A village sage once said:"Only dead people are without problems." This sage was not formally educated but he was wise. Mathematically, the statement Only dead people are without problems is a conjecture because as mortals, we can not prove it. Nonetheless, we intuitively feel its veracity in our physical realm. So, the following fundamental axiom about problems is plausible:
Problems are existential states of awareness.
The implication of this axiom is that a cognitive ability is a prerequisite for the awareness of problems. The healthier this ability, the better the awareness.
What is a problem? A problem is any unknown which we have the desire to know. We usually express this desire as a query. For example, the query "what is your name?" is a simple problem. The name of the person of interest is the unknown which we have the deire to know. The query, "how many stars are in the Universe?" is a more complicated problem. The former is an identity problem and the latter is a contanership problem. When the unknow of a problem becomes known, we say the problem has be solved.
A problem can also be a known situation with undesired and unpleasant effects. These types of problems usually result from inability to solve precursor problems (problems that cause other problems). For example, an entity that is bankrupt has a known financial problem (disequilibrium).
Problems begin in an occupied space. The occupants of the space may be any type of configured energy. In other words, a geometry (natural, or man-made, or made by any other cognitive entity) is a prerequisite for the occurrence of problems. A space that is empty can not by itself initiate problems. It is only available for occupancy. A space that has no visible object in it is not necessarily empty. The space may contain air, light or any other member of the electromagnetic energy spectrum.
Pj Problems is the group name given to 7 types of problems: containership (matter's residence in space); Identity (unique characteristic of matter); force (matter's pull or push actions. A force is a doer.); motion (unfixedness of position relative to a frame of reference); change (transition from a prior state to a new state, the new state); grouping/interaction (bringing together base on a criterion or criteria/acting on and affecting one another); equilibrium (static: absence of a resultant force. Dynamic: presence of a resultant force). The P represents problem and the j is a subscript with values 1 thru 7.
All existential problems are Pj Problems. In other words, Nature amd cognitive beings pose only Pj Problems. Consequently, all problems humans or any other cognitive have solved, are Pj Problems. In any given problem, there is always an Independent Pj Problem (usually containership), one or more Dependent Pj Problems and the Pj Problem of Interest which is the problem for which solution is sought.
The Problem Genome is the totality of all Pj Problems. It is presented as a mesh of PjProblemsStrings (SiPjAjk). Where Si is the ith space of interest, Pj is the jth problem of interest and Ajk (called Pj's Allele) is a subtype of Pj. All systems designs and analyses are designs and analysis of PjProblemsStrings. So in essence, the Problem Genome is a composite of systems.