5. Conservation is the maintenance phase of the empire. Any military operation in this phase should be closely studied and analyzed, including the human means factor. Victories and defeats alternate with each other. It is more a phase of the defensive in order to maintain conquered geographical regions.
6. In the Relative Independence phase, the strategic potential is equal to that of a nation, depending on the country’s military, economic and strategic ability.
7. Military disaster is an inexorable defeat, whether it is a campaign or a complete war.
8. The territory of a nation maintains its military potentiality towards territorial defense and an offensive potentiality, according to its geographical position, in the corresponding social cycle and in the social phase of the cycle.
9. There should be no friction between classical principles and mathematical-historical principles. These give results of the war or, in other cases, govern the total or High strategy. They are a strategic synthesis of the Law of History, that is, eternal Laws of the Art of war, that dominate the whole set. Accordingly, they are a determining factor in all strategic operations throughout the planet, not only in times of peace but also in times of war.
The author of Mathematics of History, Dr. Deulofeu, started on a different road than the one followed by other historians. The mathematics of history shows in an analysis of 5,100 years that humanity does not follow a road of ascending but oscillating progress that obeys mathematical precision.
The mathematical-historical cycle is 1,700 years, distributed thus: six and one-half centuries for the Era of Great Demographic Fractionation, and ten and one-half centuries for the Era of Great Unification, separated by a phase of Relative Independence that is indicated by a straight line. Each nucleus of union or empire, has a first aggressive process or first Period of Great Strategic Victories, as an ascending line, followed by a Great Depression, afterwards, a second aggressive process that has a unifying character, different from the first one, that is a federal characteristic. Afterwards, there follows a Military Disaster, that only affects the Armed Forces factor, afterwards, a Conservation phase and finally, Decadence or Disintegration.
If this nucleus is the first one, then the Relative independence phase follows, and if it is the second one, then the era of Great Union of ten and one-half centuries ends, and the era of Great Fractionation of the following 1,700 years begins, and so forth.
The empire Unification nuclei have an approximate duration of between five and five and one-half centuries.
In the second period of great strategic victories or second aggressive process, that is characterized by its centralization or unification of the corresponding empire, there appeared the so called Great Captains: Hannibal, in the Carthaginian Empire, Alexander the Great, in the Macedonian Empire, Julius Caesar, in the Roman Empire, Napoleon in the French Empire, etc.