What is syntax for a compound JSON expression in search filter?

What is syntax for a compound JSON expression in search filter?

The JSON I need to search is Parent_Deal/id

 "Parent_Deal": {
        "name": "01 - Parent - ACX Jags-Warm Ups & Jersey",
        "id": "4776102000000379536"
    },

What is the syntax for that in this URL for an invokeurl?

  1. https://www.zohoapis.com/crm/v2/Potentials/search?criteria=( ??????????? :equals:" + deal_id + ")