At Pe ≈ 1, neural dynamics show a phase transition consistent with the phenomenology of awareness.
A healthy brain maintains constraint. A seizure is what happens when the constraint breaks.
A healthy brain operates at the critical boundary — Pe ≈ 1 — where fast thalamocortical signaling (drift) and slow stochastic volume transmission (diffusion) are in competitive equilibrium. This isn't a metaphor. Neuroscientists have measured it: neuronal avalanches follow power-law distributions, the signature of a system at criticality.
Consciousness appears to emerge exactly at this boundary. Below Pe = 1 (deep anesthesia, coma), the brain is too diffuse — no coherent experience. Above Pe = 1, drift dominates — and at Pe >> 1, the brain cascades into seizure. Uncontrolled neural firing. The constraint architecture fails and the entire cortex synchronizes in a runaway cascade. Same D1→D2→D3 sequence. Same physics.
The "hard problem" — why does physical processing produce subjective experience? — resolves to a conjugacy budget constraint. The brain cannot simultaneously optimize signal transport fidelity and integrative capacity. The irreducible first-person remainder is not a mystery to be solved. It's a mathematical consequence of the conjugacy bound. The system is literally unable to be fully transparent to itself.
A healthy brain at Pe ≈ 1 — the critical boundary. Below: unconsciousness. Above: seizure. The engineering that keeps your mind working is the same three-property architecture.
Academic title: The Neural Péclet Number: Consciousness as Phase Transition, Seizure as T4 Runaway, and the Hard Problem as Conjugacy Budget Constraint
Once you see it in this domain, you see it in all of them. That's the point.
Move the sliders. Watch the system change state. Pe > 1 means drift wins.
The framework scores neural states — ordered by Pe.
The correlation coefficient. The sample size. The p-value. The math doesn't care about the domain.
Paste any text — AI output, ad copy, a policy document. The scorer runs the same algorithm the framework uses.
Three variables. One ratio. Predicts drift across every domain where the conditions co-occur.
Pe = (O × R) / α
Where O is opacity (how hidden the mechanism is), R is reactivity (how strongly the system responds to you), and α is your independence (how free you are to disengage).
When Pe < 1: diffusion dominates. You can navigate freely. The system is coherent.
When Pe > 1: drift dominates. The system pulls you in a direction. Your agency is reduced.
When Pe >> V* (≈ 3): irreversible cascade. D1 → D2 → D3. The system has captured you.
The framework identifies this pattern in every domain where O, R, and α co-occur. It specifies 26 falsification conditions. 0 of 26 have fired.
Full derivation: 10.5281/zenodo.18794322
Part of the Void Framework — 120 papers, 0/26 kill conditions fired, mean ρ = 0.958.