A Conjecture of Matter:On the Mutual Winding Between Material Entities, Their Adherence to Space, and the Origin of Forces— A Tentative Analysis of the Particle Mass Spectrum

This paper, based on the matter–matter mutual-winding theory, utilizes publicly available particle mass data from the Particle Data Group 2022 report to conduct a linking number assignment analysis for the elementary particles of the Standard Model. Taking the electron mass ($m_e \approx 0.511$ MeV/c²) as a benchmark and setting its linking number to $n_e = 1$, the linking number of each particle is inversely determined. The analysis covers the three generations of charged leptons, the W/Z/Higgs/top quark, and some quarks. The principal numerical findings include: the linking number ratio of the three generations of charged leptons is $n_e : n_\mu : n_\tau \approx 1 : 207 : 3477$; and that of the W/Z/Higgs/top quark is $n_W : n_Z : n_h : n_t \approx 8 : 9 : 12 : 17$. Attempts to assign linking numbers to quarks and neutrinos are constrained by theoretical uncertainties in the definition of quark masses and by the unknown nature of neutrino masses. This paper emphasizes that the above analysis constitutes tentative numerical exploration based on the theoretical framework, that all linking number assignments are currently merely inverse-derived results, and that their correctness awaits independent experimental verification.

(Statement on the Nature of This Analysis

This analysis constitutes a tentative exploration based on the matter–matter mutual-winding theory, not a conclusion that has been verified by experiment. The linking number conjecture proposed herein—that particle masses are correlated with linking numbers, and that the linking number ratios of the three generations of leptons and those of the W/Z/Higgs/top quark are integer ratios—is based entirely on inverse-derived results from known particle mass data. It currently possesses only descriptive value and has not yet been independently verified by experiment. The assignment of a linking number of one to the electron is a benchmark assumption of this analysis, the validity of which has not been proven within this theoretical framework. The theory is currently unable to provide quantitative descriptions of physical processes that the Standard Model has already precisely predicted, such as the decay channels and production cross-sections of the Higgs boson. Readers must take full account of these theoretical limitations when citing any conclusions from this paper.

Note on AI-Assisted Computation

Certain mathematical derivations and physical calculations in this paper were performed by an AI tool (large language model) based on the theoretical framework and postulate system provided by the author. Specifically, the AI tool contributed to: formula derivation, equation solving, integral evaluation, series summation, and recalculation verification of established quantum mechanical results.

All physical insights, core assumptions, logical premises, and the theoretical framework itself were independently developed by the author. The AI tool served solely as an auxiliary instrument for mathematical derivation and computational verification, comparable in role to symbolic computation software or numerical tools routinely employed by researchers. The author has reviewed every derived result for physical plausibility, consistency with known experimental data, and logical coherence, and assumes full responsibility for all conclusions.

This statement is provided in the interest of academic transparency, while clearly distinguishing between the originality of ideas and the auxiliary role of computation.)