Stop Calculating the “Whole” — Kill O(N²) for a 31x Speedup

“If accuracy is preserved, choosing 31x speed is the only logical choice.”

Ghost Drift Research introduces a definitive departure from computational brute force.

Your Global Sum is a Waste of Time

— — O(N \log N) Audit-Ready FFT Replacement: A Proven 31x Performance Leap

The Bottleneck: The Hidden Tax of Global Sums

In large-scale simulations and data processing, “Global Sums” (all-to-all interactions) are a massive tax on performance. Calculating the “literal whole” at $O(N²)$ is no longer a necessity — it’s an oversight.

The Solution: Ghost Drift’s “Finite Closure”

We have open-sourced a demo implementing the core pillar of Ghost Drift Theory: “Finite Closure.”

By leveraging our proprietary Fejer-Yukawa (FY) window, you can transform $O(N²)$ bottlenecks in physical simulations and complex calculations into high-efficiency FFT convolutions without losing mathematical integrity.

Empirical Evidence: Scaling from $O(N²)$ to $O(N \log N)$

This isn’t just a tweak; it’s a fundamental shift in algorithmic complexity.

• Speedup: 12.84s → 0.41s (31.3x Faster)
• Precision Guarantee: Error strictly maintained within tolerance $\epsilon$ ($| \Delta \text{result} | \le 1e-6$)
• Auditability: Complete verification via parameters and cryptographic hashes.

What is “Audit-Ready”?

A state where any third party can reproduce the exact same result given the same input, code, parameters, and fingerprint.

• Audit Log Schema: [hash, params, epsilon, checksum, engine_version, seed, timestamp]

Key Concepts

• Finite Closure: A methodology that takes an infinite “global” problem, fixes an error bound $\epsilon$ upfront, and “closes” the calculation into a finite window — fixing both the result and the accountability.
• Fejer-Yukawa (FY) Window: The mathematical engine of finite closure. Unlike crude “cutoffs,” it uses controlled decay to constrain errors strictly within $\epsilon$.

Technical Benchmarks

• Complexity Shift: Global Sum (Direct): $O(N²) \rightarrow$ FY window + FFT: $O(N \log N)$
• Environment: $N=2,000,000$, float64, Apple M2 Max, NumPy/FFTW backend.

It’s Not an “Approximation.” It’s a “Constraint.”

Traditional optimizations often rely on “good enough” approximations. Ghost Drift is different. We fix the error bound $\epsilon$ first, then constrain the calculation within that finite window.

This is Audit-Ready Acceleration. In an era of black-box AI and opaque quantum computing, we deliver accountability in the language of mathematics. If the hash matches, the drift is accounted for.

Get Started in 60 Seconds

1. Verify Precision: Confirm the output stays within the $\epsilon$ constraint.
2. Verify Reproduction: clone → run → Match the Fingerprint (Hash).

Experience the 31x leap and the future of verifiable computation.

https://ghostdrifttheory.github.io/global-sum-to-fft-demo/

Your Star on GitHub isn’t just a like — it’s a vote for “Computation as a Standard of Trust.”