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
Measured

Float Drift — measured vs proved

Watch a float sum drift from the exact real: the n·u worst case you can prove vs the √n·u stochastic rounding delivers, plus the cancellation lesson — relative bound dies, absolute holds.

Flagship
Proved

Boundary Map

The four walls of ELC

Measured

MachLib Pulse

Live MachLib verification status, rained into buckets by the critically-damped spring kernel we proved.

Proved

Khovanskii Counter

The constructive zero-count bound from MachLib.SingleExpKhovanskii, exposed. Pick an ExpPoly, see how loose `length + Σ deg` is against the real count.

Proved

Tower Zero-Counter

One rung up the tower: zeros of p(eˣ, e^{eˣ}) are provably finite (rolle-only, MachLib), but the explicit constant grows exponentially in the tower degree. Climb the presets and watch the gap.

Model

Phantom Attractor

Gradient descent dynamics on EML expressions

Proved

The Gap

Visualize the elementary closure gap — what EML cannot reach

Measured

Closure

Operator closure properties of the F16 family

Model

Conveyor Belt

A living system traversing the depth hierarchy in real time

Model

Cosmos

The depth hierarchy as a cosmological structure

Model

Genesis

The origins of the EML hierarchy from one operator

Proved

Shadow

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

Model

Strata

World-building stratification across the EML depth bands

Model

Depth of Room

Visualize the depth bands of any space

Measured

Catalog Browser

Search 265 equations

Measured

Decay Curve

The FMA staircase

Measured

Distribution Explorer

Probability distributions by EML cost

Model

Challenge Board

Open problems