I’m treating the message as a list of 2095 chunks of 64 bits. Let d(i,j) be the Hamming distance between the i-th and j-th chunk. The pairs (i,j) that have low Hamming distance (namely differ by few bits) cluster around straight lines with ratios j/i very close to integer powers of 2/e (I see features at least from (2/e)^-8 to (2/e)^8).
This observation is clearer when treating the 64-bit chunks simply as double-precision IEEE754 floating points. Then the set of pairs (i,j) for which xi/xj is ±2n for some n clearly draws lines with slopes close to powers of 2/e. But they don’t seem quite straight, so the slope is not so clear. In any case there is some pretty big long-distance correlation between xi and xj with rather different indices. (Note that if we explain the first line j≃(2/e)i then the other powers are clearly consequences.)
I’m treating the message as a list of 2095 chunks of 64 bits. Let d(i,j) be the Hamming distance between the i-th and j-th chunk. The pairs (i,j) that have low Hamming distance (namely differ by few bits) cluster around straight lines with ratios j/i very close to integer powers of 2/e (I see features at least from (2/e)^-8 to (2/e)^8).
This observation is clearer when treating the 64-bit chunks simply as double-precision IEEE754 floating points. Then the set of pairs (i,j) for which xi/xj is ±2n for some n clearly draws lines with slopes close to powers of 2/e. But they don’t seem quite straight, so the slope is not so clear. In any case there is some pretty big long-distance correlation between xi and xj with rather different indices. (Note that if we explain the first line j≃(2/e)i then the other powers are clearly consequences.)