[Forest Keeper]

... but when James speaks of faith, he does not make any distinction between true and claimed faith.

Huh? Of course James makes a distinction:

James 2:14, 17 : 14 What good is it, my brothers, if a man claims to have faith but has no deeds? Can such faith save him? ...... 17 In the same way, faith by itself, if it is not accompanied by action, is dead.

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Indeed there is such a thing as claimed but false faith, referred to elsewhere in the scripture, but there is no indication that true faith is not grown from work just as good works grow, in turn, from faith.

True faith can INCREASE through works, but it cannot be FORMED through works. Faith always comes first from God. If faith is formed by works then salvation is earned.

[annalex]

True faith can INCREASE through works, but it cannot be FORMED through works

I don's see the difference. However, the statement that faith can increase through works puts you in the perimeter allowed by Trent, just barely.