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)
@johnswentworth @David Lorell
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)