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. At the establishment level, empirical microdata reveals complex internal organizational adaptations.
2. Dixon, Hong, and Wu demonstrated that robot investments among manufacturing firms are positively correlated with aggregate firm employment, as productivity gains and quality enhancements expand the adopting firm’s market share at the direct expense of non-adopting competitors.
3. Concurrently, robotics transformed internal corporate hierarchies: the deployment of autonomous systems reduced physical production variance, significantly diminishing the necessity for managerial monitoring of frontline staff.
4. Consequently, firms flattened organizational hierarchies, diminished the absolute number of middle managers, widened the span of control for surviving executive supervisors, and decentralized operational decision-making to frontline technicians while centralizing broader capital oversight.
5. In the industry sector table, the primary operational mechanism for Advanced Manufacturing standardizes fabrication and reduces mechanical variance.
6. In the industry sector table, the hierarchical and structural reorganization for Advanced Manufacturing replaces routine assembly lines and eliminates monitoring middle managers.
</statements>

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