Knot-Synchronization-Adhesion Unified Theory: A Working Hypothesis on the Topological Origin of Lepton Masses

Abstract

We present a working hypothesis proposing that lepton masses originate from topological properties of knots, specifically their Möbius energy. By assigning specific knots to each lepton generation—the trefoil (3₁) to the electron, the achiral knot 6₃ to the muon, and the torus knot 7₁ to the tau—we find that the mass ratios can be reproduced with notable accuracy.

Key Findings:

1. Mass Scaling Constant: We empirically observe that the mass scaling constant $\gamma_m \approx 0.373$ closely matches the inverse of Euler's number ($1/e \approx 0.368$) with a relative deviation of only 1.4%.

2. Selection Rule: We identify a "Torus + Achiral" pattern where odd generations correspond to chiral torus knots, while the second generation (muon) corresponds to an achiral, hyperbolic knot. This structural asymmetry may offer insight into the muon's distinctive physical properties.

3. Accuracy: The proposed model reproduces the $\tau/\mu$ mass ratio with 1.3% error (fitted) or 2.6% error (theoretical $\gamma = 1/e$).

Note: This work is a result of the "Yui Protocol Project," a collaborative research framework between a human researcher and multiple AI systems (GPT, Gemini, Claude, Copilot). It is presented as a working hypothesis to stimulate further investigation into the topological foundations of particle physics.