diff --git a/paper/src/chapters/02-literature-review.tex b/paper/src/chapters/02-literature-review.tex
index b75624a..5e788ed 100644
--- a/paper/src/chapters/02-literature-review.tex
+++ b/paper/src/chapters/02-literature-review.tex
@@ -50,6 +50,7 @@ Our effort to combat contamination stems from research by \textcite{hardt_strate
 To bridge the gap between detection and robust pricing, we look at work in Distributionally Robust Optimization (DRO). As defined by \textcite{kuhn_wasserstein_2024}, DRO provides a framework for decision-making under ambiguity, where the true data distribution is unknown but lies within a ``Wasserstein ball'' of a target distribution. In our context, the ``ambiguity set'' represents the uncertainty introduced by agentic reconnaissance. By optimizing for the worst-case distribution within this set, pricing mechanisms can become resilient to the distributional shifts such as the ones caused by non-human actors, effectively robustifying the revenue function against the contamination described in our problem statement.
 
 In order to create an environment in which prices can be tested against a demand estimate generated by some behavioral model, we take inspiration from the architecture proposed by \textcite{ie_recsim_2019} in the RecSim platform built for recommendation systems. By modeling the distinct user behavior as POMDPs we can generate faithful interactions which allow us to generalize, past the constraint which is also present in recommendation systems, of rarely having enough experience with individual actor's interactions for good recommendations without generalization. The key inspiration comes from the user choice modeling which we translate to a user transition model for each distinct actor type (agent or human). We further consider the possibility of modeling our quantitative research platform using dynamic Bayesian networks for the sake of tractability within the system. The contribution or RecSim enables researchers to better understand learning algorithms in fixed environments, a gap we identify as needing to be bridged within the space of dynamic pricing.
+% TODO: mention https://github.com/meta-pytorch/OpenEnv/tree/main/envs/browsergym_env
 
 We also acknowledge the difficulty in similarly affected fields such as authorship, where \textcite{ganie_uncertainty_2025} demonstrate the theoretical limits of the distributional divergence between text authored by a human or large language model. Their approach of computing the divergence between two distributions demonstrates purely theoretically that no classifier can outperform random guessing on their particular task. This is yet another factor to take into consideration when exploring the potential mitigation strategies.
 
diff --git a/paper/src/chapters/03-methodology.tex b/paper/src/chapters/03-methodology.tex
index 62c103e..df97695 100644
--- a/paper/src/chapters/03-methodology.tex
+++ b/paper/src/chapters/03-methodology.tex
@@ -259,7 +259,7 @@ For both subsets, we model session dynamics as an MDP and estimate transition ke
 \end{equation}
 where $N(s, s')$ is the observed transition count. This allows us to construct a \textit{Contamination Generator} $\mathcal{G}(\alpha)$. Given a clean trajectory dataset, $\mathcal{G}$ injects synthetic agent trajectories sampled from $\hat{\mathcal{T}}_A$ until the effective mixing ratio reaches $\alpha$.
 
-To scale this to catalog-level pricing, we lift the base event transition structure from $T\times T$ (event states only) to $(T\cdot N + C)\times(T\cdot N + C)$, where $N$ is catalog size and $C$ captures generic events (homepage, login, checkout terminal states). This construction lets demand and behavior be product-specific while preserving shared navigation transitions.
+To scale this to catalog-level pricing, we expand the base event transition matrix from $T\times T$ into product-specific transitions using the current demand condition. In practice, we normalize the demand vector across products and use it to weight how much transition mass each product pair receives. Concretely, each cell of the base matrix becomes an $N\times N$ block (for $N$ products), so the transition matrix grows from $T\times T$ to $(T\cdot N)\times(T\cdot N)$. Finally, we add $C$ generic states (homepage, login, checkout terminal states), which gives the full kernel size $(T\cdot N + C)\times(T\cdot N + C)$.
 
 \begin{figure}[ht]
     \centering