Semantic fields are never going to be defined as clearly, either in theory or in applications, as say fermion fields in physics. If you take very strictly the idea that "a semantic field is a set of words grouped semantically (that is, by meaning), referring to a specific subject," then the answer to your title question is obvious.
Obviously each of the definitions you quote deals with a different specific subject.
By that criterion few words in any language will belong to a unique semantic field. Maybe obscure terms like "Technetium" do (an element in chemistry). But even "iron" or "sulfur" will belong to many different fields.
But in the question you ask "what underlying semantic field connects, conciliates, and unites the 4 different sets below."
The answer to that is warp in weaving.
To see this you should see specifically what warp is. When @KWeiss writes of warp threads fixed into the weaving frame, that is just for carpet (or tapestry) weaving where you use a frame fixed at the size of the carpet.
Ordinary looms such as the Han Dynasty loom reconstructed below have a fixed width but can produce a strip of fabric however long the warp threads are. (The width was normally at most the arm-span of the weaver, so the weaver can easily push the shuttle back and forth carrying the weft threads.)
This is from https://www.facebook.com/chrisbuckley.toranatribal/photos/a.10151613664370469.1073741827.8534905468/10153685553110469/?type=1&theater
Usually the warp threads are kept on rolls at the far end of the loom away from the weaver. The fabric is rolled up at the weaver's end as it is produced, and the warp threads are unrolled at the other end as needed. Different warp threads are raised at different times, by the treadles shown in the diagram. And while the diagram has just two treadles fairly early looms sometimes used more treadles to create more elaborate weave patterns. The weft is just passed back and forth each time. This is the relation of warp to "managing."
The warp and weft threads both "pass through" each other in some sense. But the warp threads run the whole length of the piece, never changing direction. The weft threads cross back and forth across the width of the fabric. Further, as Wikipedia puts it: "Because the warp is held under high tension during the entire process of weaving the warp yarn must be strong." The weft is usually less strong, and more flexible so it will bend to cover more of the warp threads it crosses. This is what links warp to constancy and enduring, and to longitude reaching from pole to pole (as opposed to lines of latitude which circle the earth), and to the Classic Books. The classics convey the warp of learning.
Warp and Weft, Chinese Language and Culture by Keekok Lee gives a much more detailed account which you can see at
That book offers reasons why the warp is even more fundamental in Chinese weaving than in western.