Moltke understood - to be polite - very few of the railway logistics, the railway department and its works and abilitities. He also said to have hjad rather few faith into them as several german general having worked this field during Moltke the Minors reign have stated, ie. Groener but also (esp. ?)
Hermann v. Staabs.
Your efforts in calculating from principly wished-for requirements stated by the german railway department is are honorable.
But ... excuse me if I trust more into the statements of someone who has for been chief of the reilway department of the Great General Staff for 3 years and after the usual 'active troop command' for another 3 years Chief of the 'Armee-Verwaltungs-Departement' (Army administration department) which at the war ministry was reposnsible for ... preparation of mobilisation until 1913.
He rendered it possible to place in East Prussia a :
1. Army at a Tilsit-Gumbinnen sector :
Guards Corps, I.Corps, II.Corps, Guards Reserve Corps
Guards Cav.Div., 2. Cav.Div.
8. Army at a Gumbinnen-Marggrabowa sector :
X.Corps, XVIII.Corps, I.Reserve Corps, X.Reserve Corps
3. Cav.Div, 1. Cav.Div
2. Army at a Lyck-Rudzanny sector
III.Corps, IV.Corps, III.Reserve Corps, IV.Reserve Corps
4. Cav.Div.
3. Army at a Ortelsburg-Soldau sector
XII.Corps, XIX.Corps, V.Reserve Corps and XII.Reserve Corps at Thorn
And ALL of these
ready to rumble on day M 15 ! of mobilisation.
These are
16 army corps - active and reserve - and 5 cavalry divisions instead of the 9 army corps and 4 cavalry divisions you calculated for M 15 at best and only hardly.
If someone might ask v.Staabs also envisaged on M 15 an additional
4. Army in midth Silesia
V.Corps, VI.Corps, VI.Reserve Corp, Landwehr Corps
5.Cav.Div, 8.Cav.Div.
as ready to rumble.