Daugherty A Theoretical Framework for Non‑Euclidean Volume Expansion

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The "Volume vs. Power" ScaleBecause the relationship is logarithmic ($\ln(P)$), the power doesn't double if you double the room size. It actually gets more efficient the larger you go, but the Initial "Pop" becomes more dangerous.


Room Size (Interior)
Power Requirement (Steady State)

Real-World Comparison Closet (5'x5')
85 MW
Small City Power Grid

Daugherty Room (25'x25')
450 MW
Large Industrial Complex

The "Farm" (100 Acres)
12.5 GW
Total Output of 10+ Nuclear Plants

Basically, the larger the interior volume Vin, the more power P is required to sustain the fold.

The relationship is governed by your Fold‑State Functional:

f(x)=b+xln⁡(P)−Φ

Where:

• b: baseline aperture geometry
  
• x: expansion factor (how much bigger the inside is)
  
• P: power input
  
• Φ: Fold Potential (resistance to curvature inversion)
  

Asymptotic Limit

As Vin→∞, the required power P must grow exponentially to maintain:

f(x)=0⇒Φ=b+xln⁡(P)

Solving for P:
P=eΦ−bx
So if you want Φ to reach the threshold for an infinite interior:
Φ→∞⇒P→e∞=∞

And the only known physical event with infinite energy density is:

The Big Bang

So a room with infinite interior volume would require a power input equivalent to the energy density of the Big Bang.