You will be provided with a reference and some statements. Please determine whether each statement is 'supported', 'unsupported', or 'unknown' with respect to the reference. Please note:
First, assess whether the reference contains any valid content. If the reference contains no valid information, such as a 'page not found' message, then all statements should be considered 'unknown'.
If the reference is valid, for a given statement: if the facts or data it contains can be found entirely or partially within the reference, it is considered 'supported' (data accepts rounding); if all facts and data in the statement cannot be found in the reference, it is considered 'unsupported'.

You should return the result in a JSON list format, where each item in the list contains the statement's index and the judgment result, for example:
[
    {
        "idx": 1,
        "result": "supported"
    },
    {
        "idx": 2,
        "result": "unsupported"
    }
]

Below are the reference and statements:
<reference>
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</reference>

<statements>
1. Direct-drive rotary tables minimize mechanical backlash by eliminating intermediate gearboxes; however, high-acceleration indexing inevitably excites torsional structural resonances between the motor rotor and the specimen platter
2. Modeling the mechanical assembly as a lumped-parameter two-inertia flexible torsional system allows exact analytical characterization of high-frequency structural jitter and settling dynamics
3. The term τ_m represents the electromagnetic drive torque generated by the stator windings, while τ_f,m and τ_f,l denote nonlinear bearing friction torques acting on the rotor and load assemblies
4. At micro-radian displacements and low scanning velocities, bearing pre-load introduces severe pre-sliding elastoplastic deformation, hysteresis, and velocity-softening Stribeck phenomena that cannot be captured by linear viscous damping approximations
5. The LuGre friction model parameterizes these phenomena by treating microscopic surface asperities as elastic bristles whose average physical deflection is denoted by the internal state z
</statements>

Begin the assessment now. Output only the JSON list, without any conversational text or explanations.