Total destruction of the building down to individual structural steel elements – obliterating the steel core structure.

The source material that A&E cites is here:

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Shredding of Steel

Twin Towers' Steel Frames Ripped to Small Pieces
This section of a larger photograph of the North Tower's destruction shows metal objects -- steel column sections and aluminum cladding -- being propelled away from the Tower.
A feature of the collapses that is less obvious than the symmetrically mushrooming tops or the vast clouds of concrete dust is their effect on the towers' steel frames.
The only large remnants of the towers standing after the collapses were base sections of the perimeter walls extending upward several stories. Some of these sections were about 200 feet wide by 80 feet tall. Virtually all of the remaining steel was broken up into small pieces:
* There were no remnants of the core structures that rose much above the rubble piles.
* Most of the perimeter walls above the standing bases were broken up into the three-floor by three-column prefabricated sections, and many of those sections were ripped apart at the welds.
* There were no large sections of the corrugated pans underlaying the floor slabs or the trussing beneath them.
If it were possible for the towers to have collapsed of their own weight, they would have exhibited a pattern of destruction very different from this. What would the collapse look like if all structure throughout a tower suddenly lost 95 percent of its strength, leaving the building too weak to support gravity loads?
* The core columns, being thicker than perimeter columns, and abundantly cross-braced, would have deflected falling rubble, and would have out-survived the perimeter walls.
* The accumulation of forces as the collapse progressed would have damaged portions of the outer wall closer to the ground more than higher portions, despite the thicker gauge of the steel lower in the tower.
* The rubble pile would have contained a stack of floor platters, since gravity would have pancaked, not shredded, them.
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1- The argument has been made that this is wrong; that the steel core was far from obliterated.

In fact, many video and still pictures show that the core in both towers was still standing moments after the collapse. The initial collapse consisted of the floors alone. However, one must take not that there was no claim made that the steel core didn't survive a few moments after the collapse. The point is it was completely destroyed at amazing speed.

In post 32, KennyJC states: "The fact is that the steel core was not obliterated. It remained in humungous chunks and was so difficult to remove from ground zero that it had to be cut into smaller sections. This prompted fools like Steven Jones to think that the beams had been cut during the collapse rather than after."

In fact, there is evidence that the certain cuts were -not- done after, but I don't have the information to differentiate the 2 on hand at present.