Published October 27, 2026 | Version v6

Topological Mechanics of Chemical Bonds: A Geometric Hypothesis of Covalent Synchronization in a Constrained 3+1+2 Manifold

Authors/Creators

  • 1. Independent Researcher

Description

Mainstream quantum mechanics and physical chemistry have traditionally approached decoherence and chemical reactions primarily through the lens of energy scalars. Extending our previous geometric hypothesis of quantum entanglement, this paper explores a constrained 3+1+2 multitemporal manifold to reinterpret covalent bonds as the macroscopic topological synchronization of 2D transverse torsional friction. Through this geometric model, we conceptually separate the macroscopic stability provided by 1D phase-anchors (atomic nuclei) from the friction-canceling mechanism of 2D entanglement (valence electrons). By formulating an exploratory geometric equation for topological dissociation energy (E_D) and performing a reverse-calibration against effective nuclear charge (Z_eff) and non-linear extrinsic curvature (K), we achieve a consistent zero-point alignment (~32,000) across different bond orders. This baseline alignment suggests that the proposed geometric equations hold meaningful internal consistency within the multitemporal hypothesis, offering a coherent conceptual pathway to interpret macroscopic chemical bonding through multidimensional constraints.

Notes

Master TOC

 

Version 6

Updated the title and refined Sections 2, 3, and 6 to emphasize the geometric reinterpretation of covalent bonding as an extension of our quantum entanglement hypothesis, incorporating the δτ peripheral elastic boundary, anti-parallel spin-gear cancellation (ω⃗₁ = -ω⃗₂), and existential phase dilution (sin²θτ). Additionally, framed the ~32,000 convergence in Section 6 as a reverse-calibrated zero-point baseline that supports the internal consistency of the derived geometric equations within the framework.

Version 4

Refined the terminology for transverse-time dimensions, replacing 'uncompactified' with 'kinematically suppressed' and 'dynamically constrained.' This update clarifies that while the extra dimensions are macroscopically extended, they are strictly bounded by the hydrostatic pressure of the constraint field.

Version 3

Minor textual refinements for overall clarity and logical consistency.

 

Mathematical formulations and logical structures were refined with the assistance of an LLM

 

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