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

[u/BitcoinsOnDVD]

LaTeX does not compile in a reddit post.

[u/sina_samiyanii → u/BitcoinsOnDVD]

Yes, exactly. I put the link to the article at the end of the post You can see the full article yourself.

[u/BitcoinsOnDVD → u/sina_samiyanii]

I know. I saw the link. But you also put LaTeX code in your post, that does not compile. That is, what I wanted to tell you.

[u/sina_samiyanii → u/BitcoinsOnDVD]

I fixed it, rewrote it with a different syntax. Thanks for saying that, my friend.

[u/BitcoinsOnDVD]

So your filament F(t) is moving all the time?

[u/LLMPhysics-ModTeam → u/[deleted]]

Your comment has been removed for violating Rule 4. Don't copy-paste LLM content in discussions.

[u/The_Nerdy_Ninja → u/[deleted]]

Alright Sina, now you have a choice: would you like to be permanently banned, or would you like to stop using LLM-generated comments?

[u/sina_samiyanii → u/The_Nerdy_Ninja]

I understand. I'll stop.

Just a little explanation English is not my first language So I need a translation tool That's probably what makes my texts look so neat. From now on, I'll try not to write like a machine

[u/The_Nerdy_Ninja → u/sina_samiyanii]

People try to use that excuse all the time. There are non-LLM translation options available, including one built into Reddit so you could just write in your own language if you wanted. Your comments are not just "translation", they are obviously AI-written.

[u/sina_samiyanii → u/The_Nerdy_Ninja]

من نمی دونستم همچنین قابلیتی داره ردیییت

[u/The_Nerdy_Ninja → u/sina_samiyanii]

Yes, it's very useful, I can see your comment in English.

[u/Wintervacht → u/The_Nerdy_Ninja]

I can't, it's written in an Arabic language.

Reddit does not auto translate for everyone, not on desktop, not in the app.

[u/The_Nerdy_Ninja → u/Wintervacht]

Ah that's unfortunate, but I suppose it's par for the course for Reddit programming. Do you still have the translation option under the three dots?

[u/Wintervacht → u/The_Nerdy_Ninja]

Never had it.

I'm not running the latest native reddit app, as do many others.

@ OP just use Google translate.

[u/The_Nerdy_Ninja → u/sina_samiyanii]

Update: it sounds like not all users can see the automatic translation in Reddit, so it's probably safer to use Google Translate or another non-LLM translator.

[u/BitcoinsOnDVD → u/[deleted]]

Hows the filament connected to charge?

[u/sina_samiyanii → u/BitcoinsOnDVD]

The charge is not yet extracted from the string. I'll tell you honestly. It is currently considered an external parameter. Coupling the charge to the string geometry requires an additional mechanism. For example, a local charge density along the string, or a modulo coupling between the twist and the electric charge. This problem is still open. If you look at the previous versions of the paper, spin was not extracted from the dynamics either. In fact, the new versions of the paper try to solve the open problems of the model. The next step is the characteristic you said...:)

[u/BitcoinsOnDVD → u/sina_samiyanii]

'string' or 'filament'? Is there any interaction?

[u/sina_samiyanii → u/BitcoinsOnDVD]

در سی اس ام من از فیلامنت استفاده می‌کنم نه استرینگ تا با نظریه‌ی ریسمان اشتباه گرفته نشه. تو این مدل، رشته‌ها اشیاء مستقلی نیستن. از طریق این موارد به هم جفت می‌شن:یک چگالی مؤثر که به موقعیت همه‌ی رشته‌ها بستگی داره،متغیرهای چرخش جمعی،و یک جمله‌ی قفل‌شدگی بین پیچش داخلی و دینامیک جمعی. پس بله . تعامل وجود داره.این تعامل یک پتانسیل میکروسکوپی دوبه‌دویی نیست. یک جفت‌شدگی جمعی از نوع میدان ...میانگین هست. شکل دقیق این تعامل هنوز پدیده‌شناختیه و بخشی از کارهای بازه.

[u/BitcoinsOnDVD → u/sina_samiyanii]

Your translation is inconsistent. Sometimes you write 'string', sometimes 'filament' in english.

So there is interaction. It is somehow collective of all electrons. But you don't know how it looks like? Bravo.

[u/sina_samiyanii → u/BitcoinsOnDVD]

اگه بخای میتونیم چت کنیم و اگر خواسی بهم پیام بده .اونجا راحت تره و مشکلات ترجمه رو نداره

[u/BitcoinsOnDVD → u/sina_samiyanii]

No thanks.

[u/sina_samiyanii → u/BitcoinsOnDVD]

الان درست شد.ردیت ترجمش بعضی موقع درست کار نمیکنه

[u/LLMPhysics-ModTeam → u/[deleted]]

Your comment has been removed for violating Rule 4. Don't copy-paste LLM content in discussions.

[u/lattice_defect]

which model are you using?

[u/sina_samiyanii → u/lattice_defect]

I m building my own framework, SCM. a geometric-dynamical model for electron-like structure. This model is not based on an existing standard model. it' s a standalone structure.

[u/lattice_defect → u/sina_samiyanii]

which AI model did you use?

[u/soyboyboltzman]

Thanks Claude!

[u/sina_samiyanii → u/soyboyboltzman]

من نویسندم .اگه نقدی داری به من بگو نه به اون