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When updating properites metadata, does this trigger a new modification date for sorting newly edited metadata on assets? If not, how would one go about sorting search results by most recent updated metadata?
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Depends on your query, if you are using lastModificationDate to sort, then updating metadata properties will impact the sorting of search results.
Last Modification Date is updated with DAM Metadata Writeback Workflow, which gets triggered when there is a change in Asset Metadata Properties. See the screen shot from AEM6.5 On prem local set up

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