4:14 Update: The final counts are still trickling in, but it looks like Exxon has held onto the crown of most valuable company by a hair. We have Apple at $345.8 billion versus Exxon at $348.32 billion.

Maybe another day Apple can close the deal.

3:13 Update: Apple has topped Exxon Mobil to become the world's most valuable company that's publicly traded.

The market hasn't closed yet, and it's seen some very wild swings, but as of this writing Apple is clear of Exxon by $1.45 billion. As recently as yesterday, Exxon's market cap was $10 billion above Apple. And during the day Exxon was $6 billion more valuable.

It's a truly incredible run from Apple to go from death's door to the top of the world in just over a decade's time.

From earlier ....

1:36 Update: It was fun while it lasted ... Exxon is back on top.

1:23 Update: Apple has passed Exxon for the first time ever to become the world's most valuable public company, per CNBC.

12:08 Update: And the gap has narrowed once again. Exxon has Apple by just $2.86 billion.

Update: Indeed, it's going to be a wild day: Exxon's lead over Apple is now at $5.79 billion. Just a few minutes ago it was $2.73 billion.

Original: We're just opening up on what is likely to be a wild day of trading, but as of this writing, Apple is $2.73 billion away from topping Exxon's market cap, making it the most valuable public company in the world.

The stocks are going to be swinging all over the place today, so there's a chance the gap gets bigger, and there's a chance the gap narrows and Apple takes the top slot.

Pretty amazing for Apple.

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Here's another look at the chart:

Apple Market Cap Stock Chart by YCharts