chore: rename to distinguishability

paper/src/chapters/01-intro.tex

@@ -8,9 +8,9 @@
 
 \section{Introduction}
 
-In this paper we present an exploration and defense against the presence of new commercial entities in digitally powered platforms, preserving market equilibrium in the age of AI. This research establishes the following contributions: definition and formalization of non-human transactors in e-commerce platforms, development of a testing-ground for capturing the behavioral essence of these transactors across a large variety of digital systems, construction of a discriminative model (to prove separability) as a strong learner for downstream mitigation of contamination by non-human entities, translation of such learned separability into existing dynamic pricing machine learning loops, and finally establishment of a high-level KPI-affecting causal effect and cost-saving framework for the future of internet commerce in the presence of such non-human learners.
+In this paper we present an exploration and defense against the presence of new commercial entities in digitally powered platforms, preserving market equilibrium in the age of AI. This research establishes the following contributions: definition and formalization of non-human transactors in e-commerce platforms, development of a testing-ground for capturing the behavioral essence of these transactors across a large variety of digital systems, construction of a discriminative model (to prove distinguishability) as a strong learner for downstream mitigation of contamination by non-human entities, translation of such learned distinguishability into existing dynamic pricing machine learning loops, and finally establishment of a high-level KPI-affecting causal effect and cost-saving framework for the future of internet commerce in the presence of such non-human learners.
 
-This research effort touches a large variety of domains, spanning behavioral economics for understanding the rationality of behavior as theorized by the concept of homo economicus, agent-based modeling to translate our learned separability into disjoint dynamic pricing systems, reinforcement learning which serves as the SOTA for price-learners, and dynamic pricing and market equilibrium theory to understand the risks of possible supra-competitive pricing phenomena in cases of adversarial pricing systems driving the market out of equilibrium. \footnote{Given the rapid evolution of the field we acknowledge all developments with a cutoff set at the date of March 1st 2026.}
+This research effort touches a large variety of domains, spanning behavioral economics for understanding the rationality of behavior as theorized by the concept of homo economicus, agent-based modeling to translate our learned distinguishability into disjoint dynamic pricing systems, reinforcement learning which serves as the SOTA for price-learners, and dynamic pricing and market equilibrium theory to understand the risks of possible supra-competitive pricing phenomena in cases of adversarial pricing systems driving the market out of equilibrium. \footnote{Given the rapid evolution of the field we acknowledge all developments with a cutoff set at the date of March 1st 2026.}
 
 \subsection{Motivation and Market Context}
 
@@ -30,7 +30,7 @@ We formally define interaction data as coming from some actor which can either b
 This dissertation is organized around one main research question and three supporting sub-questions:
 \begin{enumerate}
     \item[\textbf{Main RQ}] How can dynamic pricing systems preserve margin integrity when transaction orchestration is increasingly mediated by non-human agents?
-    \item[\textbf{SQ1}] \textit{Separability}: Can agent and human sessions be reliably distinguished from behavioral interaction signals alone, without relying on network-level or device fingerprinting?
+    \item[\textbf{SQ1}] \textit{Distinguishability}: Can agent and human sessions be reliably distinguished from behavioral interaction signals alone, without relying on network-level or device fingerprinting?
     \item[\textbf{SQ2}] \textit{Theoretical Impact}: What is the formal relationship between agent contamination levels and the erosion of pricing power in dynamic pricing systems?
     \item[\textbf{SQ3}] \textit{Robust Mitigation}: How can pricing policies be constructed to maintain margin integrity under unknown and non-stationary levels of agent contamination?
 \end{enumerate}
@@ -64,4 +64,4 @@ Extract final result $r$ from terminal state\;
 \end{algorithm}
 
 
-The previously described goal of separability allows us to formulate a task which entails taking raw interaction data for either actor and creating a composite demand estimate $\hat{q}$. We propose a robust optimization objective defined in our methodology, transforming the pricing problem into a form of Distributionally Robust Optimization \parencite{kuhn_distributionally_2025} where the learner must guard against adversarial contamination in observed demand distributors. In this setting we must learn to make decision that perform under the assumption of not having a single estimated probability distribution but under an ambiguity set of any distribution, of which we have limited information. In our case as stated is a mixture of distributions with a parameter which is unknown and non-stationary.
+The previously described goal of distinguishability allows us to formulate a task which entails taking raw interaction data for either actor and creating a composite demand estimate $\hat{q}$. We propose a robust optimization objective defined in our methodology, transforming the pricing problem into a form of Distributionally Robust Optimization \parencite{kuhn_distributionally_2025} where the learner must guard against adversarial contamination in observed demand distributors. In this setting we must learn to make decision that perform under the assumption of not having a single estimated probability distribution but under an ambiguity set of any distribution, of which we have limited information. In our case as stated is a mixture of distributions with a parameter which is unknown and non-stationary.

paper/src/chapters/02-literature-review.tex

@@ -1,6 +1,6 @@
 \section{Literature Review}
 
-To better understand all wedges of the current works, we must start by exploring the nature of agents, agentic computer use and web automation, complementing that with economic reasoning and strategic interaction. The final surface to cover, leads us to data-driven dynamic pricing under uncertainty. The key technical risk is not ``agents buying things'' per se, but agents shaping the behavioral and demand signals that downstream pricing systems consume and depend on. This latter case of agents shopping is currently pending legal action in the case of \textcite{noauthor_amazoncom_2026} which is currently being treated as a violation of the Computer Fraud and Abuse Act. The introduction of these mediating actor entities into economic systems, is further creating a threat of false-name bidding \parencite{yokoo_effect_2004}, which prior research has explored in a trading context. Other research on pseudonyms in dynamic systems, demonstrate whitewashing in AI agents which can ignore defensive mechanisms by re-entry with different identities \parencite{feldman_free-riding_2004}. Dynamic pricing assumes demand proxies are behaviorally meaningful, while bot detection aims at security and access control. The missing bridge is a principled framework for separating non-human reconnaissance from genuine human demand expression and integrating that separation into pricing heuristics without degrading legitimate user experience (in our research tracked by the user-experience index). This gap, is what our contribution aims to address, particularly for the aforementioned stakeholder groups.
+To better understand all wedges of the current works, we must start by exploring the nature of agents, agentic computer use and web automation, complementing that with economic reasoning and strategic interaction. The final surface to cover, leads us to data-driven dynamic pricing under uncertainty. The key technical risk is not ``agents buying things'' per se, but agents shaping the behavioral and demand signals that downstream pricing systems consume and depend on. This latter case of agents shopping is currently pending legal action in the case of \textcite{noauthor_amazoncom_2026} which is currently being treated as a violation of the Computer Fraud and Abuse Act. The introduction of these mediating actor entities into economic systems, is further creating a threat of false-name bidding \parencite{yokoo_effect_2004}, which prior research has explored in a trading context. Other research on pseudonyms in dynamic systems, demonstrate whitewashing in AI agents which can ignore defensive mechanisms by re-entry with different identities \parencite{feldman_free-riding_2004}. Dynamic pricing assumes demand proxies are behaviorally meaningful, while bot detection aims at security and access control. The missing bridge is a principled framework for distinguishing non-human reconnaissance from genuine human demand expression and integrating that distinguishability into pricing heuristics without degrading legitimate user experience (in our research tracked by the user-experience index). This gap, is what our contribution aims to address, particularly for the aforementioned stakeholder groups.
 
 \subsection{Agent Taxonomy and Definitions}
 

paper/src/chapters/03-methodology.tex

@@ -3,7 +3,7 @@
 % Extra notes and clarifications: we observed some humans and get their transition probabilities between event types
 % We modify behavioral profiles of transition matrices with price elasticity matrices generated by sample valuations of a distributing.
 
-This section details the theoretical and practical framework developed to address dynamic pricing under the influence of non-human actors. We begin by formalizing the problem environment and the nature of the actors. We then derive the \textit{Cost of Information} (COI) theorem, proving the erosion of pricing power in the limit of agent saturation. Following this, we outline our generative contamination strategy using GOFAI-driven separability and transition probability learning. Finally, we formulate the robust control problem as a Stackelberg game solved via Distributionally Robust Reinforcement Learning (DR-RL) with constructed ambiguity sets.
+This section details the theoretical and practical framework developed to address dynamic pricing under the influence of non-human actors. We begin by formalizing the problem environment and the nature of the actors. We then derive the \textit{Cost of Information} (COI) theorem, proving the erosion of pricing power in the limit of agent saturation. Following this, we outline our generative contamination strategy using GOFAI-driven distinguishability and transition probability learning. Finally, we formulate the robust control problem as a Stackelberg game solved via Distributionally Robust Reinforcement Learning (DR-RL) with constructed ambiguity sets.
 
 \subsection{Problem Formalization}
 
@@ -141,7 +141,7 @@ The architecture of this platform begins with the deployed web-apps posting inte
 
 \paragraph{Public Web Artifact} We transition the Kappa like architecture of the data collection to a Lambda architecture for actual learning in a surrogate environment. This allows us to move faster on data which is provided and helps us create a feedback loop for production deployment. To support further research in this intersection of fields we release P4P \footnote{\url{https://github.com/velocitatem/p4p}} as a public repository providing the interaction layer of the PHANTOM framework. This provides a configurable storefront which can be tailored to any commercial setting with a standardized session-level event tracking. We document the API adapters or what the framework expects in terms of schemas for pricing providers and log ingestion servicse. The repository is intended for controlled experimentation and method replication rather than production commerce deployment.
 
-\paragraph{Public Dataset Artifact} For reproducibility of the behavioral analysis and separability experiments, we also release the interaction dataset used in this thesis as \textit{WhoClickedIt}. The dataset is hosted on Hugging Face \footnote{\url{https://huggingface.co/datasets/velocitatem/whoclickedit}} and is distributed as one flattened event sheet (\texttt{whoclicked.csv}) with explicit labels (\texttt{actor\_type}, \texttt{is\_agent}, and \texttt{record\_type}). The associated dataset card specifies the schema, collection process, and known limitations; a full copy is included in Appendix~\ref{app:whoclicked_card}.
+\paragraph{Public Dataset} For reproducibility of the behavioral analysis and distinguishability experiments, we also release the interaction dataset used in this thesis as \textit{WhoClickedIt}. The dataset is hosted on Hugging Face \footnote{\url{https://huggingface.co/datasets/velocitatem/whoclickedit}} and is distributed as one flattened event sheet (\texttt{whoclicked.csv}) with explicit labels (\texttt{actor\_type}, \texttt{is\_agent}, and \texttt{record\_type}). The associated dataset card specifies the schema, collection process, and known limitations; a full copy is included in Appendix~\ref{app:whoclicked_card}.
 
 
 \subsubsection{DevOps Principles}
@@ -189,9 +189,9 @@ The human data collection involved 13 participants, all of whom provided explici
 
 To evaluate quality and realism of the setup, we store both structured event logs and full interaction transcripts. This lets us combine quantitative analysis with transcript-level qualitative findings. The result is an isolated system where we can control the interaction process while preserving realistic behavior.
 
-Operationally, goals and experiment runs are tracked in PostgreSQL (goal table, run table, and assignment mapping). This data-acquisition phase is the first half of the methodology and is intentionally a disconnected component that feeds the later contributions. The second half uses collected behavioral traces to separate classes $\theta \in \{A,H\}$ with session-conditioned probability estimates, then injects those estimates into the pricing learner.
+Operationally, goals and experiment runs are tracked in PostgreSQL (goal table, run table, and assignment mapping). This data-acquisition phase is the first half of the methodology and is intentionally a disconnected component that feeds the later contributions. The second half uses collected behavioral traces to distinguish classes $\theta \in \{A,H\}$ with session-conditioned probability estimates, then injects those estimates into the pricing learner.
 
-Our process follows three stages: (1) observe and \textit{vectorize} behavioral interactions, (2) learn separability to characterize human versus agent patterns, and (3) use the learned signal to train a defensive policy in a controlled dynamic-pricing simulator.
+Our process follows three stages: (1) observe and \textit{vectorize} behavioral interactions, (2) learn distinguishability to characterize human versus agent patterns, and (3) use the learned signal to train a defensive policy in a controlled dynamic-pricing simulator.
 
 \begin{figure}[ht]
   \resizebox{\columnwidth}{!}{%
@@ -298,15 +298,15 @@ In addition to behavioral events, the platform logs price observations to a sepa
 
 
 
-\subsection{Generative Contamination and Separability}
+\subsection{Generative Contamination and Distinguishability}
 
 To train a robust pricing learner, we need a simulator that can generate realistic interaction data under controlled contamination. We build this from Phantom data using a two-stage approach.
 
 
-\subsubsection{Ground-Truth Separability}
-Because sessions are collected under controlled experimental conditions where each actor is assigned a known type at the start of the trial, labels $\theta_s \in \{H, A\}$ are available as ground truth rather than as the output of a heuristic classifier. We therefore estimate separate transition kernels directly from each labeled partition $\mathcal{D}_H$ and $\mathcal{D}_A$, treating the resulting $\hat{\mathcal{T}}_H$ and $\hat{\mathcal{T}}_A$ as the ground-truth behavioral profiles for each class. We then ask a direct methodological question: are the kernels separable enough to justify downstream pricing control that depends on that separability?
+\subsubsection{Ground-Truth Distinguishability}
+Because sessions are collected under controlled experimental conditions where each actor is assigned a known type at the start of the trial, labels $\theta_s \in \{H, A\}$ are available as ground truth rather than as the output of a heuristic classifier. We therefore estimate separate transition kernels directly from each labeled partition $\mathcal{D}_H$ and $\mathcal{D}_A$, treating the resulting $\hat{\mathcal{T}}_H$ and $\hat{\mathcal{T}}_A$ as the ground-truth behavioral profiles for each class. We then ask a direct methodological question: are the kernels distinguishable enough to justify downstream pricing control that depends on that distinguishability?
 
-To answer this, we compute per-session KL divergence scores against both class-level centroids. For each session $s$ in either partition, we fit a session-level event transition kernel $\hat{\mathcal{T}}_s$ from that session's trajectory alone, then compute its average KL divergence to the human centroid ($\Delta_{H,s}$) and to the agent centroid ($\Delta_{A,s}$). The per-session separability score is the gap $\Delta_{H,s} - \Delta_{A,s}$: a negative value indicates proximity to human behavior, a positive value indicates proximity to agent behavior.
+To answer this, we compute per-session KL divergence scores against both class-level centroids. For each session $s$ in either partition, we fit a session-level event transition kernel $\hat{\mathcal{T}}_s$ from that session's trajectory alone, then compute its average KL divergence to the human centroid ($\Delta_{H,s}$) and to the agent centroid ($\Delta_{A,s}$). The per-session distinguishability score is the gap $\Delta_{H,s} - \Delta_{A,s}$: a negative value indicates proximity to human behavior, a positive value indicates proximity to agent behavior.
 
 The normality assumption cannot be made for KL divergence distributions, which are right-skewed and bounded below by zero, so we do not use a Student's $t$-test. Instead we apply a Mann-Whitney $U$ test \parencite{mann_test_1947} on the per-session gap scores between the two groups. The Mann-Whitney test is a rank-based nonparametric test that compares the stochastic ordering of two independent samples without distributional assumptions, making it appropriate for small samples drawn from skewed populations. We report $U$, the exact two-sided $p$-value, and group-level descriptive statistics for the gap scores.
 
@@ -470,7 +470,7 @@ We also consider taxation-like overlays for agent traffic under strategy-proof m
 
 \subsubsection{Pricing Mechanism Summary}
 
-We now present the complete pricing mechanism that integrates the behavioral separability, contamination estimation, and robust optimization components developed in the preceding sections. Algorithm~\ref{alg:phantom_loop_clean} formalizes the defensive pricing loop as a Stackelberg game where the platform (leader) sets prices and the aggregate demand (follower) responds through observed session trajectories.
+We now present the complete pricing mechanism that integrates the behavioral distinguishability, contamination estimation, and robust optimization components developed in the preceding sections. Algorithm~\ref{alg:phantom_loop_clean} formalizes the defensive pricing loop as a Stackelberg game where the platform (leader) sets prices and the aggregate demand (follower) responds through observed session trajectories.
 
 \begin{algorithm}[t]
 \caption{PHANTOM defensive pricing loop}

paper/src/chapters/04-results.tex

@@ -10,7 +10,7 @@
 
 \subsection{Behavioral Analysis}
 
-Separability between human and agent sessions is evaluated by computing per-session divergence gap scores $\Delta_{H,s} - \Delta_{A,s}$ and comparing the two groups with a Mann-Whitney $U$ test. The full recorded cohort contains $n_H=13$ human sessions and $n_A=16$ agent sessions, and Table~\ref{tab:divergence_significance} reports the corresponding group-level statistics and test result.
+Distinguishability between human and agent sessions is evaluated by computing per-session divergence gap scores $\Delta_{H,s} - \Delta_{A,s}$ and comparing the two groups with a Mann-Whitney $U$ test. The full recorded cohort contains $n_H=13$ human sessions and $n_A=16$ agent sessions, and Table~\ref{tab:divergence_significance} reports the corresponding group-level statistics and test result.
 
 \begin{table}[ht]
 \centering
@@ -28,7 +28,7 @@ Agent sessions & 16 & $+1.65$ & $2.83$ \\
 \end{tabular}
 \end{table}
 
-The sign structure is consistent with the theoretical expectation: human sessions produce negative gap scores (closer to the human centroid, far from the agent centroid) while agent sessions produce positive gap scores (closer to the agent centroid). The two-sided test result ($p<0.001$) at $n_H=13$, $n_A=16$ indicates strong rank separation between groups, providing evidence that the transition kernels are separable enough to justify their use as a control signal in downstream pricing.
+The sign structure is consistent with the theoretical expectation: human sessions produce negative gap scores (closer to the human centroid, far from the agent centroid) while agent sessions produce positive gap scores (closer to the agent centroid). The two-sided test result ($p<0.001$) at $n_H=13$, $n_A=16$ indicates strong rank distinction between groups, providing evidence that the transition kernels are distinguishable enough to justify their use as a control signal in downstream pricing.
 
 
 \subsection{Experimental Outcomes}
@@ -61,7 +61,7 @@ A linear slope test on run-level data ($n=95$) shows a strong negative associati
 
 
 \subsection{Interpretation and Insights}
-The Mann-Whitney result ($p<0.001$) confirms that per-session divergence gaps separate the two actor classes with near-zero overlap in rank ordering. This is the condition required for separability to act as a useful control signal in the pricing loop rather than just an auxiliary classifier score.
+The Mann-Whitney result ($p<0.001$) confirms that per-session divergence gaps distinguish the two actor classes with near-zero overlap in rank ordering. This is the condition required for distinguishability to act as a useful control signal in the pricing loop rather than just an auxiliary classifier score.
 
 The first calibration and overnight runs additionally confirm three practical points aligned with the thesis mechanism. First, the control loop is reproducible end-to-end (training, evaluation, artifact generation) across algorithms and contamination levels. Second, policy class materially changes price trajectories and resulting COI/revenue profiles under identical environment settings. Third, objective improvements from robustness are regime-dependent in the current baseline, which is consistent with the thesis claim that contamination-aware pricing needs explicit calibration rather than a one-size-fits-all penalty.
 

paper/src/chapters/06-conclusion.tex

@@ -12,9 +12,9 @@ Now we very explicitly mention what we contribute in this paper:
     \item Formalization of non-human transaction orchestration in e-commerce as a distinct source of contamination in dynamic pricing systems.
     \item Definition of the Cost of Information (COI) as a mechanism-level quantity for pricing power, together with a theorem showing its erosion under increasing agent saturation.
     \item Design and implementation of a controlled e-commerce research platform, built on a hybrid Kappa-Lambda architecture, for collecting and replaying high-fidelity interaction trajectories.
-    \item Construction and empirical validation of a behavioral separability framework that distinguishes human and agent sessions from interaction signals alone using transition kernels and KL-based divergence.
+    \item Construction and empirical validation of a behavioral distinguishability framework that distinguishes human and agent sessions from interaction signals alone using transition kernels and KL-based divergence.
     \item Development of a generative contamination mechanism that injects learned agent behavior into the pricing environment for controlled robustness experiments.
-    \item Translation of behavioral separability into a defensive pricing mechanism through a distributionally robust reinforcement learning formulation of pricing under non-stationary contamination.
+    \item Translation of behavioral distinguishability into a defensive pricing mechanism through a distributionally robust reinforcement learning formulation of pricing under non-stationary contamination.
     \item Empirical evidence that agent contamination reduces revenue and that robustness is condition-dependent, requiring explicit calibration rather than a one-size-fits-all penalty.
     \item Release of a reusable public experimental artifact for reproducing and extending research on dynamic pricing under agent-mediated traffic.
 \end{itemize}

paper/src/chapters/slacberger.tex

@@ -62,7 +62,7 @@ We propose a robust optimization objective. The platform seeks a pricing policy
 Here:
 \begin{itemize}
     \item The first term, $p_t \cdot \hat{q}_t(p_t | \theta=H)$, represents the revenue generated strictly from the estimated human segment.
-    \item $\mathcal{L}_{detect}$ is a penalty term for failing to separate distributions (the cost of confusion).
+    \item $\mathcal{L}_{detect}$ is a penalty term for failing to distinguish distributions (the cost of confusion).
     \item $\lambda$ is a hyperparameter balancing revenue exploitation vs. robust detection.
 \end{itemize}