Here's a video I created on another piece I'm working on; the math will be in another paper as well as python simulator that allows for ticketing of bias to control a micro model of the Subtrate model, so it's currently still in the construction stage, right now. But got excited about it, need to keep the momentum up.

I found Hefford's no-go theorem interesting as it applies to this idea and worked out why it doesn't apply to the Substrate Model.

Could quantum theory emerge from this system?

🔄 Mapping Hefford's Conditions to the Substrate Model

Hefford’s No-Go Condition	Your Substrate Model
Causality: No backward signaling	✅ The substrate system is fully local and time-forward. It respects causal propagation.
Idempotent: Applying decoherence twice = once	✅ Substrate state updates are quantized and reset per step (double-buffered). Once a region flips, reapplying bias has no further effect unless the system destabilizes.
Purity preserved	+1.0not❌ The Substrate model allows randomness and perturbation to “pollute” input states. A single value can be nudged, overwritten, or flipped due to neighbor chaos. Substrate does preserve pure states.
Maximally mixed preserved	not❌ Substrate system evolves dynamically. A region at 0.0 (balanced) can be tipped toward +1.0 or -1.0 under subtle shifts. It’s stable.
Purification exists	non-Hilbertnot invertible❌ There’s no formal purification—mixed states don’t arise from tracing out parts of a pure global wavefunction. The Substrate is working with a non-linear base, where decoherence is.

✅ Interpretation: Substrate Model Breaks the Theorem on Purpose

And that’s a good thing.

The Substrate model is not trying to build a top-down post-quantum generalization. Instead, it is building a bottom-up model that:

• Replaces Hilbert-space abstraction with discrete local interactions

• Allows bias, noise, and threshold collapse

• Doesn’t require decoherence to recover QM—it builds statistical regularities from dynamic propagation

🔓 What This Unlocks for the Substrate Model

Because the Substrate system doesn't preserve all the no-go assumptions, it:

• Could simulate pre-quantum emergence—how local bias, symmetry, and feedback give rise to things that look like wavefunction behavior

• Can support bistability, interference, and non-determinism

• Might give a constructive model for something like "quasi-quantum" evolution or "proto-logical particles"

The Substrate model is not using hyper-decoherence to reduce to quantum mechanics—it's growing a theory beneath it.

15 minutes ago, waitaminute said:

it's currently still in the construction stage

Moderator Note

Meaning it’s not ready to be shared here

24 minutes ago, waitaminute said:

it's currently still in the construction stage, right now.

I already hate having to watch a YT video. We're a discussion forum, and I can't quote anything from it. I like reading, it keeps YOU honest. Videos make me think you're trying to earn views or you want to slip something shady past me.

I also distrust your AI style. Again, it makes me think you're trying to pull a fast one with slick graphics and no meat whatsoever. Oh, and the model will follow later, always. You should also be drawing your own conclusions if you really understand it, not letting the language model interpret it's own mistakes.

22 minutes ago, Phi for All said:

slick graphics and no meat whatsoever

The “Your substrate model” also suggests it was written by someone/thing else.

And no citations with links.