Strict Refinement

Verify located candidate attractors using extremely high-accuracy integrations and cross-solver audits.

The Strict Refinement workflow is the final verification stage for located hidden attractor candidates. Before a candidate is promoted to a validated publication package, it must satisfy extremely tight geometric and numerical criteria across multiple independent integration backends.

Refinement Rules

The strict refinement pipeline implements the following audits:

  1. Solver Cross-Check: Re-integrate the identical initial seed (x0,y0,z0)(x_0, y_0, z_0) with an independent solver (e.g., cross-checking C-backed EFORKSolver against a full-history ABMSolver).
  2. Step Size Sensitivity: Integrate at a smaller step size (e.g., h/2h/2 or h/4h/4) to ensure that the orbit does not collapse or show numerical divergence.
  3. Centroid & Box Persistence: The resulting orbit’s bounding box and coordinate centroid must match the reference targets within a strict 0.5%0.5\% geometric tolerance.
  4. Equilibria Distance Tolerance: Measures the minimum Euclidean distance from the final 50% of the simulated orbit to the nearest equilibrium point, verifying it is truly isolated and hidden.

Usage via CLI

You can execute strict target refinement from the command line:

# Get help
hidden-attractors-strict-target-refinement --help

# Run strict refinement on a candidate folder
python tools/cli/strict_target_refinement.py --dir outputs/candidates/chua_candidate_01/ --strict --h 0.005

Python API Usage

from hidden_attractors.workflows.strict_refinement import StrictRefinementConfig, run_strict_refinement

config = StrictRefinementConfig(
    candidate_dir="outputs/candidates/chua_candidate_01",
    independent_solver="abm",
    h=0.005,
    tolerance=0.005
)

# Run strict audit
result = run_strict_refinement(config)
print(f"refinement_status={result.status} passes={result.passes_all_checks}")