Before seeing this, I came up with 3.576MB with a rough Fermi/back of the envelope method.
I am going to choose the language "English", and import two packages, "Mathematics" and "Physics", and write in a modern high level computer programming language called "Python". These packages and the English dictionary are all stored on a large hard drive on a single computer on Earth. I may use a bit of natural philosophy.
The setup is quite simple. We want to communicate "The Standard Model" to another entity. We're going to end up with a .txt file, which will then be sent over a line.
Let's imagine person A, who only speaks English and has a deep grasp of math, physics, and "The Standard Model", perhaps an experimental physicist working at CERN. This person can, with a bunch of squiggly lines, and a little notebook with twenty or so rational numbers, actually stand next to a great big machine, and tell you what numbers are going to come out it. It's truly remarkable.
Here are the squiggly lines (or a point in a high dimensional pixel space - your call):
The masses are experimentally determined, and we could define them as constants in our computer program:
unit = GeV/c^2
m1 = 0
m2 = 0
m17 = 173.1
m18 = 0.0072973525693
m22 = ...
and so on for the 22 constants.
However, we are cheating if we stop here. This person has a brain, and in that brain is the English language, no less than 50-100 courses in mathematics and physics, hundreds of papers that were poured over line by line, and the book in hand.
We'll need a mostly "self-contained" reference which discusses "The Standard Model", so let's take "Mathematical Aspects of Quantum Field Theory" by Edson De Faria and Welington de Melo. It's about 300 pages (298), and includes about 100 references (94) in the bibliography. Let's assume the number of courses is 50, and that there is 1 textbook for each course. Let's assume the references are all 50 pages, and the textbooks are all 300 pages long. For a standard .tex file, there will be some ratio of number of symbols per .pdf page. Based on one that I had, it was about $ 2000(symbol/page)=100(symbol/line)*20(line/page)$
Let's assume each symbol is a byte, so that we get $40.6MB$. Now, we need to include the size of math, physics, English, and Python. The English dictionary and Python code are easily measurable. Math and physics are a lot tougher. For the sake of this, let's say the math and physics are contained in the courses, references, and textbooks. Let's say the English language and Python together are $40.6MB$, for a total of $81.2MB$.
Now, this file is uncompressed. Let's say we have a compression ratio of 1/3, so we get $27.06MB$.
Person $\alpha$ speaks Spanish, and we'll assume they are very intelligent and well educated, but did not happen upon any math or physics at all in school. We're imagining they are both using computers, which are connected by a wire over a large distance.
In addition to the math and physics that'll need to be conveyed, person A will need to learn Spanish and person $\alpha$ will need to learn English, so we have two more dependencies, a translation neural network (or person), and a pedagogy package (or teacher):
I don't know the Kolmogorov complexity of either of those.
However, for the inferior machine versions, we can approximate.
OpenNMT is an open-source neural network based translation algorithm (https://github.com/OpenNMT/OpenNMT-py). It is $34.749MB$ zipped.
The teaching, or in other words the skill required to truly translate this information and knowledge to another, is the hardest part. Some universities pioneered an effort at automating their undergraduate math courses. This proved to be quite difficult generally, and they mostly used a hybrid model. However, some of the intro courses are completely online with video lecture supplements. If a course is 12 weeks with 4 hours of lecture per week, at ~2GB/hr, we're up in the $100GB/course$ range.
So, very roughly, an upper bound on the complexity of the Standard Model is somewhere between 61.8MB and 10TB.