Definition:
Technical mapping is the act of complete and solidly justified object placement.
The product of technical mapping is a structured technical beatmap.

Axioms in mapping:
They are statements established by the mapper in order to practice technical mapping.
In technical mapping there are some axioms that must always be used:

1. The position of every hitcircle must be justified by the state of previous objects.
2. The position of every hitcircle must be justified by the tension of the music.
3. The position of every slider-head must be justified by the state of previous objects.
4. The position of every slider-head must be justified by the tension of the music.
5. The slider-path must be justified by previous objects.
6. The slider-path can be justified by following objects.
7. The slider-path must be justified by the tension of the music.
8. The slider-path can be justified by the effects of the music.
9. The slider-tail is always justified by the slider-path.
10. The slider velocity must be justified by the tension of the music.
11. The slider velocity can be justified by the effects of the music.
12. The use of spinners must be justified by the tension and effects of the music.
13. All of the above must stay true to the created axioms.
14. Correct use of the offset, BPM and BSD is required.
15. All axioms must be adjusted according to the general difficulty of the beamtap

Properties of axioms:
Axioms are what makes a technical beatmap unique, as they tend to differ from person to person.
Here are some axioms that one could create for an STD beatmap:

1. The distance between two objects A and B is justified by the prominence of what is audible when interacting with object B.
2. A sound is more prominent when it’s volume is higher than the volume of any sound right before. A sound is less prominent for an opposite instance.
3. A sound is more prominent when the pitch is higher than the pitch of any sound right before. A sound is less prominent for an opposite instance.
4. A sound can be more prominent when it’s clearly audible and relative rare.
5. Cymbals are more prominent than kicks and snares.
6. Kicks and snares are more prominent than high-hats.
7. Sounds of the same nature are to be represented the same way excluding aesthetically.
8. The placement of an object A is also justified if it’s in an aesthetic relationship with other objects B1, B2… All objects in this relationship must be simultaneously visible.

This is merely a portion of axioms that can be created and used in order to practice technical mapping. The more axioms there are, the more solid (/justifiable) the map will be. The context of an axiom can be further clarified by defining certain phrases or by using examples of how it can be applied.

Let’s take the last mentioned axiom as an example and attempt to further clarify it: The placement of an object A is justified if it’s in an aesthetic relationship with other objects B1, B2… All objects in this relationship must be simultaneously visible. As examples of aesthetic relationships between objects we can take blankets, symmetry, stacking etc.

It’s crucial to fully understand the context of an axiom. In this instance, there is the phrase: “is also”. While it seems unimportant, it can break the structure of a beatmap if not fully understood. This phrase implies that an aesthetic relationship between objects alone can’t justify the placement of an object, but it can only help do so. Meaning that a blanket is not enough to justify the placement of a hitcircle if it doesn’t hold true to another axiom.

Conclusions:
There are several conclusions that can be made if we take more than one axiom under account at the same time. For example, if we use the axiom: The placement of an object A is justified if it’s in an aesthetic relationship with other objects B1, B2… All objects in this relationship must be simultaneously visible. And: Sounds of the same nature are to be represented the same way, excluding aesthetically. We can conclude that two sound groups that are identical but found in different parts of the song can be represented with different object patterns but must also be represented with groups of objects that are of the same spacing respectively. Meaning that the two object groups must be spaciously consistent.

Comprehending the properties of axioms in mapping can lead to the creation of some of the best technical beatmaps. However what is “best” is subjective and differs from person to person. It’s advised to always take certain axioms under account that have been created by trial and error throughout the course of mapping to ensure that the map is “pretty” or “of acceptable quality”. Several of these axioms are included in the examples provided, but there are certainly more.

Every aspect of mapping can be justified by axioms. The tick rate, the combo colors, the patterns used, the curvature of sliders etc. The reason why technical beatmaps are in such small portions in both the ranked and unranked section is because the very creation of a beatmap takes a lot of time and effort. Therefore it requires a lot of patience.

Creating axioms and learning how to use them accordingly is usually a process that takes months or even years to properly complete.
The word “structured” in the definition of “Technical Mapping” means that there is not a single instance throughout the map where axioms are not being used or counteracted.

A beatmap can be technical if axioms are consciously being used but not necessarily structured.
In layman terms: If there is a solid and explainable reason of why everything is done they way it’s done, then the product is a structured technical beatmap.

A technical beatmap is not necessarily rankable because the axioms used can go against the ranking criteria.
A technical beatmap is not necessarily “pretty” because the axioms used can go against what is commonly considered “pretty”.

It's simple:
So in order to practice technical mapping, all you have to do is place an object, give a reason for placing it this way and never go against that reasoning afterwards. For example if you have a wub and you represent that wub with a special slider, all you have to do is explain that you used this specific slider-path curvature to represent this specific wub and NOT do otherwise when the same wub comes up.