Session Default properties seems incomplete

[mp-emmett]

There are two errors on the Session Default properties:

This is the missing property from the doc
$referring_domain

Country code is incorrect:
Docs list $country_code when its mp_country_code

Skipping the big 3 makes sense, as they are minimum for the event working
$event_name | Event Name
$distinct_id | Distinct ID
$time | Time

4 Are session specific and called out
$origin_end | Session End Event Name
$origin_start | Session Start Event Name
$duration_s | Session Duration (Seconds)
$event_count | Session Event Count

Docs list these values as default session props that will compute like a first step defined funnel prop:
mp_lib | Mixpanel Library
$os | Operating System
$region | Region
$city | City
$current_url | Current URL
$browser | Browser
$device | Device
$app_build_number | App Build Number
$app_version_string | App Version
$manufacturer | Manufacturer
utm_source | UTM Source
utm_medium | UTM Medium
utm_campaign | UTM Campaign
utm_content | UTM Content