The usual definition of notability for a candidate article in the en.wp context is that multiple independent reliable sources are about this subject.
Here is an alternative definition: A person who was recognized by a large community or had a noticeable impact on a large community is notable.
If we used that definition, at least saying that a person cleared the notability bar if we could demonstrate that, it would change a little who "counts" and is remembered and documented. It is a criterion that draws in the idea that some topics have an effect, and gets away from what shows up in newspapers, magazines, journals, and books.
Let's call that a "community standard" or "community definition" of notability for the moment. Let's address: how would an editor establish that someone met this criterion? for what topics does it raise or lower the bar (the criteria) for notability?
To use a definition like this, it is necessary to establish or at least state who the community is -- is it 40,000 people in a city who voted for the person? or who watch a certain sport? Is a community large enough based strictly on its number of people or something else, like it's distinctiveness or some measure of importance?
the existence of 100,000 baseball fans is enough to make baseball players notable; likewise chessplayers, people in a political district, or people of a certain ethnic background. And it would not be necessary to show that a newspaper ever said so, if some evidence could be found.
40000 voters? I was involved in a deletion case where another editor opined that this didn't matter or didn't count. But, this kind of quantification gives information on whether people know the topic and have authority over it
That criteria might be just as appropriate as one focused on counting published sources. The two criteria might exist in parallel, that is, a topic is notable enough for an article if it has EITHER three reliable published sources, or it is shown somehow to meet a community-awareness standard. One still needs some reliable source to say much about the topic.
Should the definition be free to differ by the language of the Wikipedia? Are the notability now identical or strictly similar across languages?
One reason for them to be similar is to reach the ideal that if you see an article that it would already have cleared the bar to have a translation into another language.
One reason for them to be different is that the useful and useable notability standards for a tribe of indigenous people is properly very different from that of a community of super-literate scientists. That is, the scientists want to be able to cite one another's work, and recognize the criteria and paradigms of one another's work. The community wants an awareness of a different kind.
the argument for DIFFERENT seems more relevant and strong but could benefit from more explication