Sketch in C minor, for a movement of a Symphony, Hess 298, authorship:

Symphony Movement in minor, Hess 298. (1791/93). 
If Beethoven had completed this symphony movement (from 1791/93), it would have counted, together with the Cantata on the death of Emperor Joseph II, WoO 87, as the most important composition from the Bonn period. If the Cantata already points to the Beethoven we know and love, stronger and more passionate than his contemporaries, this symphony sketch does even more so. It is fascinating to see the youth of a mere 20 or 22 years, already writing music that is so close to the Eroica and Fifth Symphony. Sketched when Robespierre's reign of terror in France was rapidly reaching its bloody climax, one is inclined to say that this is the French Revolution in music. 

The Hess 298 sketch can be found in the Kafka Sketchbook, which is in the British Library. The heading reads: Sinfonia, and the tempo indication is Presto. It is in 3/4 time. The 111 bars long sketch is written on two staves, as if for piano. We have therefore not only the main melody, but also the bassline, which indicates unambiguously the intended harmonies. Once, in bar 91, there is an indication regarding the orchestration: obo[e]. Following this big chunk there are two little snippets, one 9 bars, the other 5 bars long. Clearly Beethoven intended to write a movement in Sonata form: the sketch covers the larger part of the expostion, with a first theme in minor (bar 1), a transition (bar 68) and a second theme in the parallel key of flat major (bar 86). The sketch breaks off halfway the second theme group. 

On the completion:
As is clear from the state in which Beethoven has left the sketch, it is impossible to complete this movement without the addition of extra material. completion can therefore never claim to be authentic. It should be stressed that the aim of such a completion is to merely provide a framework which places the notes as written by Beethoven in an appropriate context, so that they can be judged and enjoyed as real music. 

Although not authentic by definition, one can, and should, demand of a completion that it be within Beethoven's style, using only compositional techniques known by him, and intellectually up to his standard. It's to others to judge whether the present completion succeeds in doing so. Some 35 bars have been added to complete the exposition. These contain new material, which is justified since this is still the exposition. The exposition is repeated in its entirety. 

The first part of the development section is based on material from the exposition, mainly the first two bars of the first theme. The modulations in bars 316 - 325 have been derived from bars 178 - 186 of the first movement of the Eroica. The second part of the development section, starting at the 5 min. 16 sec. mark of the midi, is based on the second, 5 bar long, snippet, which also belongs to the Hess 298 sketch. That's to say, although not derived from the exposition, it is authentic Beethoven material, intended for this piece. It was a deliberate choice to model the recapitulation as closely as possible on the exposition. Beethoven himself might have made considerable changes here, but since there is no way for us to tell what they might have been, the most sensible option was to do as little as possible. One change was inevitable: the second theme group had to be transposed from flat to the tonic of major. The coda is based on motifs from bars 26 - 29 of the exposition, in particular the motif on the second and third counts of bar 26. short fugato leads to the final climax in which the motif from bar 1 is played in contrary motion.