FORTUNE -- There are three parts to the 17-page testimony Apple (AAPL) submitted Monday afternoon in advance of Tim Cook's appearance before the Senate Permanent Subcommitee on Investigations, scheduled for Tuesday:
According to the New York Times, it's in the southern Irish city of Cork that Apple pioneered its famous "double irish with a Dutch sandwich" -- a tax avoidance technique designed to take advantage of a quirk in Ireland's tax laws that allows foreign corporations to move money around the world tax free.
Perhaps anticipating that this is what the senators want to talk about, Apple spent nearly half of the 5,000-word statement it submitted Monday defending its use of five subsidiaries based in Ireland: Apple Operations International (AOI), Apple Operations, Apple Operations Europe, Apple Sales International and Apple Distribution International.
[Sure enough, the Senate subcommittee report is all about these subsidiaries. This is how it describes AOI: "a 30-year old corporation that has no employees or physical presence, and whose operations are managed and controlled out of the United States. Despite receiving $30 billion in earnings and profits during the period 2009 through 2011 as the key holding company for Apple's extensive offshore corporate structure, Apple Operations International has no declared tax residency anywhere in the world and, as a consequence, has not paid corporate income tax to any national government for the past 5 years."]
The document sheds more light on these mysterious operations than Apple has shed before. And yet, somehow, we're still in the dark.
To be fair, this is complicated stuff. But Apple doesn't make it any easier to understand by leaning on acronyms (AOI, CFC, etc.), using words instead of diagrams (unfortunately, we can't vouch for the accuracy of the Times' version at right), and leaving out key details (like how much money we're talking about and where exactly it goes).
But the points the company wants to make are clear enough:
But one comes away from the document feeling that there is much more that could be said about what Apple is up to in Cork. Take, for example, this Catch 22, offered baldly as a statement of fact:
"AOI is incorporated in Ireland; thus, under US law, it is not tax resident in the US. AOI is also not tax resident in Ireland because it does not meet the fact-specific residency requirements of Irish law."
You can tell Apple is bit defensive about all this when it lays out, in a bulleted item right on page 2, this statement of what it does not do:
Tim Cook will have one thing going for him Tuesday. I bet he understand this stuff. Odds are his Senate inquisitors don't.
UPDATE: We got a taste of where the senators are headed with two quotes given Monday afternoon to the New York Times:
"Apple wasn't satisfied with shifting its profits to a low-tax offshore tax haven," said Senator Carl Levin, a Michigan Democrat. "Apple sought the holy grail of tax avoidance. It has created offshore entities holding tens of billions of dollars while claiming to be tax resident nowhere."
John McCain, the Arizona Republican who is the ranking member on the committee, added: "Apple claims to be the largest U.S. corporate taxpayer, but by sheer size and scale, it is also among America's largest tax avoiders."
UPDATE 2: The Wall Street Journal fills in some of the blanks with details from the subcommitee's staff report: (I quote from a story titled Apple Pays No Tax on Much of Its Overseas Income, Senate Panel Finds)
Get out the popcorn. This could get hot. The hearings are scheduled to start at 9:30 a.m. Eastern. Cook, CFO Peter Oppenheimer and Phillip Bullock, head of Apple's tax operations (hired from Symantec a year ago last April), are in the second panel.
For the TV schedule, check C-Span Tuesday morning.
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