Solar noon depends on the observer's exact longitude relative to what feature to explain discrepancies with $12:00$ PM clock time?
Answer
The center of their time zone
Clock time is standardized across wide longitudinal bands, but solar noon occurs when the sun crosses the local meridian. Therefore, an observer's exact position east or west within that standard time zone dictates the difference between local solar noon and the standardized $12:00$ PM time.
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