Improve synthetic phi recovery using direct curve fitting#15
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Replaced the existing synthetic phi recovery notebook with a new version that utilizes direct non-linear curve fitting of the correlation function instead of CHSH magnitude estimation. This provides first-order sensitivity to small phase shifts (phi < 0.1), enabling reliable recovery of injected signals. Key changes: - Implemented direct fit: E(theta) = -cos(theta + phi). - Added model comparison (Standard QM vs Shifted X-Theta) with chi-squared, AIC, and BIC metrics. - Added residual signature test for the X-Theta unique sine-shaped residual pattern. - Added Milestone 4 section detailing the unique physical prediction of the theory. - Automated generation and saving of validation plots to the outputs directory.
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The synthetic phi recovery notebook was updated to address the measurement-design problem where small phase shifts were undetectable due to the second-order nature of the CHSH magnitude's dependence on phi. By shifting to direct correlation curve fitting, the sensitivity is improved to first-order, allowing for stable recovery of small phi values (e.g., 0.005, 0.01). The notebook now also includes formal model comparison and the X-Theta residual signature test.
PR created automatically by Jules for task 5973336430852611189 started by @divyang4481