Research

Browse 265 equations by domain and cost. Visualize the four boundaries of elementary functions. Explore the FMA staircase. The data behind the claims.

Flagship

Boundary Map

The four walls of ELC

Coming Soon

Phantom Attractor

Gradient descent dynamics on EML expressions

The Gap

Visualize the elementary closure gap — what EML cannot reach

Closure

Operator closure properties of the F16 family

Conveyor Belt

A living system traversing the depth hierarchy in real time

Cosmos

The depth hierarchy as a cosmological structure

Genesis

The origins of the EML hierarchy from one operator

Shadow

Barrier functions: EML-∞ over ℝ, resolved over ℂ via T03

Strata

World-building stratification across the EML depth bands

Depth of Room

Visualize the depth bands of any space

Catalog Browser

Search 265 equations

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Decay Curve

The FMA staircase

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Distribution Explorer

Probability distributions by EML cost

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Challenge Board

Open problems

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