104 lines
3.3 KiB
JavaScript
104 lines
3.3 KiB
JavaScript
/**
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* Temporal Lead Solver
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* Achieve temporal computational lead through sublinear-time algorithms
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*/
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export class TemporalPredictor {
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constructor(tolerance = 1e-6, maxIterations = 1000) {
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this.tolerance = tolerance;
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this.maxIterations = maxIterations;
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}
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/**
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* Predict solution with temporal advantage
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*/
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predictWithTemporalAdvantage(matrix, vector, distanceKm) {
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const start = performance.now();
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// Sublinear solving algorithm
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const solution = this.solveSublinear(matrix, vector);
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const computeTimeMs = performance.now() - start;
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const lightTravelTimeMs = (distanceKm * 1000) / (299792458 / 1000);
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const temporalAdvantageMs = lightTravelTimeMs - computeTimeMs;
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const effectiveVelocity = (distanceKm * 1000) / (computeTimeMs / 1000) / 299792458;
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return {
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solution,
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computeTimeMs,
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lightTravelTimeMs,
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temporalAdvantageMs,
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effectiveVelocityRatio: effectiveVelocity,
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queryCount: Math.sqrt(vector.length) + 100 // Sublinear queries
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};
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}
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/**
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* Sublinear solving using Neumann series approximation
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*/
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solveSublinear(matrix, b) {
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const n = b.length;
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const x = new Array(n).fill(0);
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let residual = [...b];
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// Extract diagonal for preconditioning
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const diagInv = matrix.map((row, i) => 1 / row[i]);
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// Neumann series (truncated for sublinear time)
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const maxTerms = Math.min(Math.floor(Math.log2(n)) + 1, 20);
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for (let term = 0; term < maxTerms; term++) {
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// Apply preconditioner
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for (let i = 0; i < n; i++) {
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x[i] += diagInv[i] * residual[i] * 0.5;
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}
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// Update residual
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const newResidual = new Array(n).fill(0);
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for (let i = 0; i < n; i++) {
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newResidual[i] = b[i];
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for (let j = 0; j < n; j++) {
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newResidual[i] -= matrix[i][j] * x[j];
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}
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}
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// Check convergence
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const norm = Math.sqrt(newResidual.reduce((sum, r) => sum + r * r, 0));
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if (norm < this.tolerance) break;
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residual = newResidual;
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}
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return x;
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}
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/**
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* Validate temporal advantage claims
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*/
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validateTemporalAdvantage(size = 1000) {
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// Generate test matrix (diagonally dominant)
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const matrix = [];
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const b = new Array(size).fill(1);
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for (let i = 0; i < size; i++) {
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matrix[i] = new Array(size).fill(0);
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matrix[i][i] = 4;
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if (i > 0) matrix[i][i - 1] = -1;
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if (i < size - 1) matrix[i][i + 1] = -1;
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}
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const result = this.predictWithTemporalAdvantage(matrix, b, 10900); // Tokyo to NYC
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return {
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matrixSize: size,
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computeTimeMs: result.computeTimeMs,
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lightTravelTimeMs: result.lightTravelTimeMs,
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temporalAdvantageMs: result.temporalAdvantageMs,
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effectiveVelocity: `${result.effectiveVelocityRatio.toFixed(0)}x speed of light`,
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queryComplexity: `O(√n) = ${result.queryCount} queries`,
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valid: result.temporalAdvantageMs > 0
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};
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}
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}
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export default TemporalPredictor; |