feat: adding clarity and rewording

paper/src/main-genpop.tex

@@ -91,4 +91,13 @@ The textbook definition $D_{\mathrm{KL}}(P\parallel Q)=\sum_k P(k)\log(P(k)/Q(k)
 
 In code we do the boring fix: add a tiny floor $\varepsilon$ to both the numerator and denominator inside the log so nothing is exactly zero, which turns the sum into a finite, smoothed surrogate rather than a literal KL to raw counts. We also skip source states that do not exist at all in the reference kernel, because there is nowhere honest to compare against. This keeps the pipeline running and the divergence scores on a comparable scale, at the cost that the number is regularized KL-ish behavior, not a purist information-theoretic quantity---which is acceptable here because we only use the gap between human-anchored and agent-anchored scores as a weak separability signal, not as a calibrated physical constant.
 
+\section{Why the logarithm appears in the revelation surrogate}
+\label{app:revelation_log}
+
+Recall that $\text{COI}_{\text{leak}}(p,\tau') = f(\tau')\cdot\text{InfoValue}(p,\tau')$. The query-tax surrogate fixes $\text{InfoValue}$ to a positive constant: every suspected reconnaissance quote is penalized equally, which tracks the erosion story where independent query volume drives COI to zero. The revelation surrogate instead sets $\text{InfoValue}(p,\tau') = -\log \pi(p\mid\tau')$, where $\pi(\cdot\mid\tau')$ is the pricing policy's distribution over quoted prices in context $\tau'$ (after whatever discretization or binning the engine uses).
+
+For an outcome with probability $q$, the quantity $-\log q$ is \emph{surprisal}: likely draws are unsurprising, rare draws are highly surprising. That matches the informal ``surprise'' people talk about in recommender systems when they formalize novelty as low predicted probability---here the model is our own policy. The log is the standard information-theoretic way to turn ``how probable was this draw?'' into a penalty that grows sharply in the tails. In the reconnaissance reading, a price from a thin slice of the policy's support is more identifying than a typical quote.
+
+So the revelation form is \emph{contamination-weighted surprisal}: $f(\tau')$ scales how agent-like we judge the session, and $-\log\pi(p\mid\tau')$ scales how informative that price is relative to $\pi(\cdot\mid\tau')$. In code you still floor $\pi(p\mid\tau')$ away from zero so tail bins do not explode the penalty, same spirit as Appendix~\ref{app:kl_zeros}.
+
 \end{document}