Here is my attempt at the definitive ontology in a nutshell.

Reality consists of objects and relations between them (as opposed to nothing).

Objects can be divided into concrete and general. A general object is a property that is shared by other objects that are similar with respect to the given property while a concrete object is not a property of any other object. For example, circle as a general object (circleness) is a property shared by all concrete circles while a concrete circle is not a property of any other object. Also, more general objects are properties of less general objects. For example, geometric object as a general object is a property of circle as a general object (as well as a property of all concrete circles). Relations can be similarly divided into concrete and general too. Concrete and general are thus interwoven and inseparable. Some people regard general objects as merely words (linguistic symbols in written or spoken form) but I hold that they are involved in the nature of concrete objects.

There is a principle of composition, which means that if there are some objects, whatever they are, they automatically make up another object that is a collection or combination of those objects. And this larger object automatically combines with other objects into even larger objects, and so on. So every possible object is either composed of other possible objects or is a non-composite object. A non-composite object is a collection or combination of no objects.

There is no difference between a possible and a “real” object, so reality consists of all possible objects (and relations between them).

Pure set theory can in principle describe all possible objects; non-composite objects are called empty sets and composite objects are non-empty sets that are built up from empty sets. Pure set theory is also a foundational theory for mathematics because it is able to represent all mathematical objects or properties (numbers, spaces, functions, etc.) as pure sets. That's why reality is mathematical.

But mathematics is just the structural aspect of reality, the relations between sets, or structures of relations, reducible to the set membership relation (the composition relation). The objects that stand in those relations, the sets "in themselves", are something unstructured, partless (even though they stand in relations to objects that are their parts, that is, to the sets that compose them). The unstructured nature of objects in themselves is the basis for the qualitative aspect of consciousness (qualia), since consciousness apparently consists of unstructured "stuffs" or qualities (for example the experience of red color seems to be a non-decomposable, monadic redness).

A space is a special kind of object that has a continuity between its parts (as defined in pure set theory). Time is a special kind of space (as defined in theory of relativity). We live in a 4-dimensional space called spacetime (3 dimensions of space + 1 dimension of time). The number of dimensions of a space is the number of coordinates necessary to specify a location (part) inside the space. The structure of our spacetime has certain regularities that we call laws of physics and its parts (objects in spacetime) are distributed, in accordance with these regularities, in such a way that their spatial entropy (disorder) increases along the time dimension, thereby constituting the “arrow of time” which we experience as the difference between the past and the future and as the “passage” of time.

Mass/energy is defined in physics as the ability of an object to exert a force. In other words, it is the property of an object in spacetime of having causal relations to other objects, and causal relations are a special kind of mathematical relations in spacetime where consequences (events at a later point in the direction of time) logically follow from causes (events at an earlier point in the direction of time) and laws of physics. Unpredictability/randomness in quantum physics is the result of an interruption or weakening of causal relations because some events (measurement outcomes) cannot be derived (logically deduced) from preceding events and only the probabilities of possible outcomes can be derived.

Consciousness as we know it seems to consist of qualities of spatiotemporal objects that have a high degree of dynamic organized complexity (many different parts with many causal connections). Two prominent qualities of consciousness are pleasure and pain (which come in many forms and intensities). Pleasure is the quality of accepting a present state while pain is the quality of resisting a present state, because enjoying a pleasant state means we allow or maintain it while suffering in a painful state means we resist it and try to change it. (There may be complexities involved such as allowing some degree of pain with the expectation of achieving pleasure in the future, an expectation that itself gives pleasure that surpasses the pain in the present moment.) These behaviors and associated qualia are often triggered automatically by the body but some can be influenced deliberately. Evolution tends to ensure that we accept (and thus enjoy) states that are conducive to survival and reproduction and that we resist (and thus dislike) states that threaten survival or reproduction.

Necessarily, we live in a world (a part of reality) that has the conditions suitable for consciousness of our kind (anthropic principle). These conditions probably include regularities such as stable laws of physics because otherwise the world would be too random or chaotic to support the formation of living organisms, let alone conscious beings such as us, with our evolved predictive neurological apparatus. That would explain why the laws of physics in our world have been stable for billions of years: it is the kind of world in which we would necessarily find ourselves, as we couldn't have evolved in an unstable world. Why we should expect the laws of physics to remain stable also in the future may be less clear but an answer might lie in Solomonoff induction: given the stable regularities of the world such as laws of physics in its long evolution so far, if the regularities continue in the future then the world is in an algorithmic sense much more simple than if the regularities are discontinued, and more simple worlds are more likely (more frequent in the collection of all possible worlds) than more complex worlds. Continuing stability of laws of physics and causality is thus not guaranteed but very likely.

A fact is a true proposition. Propositions are declarative sentences (or their meaning). They are a tool of verbal communication; they convey information by claiming that an object has a certain property. If the object indeed has the claimed property, the proposition is true, otherwise it is false. Verbal communication also uses other kinds of sentences: interrogative (requests for information), imperative (commands), and exclamatory (expressions of strong emotion).