I agree completely, all of these kinds of conjectures are shaped by what is detectable. If there are any "dark matter" programs out there, they by definition will be difficult to find. That said, I find it entirely plausible that the champions will win by exploiting complex and exotic mathematical facts, while the implementations of the math do not themselves need to be complex or exotic at the code level.

More rambling thoughts about this: https://nickdrozd.github.io/2021/09/25/spaghetti-code-conjec...

Rough sketch of an argument:

Let's construct a number from all intermediate states of the machine concatenated. The number of digits of this number should correspond to the runtime (sketchy). We only care about the halting machines, so it's finite. We know that it must be unique because if a smaller machine computes the same number, we could get a bigger number by simply running the smaller program and doing other nonsense. That means the biggest programs are komolgorov optimal, and the numbers themselves should be k-trivial and thus nearly but not quite computable. Since they're not computable, the programs themselves can't follow a structure to generate them (since that would be computable in turn for larger values).

[1] https://oeis.org/A114852

  int main(void) {
    void* A[] = {&&A0, &&A1, &&A2, &&A3};
    void* B[] = {&&B0, &&B1, &&B2, &&B3};
    void* C[] = {&&C0, &&C1, &&C2, &&C3};
    goto *A[SCAN];
    A0: WRITE(1); RIGHT; goto *B[SCAN];
    A1: WRITE(3); LEFT ; goto *B[SCAN];
    A2: WRITE(1); RIGHT; HALT; return 0;
    A3: WRITE(2); RIGHT; goto *A[SCAN];
    B0: WRITE(2); LEFT ; goto *C[SCAN];
    B1: WRITE(3); RIGHT; goto *B[SCAN];
    B2: WRITE(1); LEFT ; goto *C[SCAN];
    B3: WRITE(2); RIGHT; goto *A[SCAN];
    C0: WRITE(3); RIGHT; goto *B[SCAN];
    C1: WRITE(1); LEFT ; goto *B[SCAN];
    C2: WRITE(3); LEFT ; goto *C[SCAN];
    C3: WRITE(2); RIGHT; goto *C[SCAN];
  }

Because A and C only jump to B it is possible to structure this using only loops and one boolean. Let us use Rust to demonstrate as it lacks GOTO:

    let mut a = true;
    loop {
        loop {
            if a { // state A
                match scan() {
                    0 => { write(1); right(); break }
                    1 => { write(3); left(); break }
                    2 => { write(1); right(); return }
                    3 => { write(2); right() }
                }
            } else { // state C
                match scan() {
                    0 => { write(3); right(); break }
                    1 => { write(1); left(); break }
                    2 => { write(3); left() }
                    3 => { write(2); right() }
                }
            }
        }

        a = loop { // state B
            match scan() {
                0 => { write(2); left(); break false }
                1 => { write(3); right() }
                2 => { write(1); left(); break false }
                3 => { write(2); right(); break true }
            }
        }
    }

Collaborating on Discord is fine. Important results, including citations backing them, should really be published or at least replicated in more durable medium that's less susceptible to link rot, and easier to archive. Today, that's PDFs in paper repositories, or even regular blog posts.

1. Outright fraud

2. Lack of independent verification of results before building up a body of work resulting in a bunch of garbage. Contributes to making #1 “easy”.

3. Financial pressures to publish or perish contributing to 1 & 2. If peer review didn’t exist you’d still something similar about producing “recognized” results. This is also probably why we haven’t done any major breakthroughs in particle physics which now has a much longer term thinking phase to come up with anything.

The biggest problem with peer review is actually the establishment of an orthodoxy which discourages itself being upended by controlling the career success of anyone who dare challenge it - you have to support the orthodoxy to get career success and you fail to get recognition if your idea challenges the peer reviewers ideas and careers. That being said, such pressures existed before, but at least you could try to build your own following and it was competing orthodoxies instead of a single one winning out.

What I think you are doing here is to DEFINE "foundational work" as something that gets published in a journal.

I don't mind if you use that definition, but if you do then the fact that all foundational work is published in journals is not insightful or informative, it is merely the definition.

If, on the other hand, you intended for the statement to say something meaningful about how important scientific and mathematical work is communicated, then you need a different definition of "foundational". And you would have to look to that definition to decide whether this work was foundational, because if it was then it disproves your hypothesis: it would be a counter example that illustrates that some foundational work is shared in places other than journals.