Dimensional Scaling of Tensor Identities

The documents outline a Python-based computational framework for simplifying tensor contractions, specifically focusing on the relationship between the Levi-Civita symbol ( $\epsilon$ ) and the Kronecker delta ( $\delta$ ) across different dimensions. By moving from 2D to 5D, the system demonstrates that the resulting scalar constants follow the factorial-based general formula $(n-1)!$, where $n$ represents the dimension. This process simplifies complex, highinteraction summations into efficient "direct mapping signals". These mathematical results are then mapped to geometric equivalents: for instance, the 3D identity $2 \delta_{i l}$ corresponds to the BAC-CAB vector identity, while 4D results relate to hyper-volume scaling.

🍁Compositing

Flowchart and Mindmap: Levi-Civita and Kronecker Delta Identities (LC-KDI)
Illustration: Simplify Tensor Products with Epsilon-Delta (TP-ED)
Demo: Comparative Analysis of Dimensional Scaling (DS)
Direct to MCP server:

Simplifying Levi-Civita and Kronecker Delta Identities (LC-KDI) | Cross-Disciplinary Perspective in MCP (Server)

🏗️Structural clarification of Poof and Derivation

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🗒️Downloadable Files - Recursive updates (Feb 10,2026)

Copyright Notice

All content and images on this page are the property of Sayako Dean, unless otherwise stated. They are protected by United States and international copyright laws. Any unauthorized use, reproduction, or distribution is strictly prohibited. For permission requests, please contact [email protected]

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