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## Ontomathematics

Ontoaxiomatics is the axiomatic foundation of substantiality (things that can exist, do necessarily exist, but each in its corresponding causal connectome).

Infinite ontoaxiomatics and universes exist, but it's impossible to travel in nonparallelisable universes with different ontophysics. Not all substantialities are universes, but they are universe-like in order they provide the required operation space (complex phase space; usually multidimensional) for causal relations and interactions/processing.

Each ontoaxiomatics has to be causally coherent and be created by the same blockchain-like algorithm. Scientoaxiomatics (axiomatics is science) don't have to be created by the same algorithm; but they have to create useful mathematics; sensical mathematics for science).

Any axiom has to be rigorously logical (otherwise it's not an axiom), based to some form of mathematics (infinite mathematics result from infinite mathematical types of axiomatics).

What is the difference of scientomathematics (as used in science) and ontomathematics (being the logical foundation of ontoaxiomatics)?

Scientomathematics has to create useful and practical science. It is possible to create (different) mathematics (from different axiomatics) which are needlessly complex, or with very limiting/operationally hindering axiomatics that might create equivalent mathematics but in an unnecessarily convoluted way.

Ontomathematics doesn't have to meet the scientific criterion of usefulness. Ontomathematics simply have (infinite ontoaxiomatics are possible) to be based on coherent [onto]axiomatics; more coherent than scientoaxiomatics, because each substantiality holds itself as one Everettian (manyworlded) universe due to its coherent causal connectome. Ontomathematics don't (in plural) have to generate mathematics of generic usefulness. Ontomathematics along with ontoaxiomatics provide the self-causal foundations of substantiality. Any ontoaxiomatics based on correct (not contradictory) ontomathematics, guarantee the existential necessity of the particular ontophysical substantiality (universe and objects in it, or universe-like phase space with permitted interactions).

Can we clearly differentiate ontomathematics from ontoaxiomatics?

No. Theoretically ontomathematics (they [in plural being infinite; one for each universe] don't physically exist) are the logical foundations of ontoaxiomatics (neither do they), and ontoaxiomatics define each different ontophysics. Here these terms are hierarchically presented from the most ideal to the most physical: ontomathematics > ontoaxiomatics > ontophysics > substantialities (universes, physical fields, objects, etc.). But practically the substantiality hierarchy of ontomathematics versus ontoaxiomatics isn't clear (both create a causal connectome with non-absolute functional differentiations).

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Are the infinite different ontomathematics compatible with/transcribable into the infinite different mathematics?

generalised: Are the infinite different fields of rigorous logic (mathematics, physics, geometry, etc.) mutually transcribable, and to what extent (for practical descriptions or at their axiomatic foundations)?

Different fields of rigorous logic are mutually transcribable for descriptions (but that isn't practical; we can use a computer program to transform each mathematical problem to a geometric one, and when we face an axiomatic vagueness between mathematics and geometry we can create descriptions (particular to each problem; not generalisable) with other shapes; thus we can transcribe (as a[n im]practical description not axiomatically based) every mathematical problem into a geometrical one [with totally impractical huge shapes] and without using the rigorous techniques of Euclide [that is "false geometry" according to the Euclideanists]). We can transcribe each mathematical problem and solution into geometry-like formalisms, but not in Euclidean axiomatic geometry.

Different fields of rigorous logic are mutual transcribable as comments and notes; but without axiomatic identity (the omniaxiomatics: the axiomatics of all axiomatics doesn't exist).

(Can we transcribe ontomathematics into mathematics, physics into mathematics, etc. Answer: same as above)

### comment:

Even if string theory were a possible family of ontoaxiomatics; it's by no means the only family of ontoaxiomatics.