That said, let's just say that there is something very obvious hidden in plain sight, when dealing with all modular arithmetics, be it the discrete logarithm, ECDLP or prime factorization problem. Let me just say this: a hash algorithm can always collide. But the real math, like actual good programming, doesn't work without guarantees. Take everything you have at your disposal, modular math is like "losing" information and pretending it can never be retrieved back, and calling it a "discrete problem". I do have some pen and paper results taken out from ideas you will never find in any study, ChatGPT, or school. Are there chances for any of them to break EC? Maybe, maybe not. But if it does, puzzle 66 may be the last of your problems.
Regardless of the math used, eventually you have to transform the math into something, a public key, a h160, whatever type collision/match you are looking for.
But let us say it's pure math, do the "math" for how long it takes a current CPU to do straight additions, just using numbers. And use a higher end CPU with say 5.0 mghz capability.
IMO, you have to eventually transform the pure math into what you are searching for, or have a precomputed list of something...so to me, it can never be, just math.
I can give you a public key in a small bit range, and just using math, you would never solve/know if a match was found. Understand?