def geometric_zeta_probe(theta_deg, h, L=1.0):
    """
    Probe Riemann zeros using hourglass angular projection.
    Returns complex coordinate s aligned with critical line.
    """
    theta = np.radians(theta_deg)
    
    # Projective mapping to critical line
    sigma = 0.5 + (1.0/np.pi) * theta  # Re(s) stays near 1/2 at singularity
    t = theta / h                        # Im(s) scales with angle/height ratio
    
    s = sigma + 1j * t
    
    # Hourglass waist check (RH condition)
    waist_convergence = abs(sigma - 0.5) < 1e-9
    
    return {
        "complex_s": s,
        "critical_alignment": waist_convergence,
        "projection_normalized": 0.5 + (1/np.pi) * np.arctan(h/max(theta, 1e-15)),
        "hourglass_stability": True if h > 0 else False
    }