Persevering through trials proves what? to whom?

I am following the Daily Bible Reading Plan as presented in the ESV Study Bible. It will be the first time in awhile that I have read through the Bible in a year.

Today I read from 1 Peter 1, which was actually yesterday's reading. I was catching up this morning. Verses 6 and 7 of 1 Peter 1 caught my attention.

1 Peter 1: 6-7
6 In this you rejoice, though now for a little while, if necessary, you have been grieved by various trials, 7 so that the tested genuineness of your faith—more precious than gold that perishes though it is tested by fire—may be found to result in praise and glory and honor at the revelation of Jesus Christ.

Peter speaks of the 'tested genuineness of your faith'. That is, the trials show the genuineness of your faith. Is this test given so that God will recognize the genuineness of our faith? Does an all-knowing God really need to gather knowledge? Consider what Jonathan Edwards says about trials and testing in A Treatise Concerning Religious Affections:

If we put true gold into the furnace, we shall find its great value and preciousness: so the truth and inestimable value of the virtues of a true Christian appear when under these trials: 1 Pet. 1:7, "That the trial of your faith, being much more precious than of gold that perisheth, might be found unto praise, and honour, and glory." True and pure gold will come out of the furnace in full weight, so true saints, when tried, come forth as gold... Christ distinguishes true grace from counterfeit by this, that it is gold tried in the fire... So that it is evident, that these things are called trials in Scripture, principally as they try or prove the sincerity of professors. And, from what has now been observed, it is evident that they are the most proper trial or proof of their sincerity; inasmuch as the very meaning of the word trial, as it is ordinarily used in Scripture, is the difficulty occurring in the way of a professor's duty, as the trial or experiment of his sincerity...And this is the most proper proof and evidence to the conscience of those that are the subjects of these trials. For when God is said by these things to try men, and prove them, to see what is in their hearts, and whether they will keep his commandments or no; we are not to understand, that it is for his own information, or that he may obtain evidence himself of their sincerity (for he needs no trials for his information); but chiefly for their conviction, and to exhibit evidence to their consciences. (Emphasis mine)

It seems the testing, as far as proving genuineness goes, is for our benefit and the benefit of others. It testifies to the genuineness of our own faith. We are to see what God has brought us through, by his grace, and see that either our faith is true or that it is false.

What do you think?