The bulk of a TARDIS is made up of Block-Transfer Mathematics. This form of Distributed Cluster Algebra was first developed by the people of the planet Logopolis. It is based on the idea that the essence of matter is structure and the essence of structure is mathematics. Using the hexadecimal notations of Block-Transfer it is possible to create Space-Time Events through pure calculation. An event or object can be described by thinking the correct Block-Transfer equations and it will instantly become reality.
Block-transfer equations can alter history itself. A sufficiently adept mathematical genius can project a temporary block transfer projection of himself through space and time just by reciting the right equations. With 11 other people reciting the right block transfer numbers it is possible, though difficult, for a Time Lord to track his TARDIS through space and time.

Block Transfer
might
work by using pure mathematics to model the possible existence of a specific space-time event or piece of matter
in a quantum alternate of this universe. Part of that model would be the probability/uncertainty that such a quantum possibility could exist. Once this model has been created then the relevant parts of that quantum universe can be transferred into this universe in discrete blocks of information - hence the term Block-Transfer.
Thus any matter (or other space time event) can be created out of pure mathematics if its
quantum possibility
can be modelled.
Because
the equations have to function in multiple timelines, block transfer equations used in creating a TARDIS use Base Code Numerals
which are numbers that are true in all Universes. They are a temporally invariant form of numeric representation.
These calculations are powered by raw Artron Energy. Block-Transfer Mathematics can only be computed with an organic brain because the mathematics alter the nature of reality. This would cause a traditional computer to malfunction. The original equations can however be recorded in traditional non-organic storage media such as bubble memory.

Matter created by a TARDIS using block transfer will have enhanced temporal properties and be resistant to being retro-annulled
This also makes it immune to the normal Vortex energies.
Some (but not all) Gallifreyan technology is made of non-atomic matter.