curl --request POST \
  --url https://api.valyu.ai/v1/deepresearch/tasks/{id}/public \
  --header 'Content-Type: application/json' \
  --header 'X-API-Key: <api-key>' \
  --data '{
  "public": true
}'

{
  "success": true,
  "message": "Public flag updated",
  "deepresearch_id": "a1b2c3d4-e5f6-7890-abcd-ef1234567890",
  "public": true
}