分裂给出基线比值 χw=1/4\chi_{\mathrm{w}}=1/4χw​=1/4。本文将其理解为一种几何电弱参考值，而非对标准量子场论中具有重整化方案与能标依赖的弱混合角的完整推导。此外，文中提出了一个对数归一化的算子重叠响应假设，用以刻画引力响应模量，并给出一个局域 Dirichlet 边界条件下的边界束缚玩具模型，以说明离散几何质量尺度如何出现。全文明确区分结构公设、投影规则、响应假设、玩具模型与解释性主张，从而使当前弧几何表述能够在高标准学术框架内被审视、讨论与检验。