Within the extended MEST-TPC framework, we treat the macroeconomic system as a “mass–energy–spacetime economic density field”
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(
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,
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, in which production, consumption, and finance are merely projections of the same structural tensor onto different subspaces.
To characterize the geometric features of economic activity, we introduce three structural modes:
1. Steep structure
This refers to regions where the gradient
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is significantly amplified and resources and power are highly concentrated.
In the real economy, capital-intensive production sectors, large corporate groups, and mainstream institutional capital
typically constitute the primary carriers of steep structure.
2. Smooth structure
This refers to a background field that is broadly distributed across space and agents, with relatively low gradients.
The dispersed consumption activities of millions of households, together with a large number of small, capital-constrained retail investors,
form the smooth structural base of the economic system.
3. Turning-point structure
This refers to structural components where second derivatives or curvature change significantly,
allowing the system’s trajectory to be altered rapidly in local regions.
It corresponds to accelerators, reversal points, and amplifiers in the economy.
In the financial domain, interest rates, credit expansion, leverage, and high-frequency trading
operate precisely by creating local turning points that reshape the distribution of energy and risk
between the steep and smooth structures.
In this sense, we can write a first-order approximate decomposition of economic structural variables as follows:
• Production structure and institutional capital contribute primarily to the steep structural component of the economic tensor;
• Consumption structure and retail capital form the main smooth structural component of the economic tensor;
• Financial structure together with speculative capital and leveraged trading manifests chiefly as the turning-point structural component,
which alters the relative weights of the first two and triggers system-level transitions at critical moments.
It is important to emphasize that this is not an essentialist labeling of production, consumption, or finance,
but a structural decomposition:
the same agent can simultaneously possess steep, smooth, and turning-point components in different phases and contexts.
However, in today’s global economic configuration, the associations
“production + institutions ≈ steep,” “consumption + retail ≈ smooth,” and
“finance + speculative capital ≈ turning-point”
provide a useful zeroth-order approximation with considerable explanatory power.
On this basis, we can further embed the financial turning-point tensor into the unified MEST-TPC framework,
using a common turning-point computation method to describe transition risks in both galactic structures
and financial structures within a single mathematical language.
在 MEST-TPC 的扩展框架下，我们将宏观经济系统视为一个“质能—时空经济密度场”
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(
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，其中生产、消费与金融只是同一结构张量在不同子空间中的投影形式。
为了刻画经济活动的几何特征，我们引入三类结构模式：
1. “陡峭结构（steep structure）：
指在某些方向上梯度
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∇
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∣
显著放大、资源与权力高度集中的区域。
在现实经济中，资本密集型的生产部门、大型企业集团以及主流机构资金，
通常构成陡峭结构的主要载体。”
2. “平滑结构（smooth structure）：
指在空间与主体维度上分布广泛、梯度较低的背景场。
分散在千家万户的消费活动，以及数量众多、资金有限的散户投资者，
构成了经济系统的平滑结构底座。”
3. “拐点结构（turning-point structure）：
指二阶导数或曲率变化显著、能够在局部区域内迅速改变系统演化方向的结构分量，
对应经济中的加速器、反转点与放大器。
在金融领域，利率、信用扩张、杠杆与高频交易等，
正是通过制造局部拐点来改变陡峭结构与平滑结构之间的能量与风险分布。”
在这个意义上，我们可以将经济结构变量作如下一阶近似分解：
• “生产结构与机构资金，主要贡献经济张量的“陡峭结构分量”；”
• “消费结构与散户资金，主要构成经济张量的“平滑结构分量”；”
• “金融结构与游资、杠杆交易，则主要表现为“拐点结构分量”，
用以改变前两者的相对权重，并在关键时刻触发系统级转折。”
需要强调的是，这并非对生产、消费或金融的本质标签，而是一种结构分解：
同一主体在不同阶段和情境中，可以同时具有陡峭、平滑与拐点三种成分。
但在今天的全球经济格局下，“生产–机构 ≈ 陡峭”，“消费–散户 ≈ 平滑”，
“金融–游资 ≈ 拐点”，是一个具有解释力的零阶近似。
在此基础上，我们可以进一步将“金融拐点张量”接入 MEST-TPC 的统一框架之中，
用统一的拐点计算方法同时刻画星系结构和金融结构的转折风险。