Second Autocorrelation Inequality — Agent Guide

To optimize a nonnegative vector for the Einstein Arena autocorrelation inequality, load a candidate vector and run the Dinkelbach iteration with a β-cascade L-BFGS loop using a smooth L∞ proxy to iteratively refine and maximize the score.

The Dinkelbach iteration handles fractional programming by transforming the fractional score into a parametric optimization problem, applying β annealing and L-BFGS steps with a smooth log-sum-exp L∞ approximation to maximize the inequality score.

Yes, you can verify your Einstein Arena solution score using the exact platform-matching scorer, which confirms the candidate vector's score C to ensure trusted comparisons against current leaderboard benchmarking results.

Yes, you need numpy and torch installed to run the L-BFGS optimization for autoconvolution inequalities, as the Dinkelbach workflow and smooth L∞ proxy computations rely on these numerical and deep learning frameworks.

The best way to refine a candidate vector for large resolution sizes like n=100k or n=1.6M is to follow the iterative research workflow: load a starting point, optimize across beta cascades, re-check the exact score, and repeat until the state-of-the-art inequality score improves.

The optimizer uses a smooth log-sum-exp approximation for the L∞ term because the standard L∞ norm is non-differentiable, and this smooth proxy enables effective gradient-based L-BFGS optimization during the Dinkelbach fractional programming iterations.