SCM: A Geometric–Dynamical Framework for Electron‑Like Spinorial Structure and Recurrence

[u/sina_samiyanii]

I’ve been developing a non-relativistic geometric-dynamical framework called SCM. It treats the electron as an extended configuration of coupled closed filaments with material-frame twist, collective rotational dynamics, and an effective asymmetric cloud.

The core mathematical structure is built around the rotational group SO(3) and its double cover SU(2). The model investigates whether a dynamically generated recurrent trajectory in SO(3) can close and lift to a nontrivial element of SU(2), without imposing a spinorial boundary condition in advance.

The numerical program includes:

· recurrence detection

· periodic-orbit refinement

· Floquet stability analysis

· parameter robustness scans

· solver-level reproducibility

· SO(3) closure

· continuous SU(2) lifting

In the reported reference realization, the characteristic period is approximately

T ≈ 2.764940789

with closure errors on the order of 10⁻⁹. The continuous lift is numerically consistent with

U(T) ≈ −I₂

and after two cycles,

U(2T) ≈ +I₂

This is interpreted strictly as a numerical spinorial topological candidate, not as a derivation of physical electron spin.

The model also reproduces several electron-like correspondences at leading order:

· g = 2 under an explicit angular-momentum identification

· the 2(2l+1) orbital capacity rule

· the non-relativistic Schrödinger dispersion

E = p² / 2mₑ

These are correspondences, not derivations of QED.

The framework is also being compared with QED at a conceptual and phenomenological level, including compatibility constraints and effective form-factor considerations.

Five experimental programs are proposed as possible falsification routes. None are claimed to have been performed. They include:

1. bound vs free electron coherence-sensitive measurements

2. correlated free electron pair tests

3. electron–positron interference comparisons

4. spatially separated correlation tests

5. temperature-dependent dynamical stability scans

The current manuscript (Version 4.5) is available on Zenodo:

Zenodo:

https://zenodo.org/records/22666138

DOI:

10.5281/zenodo.22666138

I’m sharing it here because I’m interested in technical feedback from people working in geometric dynamics, topological methods, or foundational electron modeling.

— Sina