Absent feedback, today I read further, to the premise of the maxent conjecture. Let X be 100 numbers up to 1 million, rerolled until the remainder of their sum modulo 1000000 ends up 0 or 1. (X’ will have sum-remainder circa 50 or circa −50.) Given X’, X1 has a 25%/50%/25% pattern around X′1. Given X2 through X100, X1 has a 50%/50% distribution. So the (First/Strong) Universal Natural Latent Conjecture fails, right?
Absent feedback, today I read further, to the premise of the maxent conjecture. Let X be 100 numbers up to 1 million, rerolled until the remainder of their sum modulo 1000000 ends up 0 or 1. (X’ will have sum-remainder circa 50 or circa −50.) Given X’, X1 has a 25%/50%/25% pattern around X′1. Given X2 through X100, X1 has a 50%/50% distribution. So the (First/Strong) Universal Natural Latent Conjecture fails, right?
I believe no natural latent exists in that case?
The Universal Natural Latent Conjecture doesn’t say X’ is always a natural latent, it says X’ is a natural latent if any natural latent exists.