15:I[981,["658","static/chunks/658-a698693f56d0116a.js","183","static/chunks/183-6beeeb801c274aaa.js","474","static/chunks/app/%5Btype%5D/layout-631c4730b83c8223.js"],"Posts"] 16:T4da,I’ve spent the last few months formalizing a new structural foundation for mathematics called Theory of Systems (ToS) in Coq.

The goal was to derive classical results (like the uncountability of [0, 1]) from a single principle of distinction ("A = exists") rather than starting with ZFC axioms.

Key Technical Highlights:

135 theorems, 0 Admitted for the main uncountability proof.

Solves Digit Stability: Instead of digit extraction, it uses geometric interval trisection to prove uncountability constructively.

L5-Resolution: Implements a deterministic "leftmost" rule for argmax, ensuring that optimization processes are Cauchy even on flat plateaus.

No Axiom of Infinity: The infinite emerges as a property of the process levels (P4).

I'm currently looking for an ArXiv endorsement (cs.LO or math.LO) to publish the full 60-page preprint.

Repo: https://github.com/Horsocrates/theory-of-systems-coq

I'd love to hear your thoughts on the E/R/R (Elements/Roles/Rules) framework and the inclusion of the "Law of Order" as a 5th law of logic.17:T4c9,I’m trying to do the “voice assistant” thing fully locally: mic → model → speaker, low latency, ideally streaming + interruptible (barge-in).

Qwen3 Omni looks perfect on paper (“real-time”, speech-to-speech, etc). But I’ve been poking around and I can’t find a single reproducible “here’s how I got the open weights doing real speech-to-speech locally” writeup. Lots of “speech in → text out” or “audio out after the model finishes”, but not a usable realtime voice loop. Feels like either (a) the tooling isn’t there yet, or (b) I’m missing the secret sauce.

What are peo

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