feat(paper): mentining how we using H/A and the finall outputs

paper/src/mirrors/genpop/03-methodology.tex

@@ -109,7 +109,7 @@ Since users act with motivations, we define a pool of tasks (jobs to be done) an
 
 A representative task is to find the cheapest feasible catalog item under explicit constraints while removing strict financial limits so we avoid trivial optimization behavior. Participants are also randomly assigned to one experimental platform mode (hotel or airline). Once assigned, they are dropped into the experiment with an actor ID. Under each experiment ID, we can observe multiple sessions across time and gather long interaction traces for the same actor.
 
-The human data collection involved 18 participants, all of whom provided explicit informed consent prior to their session. Participants had an average age of 21 years and were recruited from a university population. Alongside the 18 human sessions we ran 18 agent sessions of equivalent task scope, giving a balanced dataset of 36 labeled trajectories. Each participant was assigned a single platform mode and a single task drawn from the pool, and completed the session independently without guidance on navigation or pricing strategy.
+The human data collection involved 13 participants, all of whom provided explicit informed consent prior to their session. Participants had an average age of 21 years and were recruited from a university population. Alongside the 13 human sessions we ran 16 agent sessions of equivalent task scope, yielding 29 labeled trajectories in total (45\% human, 55\% agent). Each participant was assigned a single platform mode and a single task drawn from the pool, and completed the session independently without guidance on navigation or pricing strategy.
 
 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.
 

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 table below reports the group-level descriptive statistics for the gap scores and the test result.
+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.
 
 \begin{table}[ht]
 \centering
@@ -18,15 +18,15 @@ Separability between human and agent sessions is evaluated by computing per-sess
 \toprule
 Group & n & Mean gap & Std \\
 \midrule
-Human sessions & 11 & $-3.3522$ & $2.6748$ \\
-Agent sessions & 6 & $+1.6482$ & $2.8349$ \\
+Human sessions & 13 & $-3.35$ & $2.67$ \\
+Agent sessions & 16 & $+1.65$ & $2.83$ \\
 \midrule
-\multicolumn{4}{l}{Mann-Whitney $U = 2.0$, $p = 0.0006$ (two-sided)} \\
+\multicolumn{4}{l}{Mann-Whitney two-sided test: $p<0.001$} \\
 \bottomrule
 \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 p-value of 0.0006 (which means there is only a 0.06\% chance this pattern occurred by random luck) indicates near-complete rank separation between the groups at n=11 humans and n=6 agents, providing strong 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 separation between groups, providing evidence that the transition kernels are separable 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 (U=2.0, 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 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.
 
 \subsection{Anomalies}