<think>
Okay, I need to implement the field_mean function. Let's see the requirements. The function takes a list of records and a field name, and returns the mean of that field across all records. But if a record doesn't have the field, it's skipped. If none of the records have the field, it returns nothing, which I think means returning 0? Or maybe an empty value? Wait, the problem says "a set in which none carry it averages to nothing." So maybe returning 0 in that case?

Wait, the function is supposed to return an integer, the mean rounded down. So if there are no valid entries, then the mean is nothing, so perhaps return 0? Or maybe return an empty value? But the function's return type is int. So maybe when there are no valid entries, return 0?

But let me think again. The problem says that if none of the records have the field, the average is nothing. So in that case, the function should return 0? Or maybe raise an error? But the problem says that records lacking the field are passed over. So, for each record, check if it has the field. If it does, take the value. Otherwise, ignore it.

So first, I need to collect all the values of the field from the records. Then compute the mean. But if there are no such values, return 0? Or maybe return an empty integer? But the function returns an int. So perhaps 0 is the correct value when there are no entries.

So the steps are:

1. Iterate through each record in the records list.
2. For each record, check if the field exists and is a number.
3. Collect all valid numeric values of the field.
4. If there are no valid values, return 0.
5. Otherwise, compute the sum of these values, divide by the count, and round down (floor division).
6. Return the result as an integer.

But wait, how do I check if the field is a number? The problem says that each record may carry a named numeric field. So perhaps the field is a number, but what if the field is not a number? For example, if a record has a string in that field. But the problem says that a record lacking the field is passed over. So maybe the field is expected to be a number. But the problem says that if a record doesn't have the field, it's passed over. So, for records that do have the field, we need to check if it's a number. But the problem says that the field is a numeric field. So maybe the records are guaranteed to have the field as a number. But the problem says that if a record's field is not a number, it should be passed over. Wait, the problem says that the function is supposed to handle records that may carry a named numeric field. So perhaps the function should check if the field is a number. If not, skip it.

But the problem says that the function should return the mean of that field. So, for each record, if the field exists and is a number, include it. Otherwise, skip.

So, for each record in records:

- Check if the field is present in the record.
- If present, check if it's a number (int or float?).
- If yes, add to the list of values.
- If not, skip.

But how to check if the field is a number? For example, if the field is a string that can be converted to a number. But the problem says that the field is a numeric field. So maybe the records are structured such that the field is a number. But the problem says that if a record's field is