Thank you very much, John! I’m really grateful for this post, and especially for taking my counterexample seriously and accepting it as a meaningful result. It means a lot to me to see my work mentioned here.
I’m also very glad that this became one small example of how LLMs, together with formal verification tools like Lean, can help independent researchers contribute to mathematics.
Hi! My name is Grisha Pochuev. This is a beautiful and inspiring conjecture, but unfortunately I have found a counterexample to its dimension-free linear formulation.
The construction is quite simple: let (X_1=S) be a uniformly random (n)-bit string, and let (X_2) reveal the whole string except with probability (\varepsilon), when the entire string is erased. Every individual bit (S_j) is then an admissible (\varepsilon)-redund. Approximate maximality forces (\Omega) to retain information about all (n) bits, including on the era... (read more)
Thank you very much, John! I’m really grateful for this post, and especially for taking my counterexample seriously and accepting it as a meaningful result. It means a lot to me to see my work mentioned here.
I’m also very glad that this became one small example of how LLMs, together with formal verification tools like Lean, can help independent researchers contribute to mathematics.