If you install my Hashcash for Gmail google script to scan & validate your incoming email according to the presence or absence of hashcash stamps, and you just want notifications for verified emails coming in, you can tweak how the inbox notifies you on your mobile phone. Here's one possible setup:
It's quickest to set this up from the desktop:
- From the gmail web interface Gear->Settings
- Inbox tab
- Inbox type 'Priority'
- For Inbox sections 1-4, Options->Remove Section
- Redefine Inbox section 1. Options->More Options...->Show All From Label [#$]
- Save Changes
Then on your Android phone, configure Gmail:
- Account Settings->[your email address]
- -Check Priority Inbox (make default for this account)
- -Labels to Notify
- ->Inbox: off
- ->Priority Inbox: off (was: [subtle, always, notify for every msg])
- -> [#$]: [subtle, always, notify for every msg]
If you look into Gmail's Priority inbox rules it's a pretty powerful way to tailor how/when you get notifications.