/home/pc/Documents/Cline/Fractal_Correction_Engine/Axis of Evil/cmb_axis_simulator/src/fractal_correction_engine.py:83: HealpyDeprecationWarning: "verbose" was deprecated in version 1.15.0 and will be removed in a future version. 
  current_map = hp.alm2map(alm, self.cmb_params.nside, verbose=False)
/home/pc/Documents/Cline/Fractal_Correction_Engine/Axis of Evil/cmb_axis_simulator/src/fractal_correction_engine.py:355: HealpyDeprecationWarning: "verbose" was deprecated in version 1.15.0 and will be removed in a future version. 
  'map': hp.alm2map(initial_alm, self.cmb_params.nside,
/home/pc/Documents/Cline/Fractal_Correction_Engine/Axis of Evil/cmb_axis_simulator/src/fractal_correction_engine.py:361: HealpyDeprecationWarning: "verbose" was deprecated in version 1.15.0 and will be removed in a future version. 
  'map': hp.alm2map(current_alm, self.cmb_params.nside,
/home/pc/Documents/Cline/Fractal_Correction_Engine/Axis of Evil/cmb_axis_simulator/src/visualization.py:122: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.
  plt.tight_layout()
/home/pc/Documents/Cline/Fractal_Correction_Engine/Axis of Evil/cmb_axis_simulator/src/visualization.py:126: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
  plt.show()
/home/pc/Documents/Cline/Fractal_Correction_Engine/Axis of Evil/cmb_axis_simulator/src/visualization.py:54: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
  plt.show()
/home/pc/Documents/Cline/Fractal_Correction_Engine/Axis of Evil/cmb_axis_simulator/src/visualization.py:154: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
  plt.show()
/home/pc/Documents/Cline/Fractal_Correction_Engine/Axis of Evil/cmb_axis_simulator/src/fractal_correction_engine.py:83: HealpyDeprecationWarning: "verbose" was deprecated in version 1.15.0 and will be removed in a future version. 
  current_map = hp.alm2map(alm, self.cmb_params.nside, verbose=False)
/home/pc/Documents/Cline/Fractal_Correction_Engine/Axis of Evil/cmb_axis_simulator/src/fractal_correction_engine.py:355: HealpyDeprecationWarning: "verbose" was deprecated in version 1.15.0 and will be removed in a future version. 
  'map': hp.alm2map(initial_alm, self.cmb_params.nside,
/home/pc/Documents/Cline/Fractal_Correction_Engine/Axis of Evil/cmb_axis_simulator/src/fractal_correction_engine.py:361: HealpyDeprecationWarning: "verbose" was deprecated in version 1.15.0 and will be removed in a future version. 
  'map': hp.alm2map(current_alm, self.cmb_params.nside,
/home/pc/Documents/Cline/Fractal_Correction_Engine/Axis of Evil/cmb_axis_simulator/simulate_axis_of_evil.py:184: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
  plt.show()
CMB Axis of Evil Simulator — Emergent Alignment Test
============================================================

1. Single Simulation Run (Emergent Dynamics)
----------------------------------------
Initial alignment angle:   89.6 deg (0-90 range)
Corrected alignment angle: 13.0 deg
Alignment improvement:     76.7 deg
Converged in 100 iterations
Null p-value (isotropic):  0.0254
Expected random mean:      ~57.3 deg

FCE Pi-Curvature Analysis:
  l_2: winding = 0.166, spectral_slope = 2.135, converging = False
  l_3: winding = 0.128, spectral_slope = 2.909, converging = False
  l_4: winding = 0.101, spectral_slope = 2.848, converging = False
  l_5: winding = 0.073, spectral_slope = 1.993, converging = False

2. Statistical Analysis (100 simulations)
----------------------------------------
Running Monte Carlo analysis...

Uncorrected CMB:
  Mean alignment angle: 61.0 deg +/- 18.7 deg

Corrected CMB (with recursive attractor):
  Mean alignment angle: 0.9 deg +/- 0.8 deg

Alignment improvement: 60.1 deg

Null Hypothesis Test (analytic):
  p-value: 0.0001
  Significant at 5%: True

Monte Carlo Null Test:
  p-value: 0.0001
  Mean random angle: 57.3 deg

============================================================
INTERPRETATION:
The recursive attractor mechanism uses emergent dynamics
(entropy gradient + mode coupling) with NO preferred axis.
Any alignment is a result of nonlinear multipole interactions.

Compare corrected angle distribution against the isotropic
null hypothesis P(alpha) = sin(alpha) to assess significance.

RESULT: The corrected alignment is statistically significant
at the 5% level (p = 0.0001).

Results saved to data/simulation_results.npz
Visualizations saved to visualizations/
