This data is user's metadata https://codex.wordpress.org/Function_Reference/get_user_meta
As you say, this is your metadata. Two things here: first of all, I'll store all that data together inside a single key and I'll remove the uneeded single-element array:
[my_plugin] => Array( [1012] => 1, [1013] => 0 ...)
That lowers the possibility of your data mixing with other's plugin data, having conflicts, etc. Also, as second array is probably not needed, it will make access to it a little simpler.
When you have that, it's only a matter of accessing the value like this:
if ($all_meta_for_user['my_plugin'][$id] == 1) show_the_post()
where $id is the post ID.
To use a single key, I'll do something like this (untested):
$posts_meta_for_user = get_user_meta(get_current_user_id(), 'my_plugin', true);
if (is_array($posts_meta_for_user)) {
$posts_meta_for_user[$new_id] = $new_value;
update_user_meta(get_current_user_id(), 'my_plugin', $posts_meta_for_user);
} else {
$posts_meta_for_user = array($new_id => $new_value);
add_user_meta(get_current_user_id(), 'my_plugin', $awesome_level);
}
Notice that we get only the meta value named 'my_plugin' and test it already had a value by checking that is an array. If it is, we update it, and if it's not, we create a new one. $new_id
is the post ID you want to store and $new_value
the value.