chore: rename to distinguishability

paper/src/mirrors/genpop/01-intro.tex

@@ -2,9 +2,9 @@
 
 \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}
 
@@ -25,7 +25,7 @@ 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}
@@ -59,4 +59,4 @@ Extract final result 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. 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. 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/mirrors/genpop/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/mirrors/genpop/03-methodology.tex

@@ -1,6 +1,6 @@
 \section{Methodology}
 
-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}
 
@@ -113,9 +113,9 @@ 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. 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 (agent vs human) with session-conditioned probability estimates, then injects those estimates into the pricing learner.
+Operationally, goals and experiment runs are tracked in PostgreSQL. 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 (agent vs human) with session-conditioned probability estimates, then injects those estimates into the pricing learner.
 
-Our process follows three stages: (1) observe and 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 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}{!}{%
@@ -209,15 +209,15 @@ In the simulator baseline this order is encoded with a compact fixed scale: cart
 
 In addition to behavioral events, the platform logs price observations to a separate Kafka topic. Each price query generates a record associating the product, displayed price, requesting session, platform mode, and timestamp. This dual-stream architecture enables joint analysis of price exposure and behavioral response.
 
-\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}
+\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 (human or agent) 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, treating the resulting human and agent kernels 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?
+Because sessions are collected under controlled experimental conditions where each actor is assigned a known type at the start of the trial, labels (human or agent) 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, treating the resulting human and agent kernels 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 divergence scores against both class-level centroids. For each session in either partition, we fit a session-level event transition kernel from that session's trajectory alone, then compute its average divergence to the human centroid and to the agent centroid. The per-session separability score is the gap between these two divergences: a negative value indicates proximity to human behavior, a positive value indicates proximity to agent behavior.
+To answer this, we compute per-session divergence scores against both class-level centroids. For each session in either partition, we fit a session-level event transition kernel from that session's trajectory alone, then compute its average divergence to the human centroid and to the agent centroid. The per-session distinguishability score is the gap between these two divergences: a negative value indicates proximity to human behavior, a positive value indicates proximity to agent behavior.
 
 We cannot assume normal distributions for divergence scores, 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 ordering of two independent samples without distributional assumptions, making it appropriate for small samples drawn from skewed populations.
 
@@ -305,7 +305,7 @@ 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. The defensive pricing loop algorithm formalizes the process 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. The defensive pricing loop algorithm formalizes the process 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/mirrors/genpop/04-results.tex

@@ -8,7 +8,7 @@
 
 \subsection{Behavioral Analysis}
 
-Separability between human and agent sessions is evaluated by computing per-session divergence gap scores (how much closer each session is to the human baseline versus the agent baseline) and comparing the two groups with a Mann-Whitney U test. The full recorded cohort contains 13 human sessions and 16 agent sessions, and the table below reports the corresponding group-level statistics and test result.
+Distinguishability between human and agent sessions is evaluated by computing per-session divergence gap scores (how much closer each session is to the human baseline versus the agent baseline) and comparing the two groups with a Mann-Whitney U test. The full recorded cohort contains 13 human sessions and 16 agent sessions, and the table below reports the corresponding group-level statistics and test result.
 
 \begin{table}[ht]
 \centering
@@ -26,7 +26,7 @@ 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 less than 0.001) at n=13 humans and n=16 agents 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 less than 0.001) at n=13 humans and n=16 agents 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}
 
@@ -50,6 +50,6 @@ This comparison isolates the effect of robustness terms from model capacity and
 
 \subsection{Interpretation and Insights}
 
-The Mann-Whitney result (p less than 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 less than 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.
 
 \subsection{Anomalies}