The Spaghetti-Cloud Model of the Electron: A Geometric Filament Framework from Dynamical Gap to Topology

The Spaghetti–Cloud Model (SCM) of the Electron: Version 4 presents a speculative geometric, dynamical, numerical, and topological phenomenological framework for investigating whether an extended rotational configuration can dynamically generate nontrivial topology without imposing spinorial boundary conditions from the outset.

The model represents an electron-like configuration through an ensemble of closed filaments, local material frames, internal twist, collective rotation, and an effective asymmetric cloud. Its central mathematical object is a dynamical trajectory in the rotation group SO(3), followed by an independent topological diagnosis through continuous lifting to its double cover SU(2).

The numerical validation program follows a structured hierarchy:

geometry → reduced dynamics → recurrence → periodic-orbit identification → local stability analysis → parameter robustness → solver reproducibility → SO(3) closure → SU(2) classification.

For the reported reference realization, the numerical trajectory exhibits a characteristic recurrence period of approximately T ≃ 2.764940789, with recurrence and rotational closure errors at approximately the 10⁻⁹ level. The continuous quaternion lift is numerically consistent with q(T) ≈ −q(0), corresponding, under the normalization U(0) = I₂, to an endpoint consistent with U(T) ≈ −I₂. After two cycles, the lift is consistent with U(2T) ≈ +I₂.

Within the specified reduced equations and tested numerical regime, the resulting trajectory is therefore interpreted conservatively as a numerical candidate for the nontrivial element of π₁(SO(3)) ≅ ℤ₂.

The SCM is not presented as a replacement for quantum mechanics, quantum field theory, or quantum electrodynamics. It does not derive the Dirac equation, electron mass, electric charge, the Born rule, canonical commutation relations, Fermi statistics, or the anomalous magnetic moment. Instead, Version 4 establishes a structured phenomenological research program focused on geometric dynamics, recurrence, rotational topology, numerical reproducibility, and future routes toward falsifiable quantitative predictions.

The central research question is:

Can an extended dynamical geometric configuration generate a nontrivial rotational topology dynamically, without assuming spinorial behavior as an initial boundary condition?

This work is intended as a speculative but explicitly falsifiable mathematical and numerical investigation. Its principal future objective is to derive at least one parameter-independent quantitative prediction that can be confronted with experiment.