spectral math
Spectral Math
Universal mathematical library for language clarity analysis. TypeScript, JavaScript, Python, Cloudflare Workers.
Measure language clarity as brain oscillation frequency (4–12 Hz theta-alpha band). See also: clarity →
the math
Frequency prediction:
f = 5 + 2.5·log(Δλ + 1)
Range: 4–12 Hz (theta-alpha brain oscillations)
Confidence score:
C = 1 / (1 + exp(-10·(Δλ - 0.5)))
Sigmoid centered at Δλ = 0.5, range [0, 1]
Spectral gap:
Δλ = λ₁ - λ₂
Structure clarity: largest two eigenvaluesλ₁, λ₂ computed via power iteration on the adjacency matrix. Identical implementation across all platforms.
installation
npm install spectral-mathAvailable on npm. Works in Node.js, browsers, Cloudflare Workers, and Deno.
usage
import { computeEigenvalues, predictFrequency } from 'spectral-math'
const matrix = [
[0, 1, 0.5, 0],
[1, 0, 1, 0.5],
[0.5, 1, 0, 1],
[0, 0.5, 1, 0]
]
const eigenvalues = computeEigenvalues(matrix) // [2.081, 0.0]
const delta = eigenvalues[0] - (eigenvalues[1] || 0)
const frequency = predictFrequency(delta) // 7.81 Hzapi reference
computeEigenvalues(matrix: number[][]): number[]
Power iteration algorithm for largest two eigenvalues.
predictFrequency(deltaLambda: number): number
Brain oscillation frequency from spectral gap (Hz).
predictConfidence(deltaLambda: number): number
Analysis confidence score [0, 1].
spectralGap(eigenvalues: number[]): number
Structure clarity measure (λ₁ - λ₂).
analyze(matrix: number[][]): SpectralAnalysis
Full pipeline: eigenvalues → frequency → confidence.
implementation notes
Power Iteration — Efficient eigenvalue computation that works in constrained environments (Cloudflare Workers, browsers).
Deflation Method — Extract second eigenvalue via matrix deflation, identical to dense solvers.
Convergence — 20 iterations typically sufficient; adaptive tolerance (1e-6).
Numerical Stability — Clamping and normalization prevent overflow/underflow.
Cross-Platform — Identical TypeScript implementation used in Workers, browsers, Node.js, Python (via porting).
Spectral grammar measures language clarity as brain oscillation. Same math across all platforms. Open, transparent, universal.