First Principle vs 2nd principle
My understanding was:
1st principle: Performance data derived directly from a physics-based simulation of the aircraft. ("Octopus" program on airbus)
2nd principle: Performance data derived from lookup tables, diagrams, electronically stored tables etc., generally what is called "tabulated" data. Performance for one certain point (Weight, alti, temp...) is derived from interpolation in this data.
Historically, 2nd principle was used for perfo calculations, until computers became fast enough to do a 1st principle calculation within a reasonable time.
Certified performance can be either 1st or 2nd principle.
I have no idea, however, why they are called 1st and 2nd principle.