A Mathematical Certainty of Fraud

Stephen Braddy
Software Engineer
stephenbraddy@gmail.com

In my opinion it is a mathematical certainty that the CBS Bush National Guard documents are fraudulent. This image is an overlay of one of the so-called Bush National Guard documents with a document created during the week of September 6, 2004 using Microsoft Word 2002. As anybody can see they are a perfect match.

In order to understand why this image can lead to a mathematically-sound conclusion of fraud, one must first have a basic awareness of kerning. Kerning is the process of placing typed characters on a page. Any mechanical device (typewriter) or software system (Microsoft Word) that performs a kerning process must take into account all of the many aspects of typed text, including the shape, width, and height of each individual character in the font, the horizontal spacing between each character, the vertical spacing between each line of text, the support of superscripts and/or subscripts, the support of automatic word wrapping, etc.

So how can one conclude that the image above demonstrates a mathematical certainty of fraud? The answer is that any tiny difference between two kerning systems will cause compounding deviations in documents that they create.

In order to understand this, one should try to imagine a typewriter or word processor placing characters one-by-one on a line of text on a page. The placement of each character on the page will affect the placement of all letters that come after it. This is how the deviation is compounded in documents that are created by two slightly different kerning systems – each letter that is placed on a page increases the deviation in the rest of the document.

Imagine a scenario where two different kerning systems are exactly alike in all respects, except that they exhibit a mere 0.01mm difference in horizontal spacing between each character. Imagine that 80 characters are placed in a line on an otherwise blank page by those two kerning systems. If the two resulting documents are then aligned at the left edge and subjected to the overlay test, then the deviation at the right end of the page will have compounded to 0.8mm, and the difference between the two documents would be dramatically apparent. The compounding nature of deviation in kerning would cause the text at the left side of the document to line up rather well, but further to the right the deviation would be so severe that the text would be illegible. In reality, it would take much less than a 0.01mm difference in character spacing to yield two blatantly different documents in an overlay test.

The formula for calculating the deviation at the end of a line of text that has been generated by two kerners with different character spacing can be expressed as follows.


Dt = Dc * Ct

Dt = total spacing deviation at the end of a line of text
Dc = spacing deviation per character
Ct = total characters on a line of text


One can see that any difference in the amount of spacing per character between two kerning systems, no matter how miniscule, will eventually be exposed by the overlay test if the document is long enough.

Furthermore, character spacing deviation is only one scenario where compounding deviation between documents can occur. Any difference in line spacing between two kerning systems would also cause compounding deviation in the resulting documents that would be clearly visible during an overlay test; each line of text down the page would increasingly deviate between the two documents.

The fact that the CBS Bush National Guard overlay matches perfectly and shows no signs of compounding deviation makes it a mathematical certainty that the two documents were both created by Microsoft Word, and therefore not in 1973. It is nearly impossible to create two documents with two different kerning systems that can survive the overlay test, especially if those two kerning systems are separated by 30 years in technology and design.

Those that still believe that these documents are authentic should also consider the imperfect nature of mechanical kerning systems (typewriters). It would be difficult to reliably and consistently produce documents with the very same typewriter that can survive the overlay test. There would be deviations caused by the inherent nature of a mechanical device such as a typewriter. For example, each time the line feed mechanism is used to advance to the next line of text the placement of that new line may deviate by a tiny amount. By the time the operator has typed two whole seemingly identical pages of text, any tiny deviations in line spacing will be painfully obvious in the overlay test. In other words, one would be hard-pressed to produce an overlay as perfect as the one shown above even if they had access to the so-called 'Air Guard typewriter'. In this case the deviation at the end of a page could be calculated using a measurement of the average demonstrated deviation of the machine's line feed mechanism and would be expressed in terms of maximum possible deviation.

In defense of the authenticity of Bush National Guard documents, CBS has made many claims about the availability of typewriters with particular capabilities and the existence of certain font styles prior to 1973. They have also made claims about the authenticity of the hand-written signatures on the documents. However, all of these defensive claims are nullified by the simple fact that the overlay test proves beyond a mathematical doubt that the Bush National Guard documents were created with Microsoft Word.

CBS has also claimed that detailed analysis of the documents is futile because of the degradation caused by the photocopying and faxing of documents prior to their acquisition of the documents. Photocopying and faxing can cause the cosmetic appearance of each character on a page to degrade, but will never affect a character's relative position to all of the other characters in the document, which is the one and only symptom of compounding deviation. No amount of photocopying or faxing can affect the outcome of the overlay test. The simple fact is that the so-called Bush National Guard documents pass the overlay test when compared to documents created with Microsoft Word, and the only possible way to explain this is to say that the so-called Bush National Guard documents were originally kerned by Microsoft Word.