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updating docs and paper

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Daniel Rosel
2026-03-10 14:11:41 +01:00
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<!-- ========================================================= -->
<!-- COLUMN 1: THE THREAT (COI & SATURATION) -->
<!-- ========================================================= -->
<text x="60" y="80" font-family="Georgia, serif" font-size="28" font-weight="bold" fill="#333333">1. The Vulnerability</text>
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<text x="0" y="30" font-size="24" font-weight="bold" fill="#444">Cost of Information from First Principles</text>
<text x="0" y="70" font-family="Georgia, serif" font-style="italic" font-size="22" fill="#8C7A6B">P ~ π(τ)</text>
<text x="0" y="105" font-family="Georgia, serif" font-style="italic" font-size="22" fill="#8C7A6B"><tspan text-decoration="underline">p</tspan> = reservation price</text>
<text x="0" y="140" font-family="Georgia, serif" font-style="italic" font-size="22" fill="#8C7A6B">M = P - <tspan text-decoration="underline">p</tspan></text>
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<text x="310" y="118" font-family="Georgia" font-style="italic" font-size="22" fill="#E37862" font-weight="bold" text-anchor="middle">COI := E[P] - p</text>
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<text x="0" y="30" font-size="24" font-weight="bold" fill="#444">Why COI Erodes with Agent Saturation</text>
<text x="0" y="75" font-family="Georgia, serif" font-style="italic" font-size="22" fill="#8C7A6B">p<tspan font-size="14" dy="5">(1)</tspan><tspan dy="-5"> = min(p</tspan><tspan font-size="14" dy="5">1</tspan><tspan dy="-5">, ..., p</tspan><tspan font-size="14" dy="5">N</tspan><tspan dy="-5">)</tspan></text>
<text x="0" y="115" font-family="Georgia, serif" font-style="italic" font-size="22" fill="#8C7A6B">P(p<tspan font-size="14" dy="5">(1)</tspan><tspan dy="-5"> > t) = [1 - F(t)]</tspan><tspan font-size="14" dy="-10">N</tspan></text>
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<text x="390" y="220" font-size="16" fill="#4EA5D9" font-weight="bold">N=1</text>
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<text x="390" y="250" font-size="16" fill="#85B589" font-weight="bold">N=4</text>
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<text x="260" y="420" font-size="20" fill="#555" text-anchor="middle">As independent query count grows,</text>
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<text x="700" y="80" font-family="Georgia, serif" font-size="28" font-weight="bold" fill="#333333">2. The Behavioral Signals</text>
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<text x="0" y="30" font-size="24" font-weight="bold" fill="#444">From Session Paths to Transition Kernels</text>
<text x="0" y="75" font-size="20" fill="#85B589" font-weight="bold">human: start → view → detail → cart → purchase</text>
<text x="0" y="115" font-size="20" fill="#E37862" font-weight="bold">agent: start → view → detail → view → detail</text>
<text x="0" y="170" font-family="Georgia, serif" font-style="italic" font-size="24" fill="#8C7A6B">
P&#770;(s'|s) = <tspan font-size="18" dy="-12">N(s,s')</tspan> / <tspan font-size="18" dy="12">Σ N(s,k)</tspan>
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<text x="125" y="250" font-size="16" fill="#4EA5D9" text-anchor="middle">transition counts N(s,s')</text>
<text x="375" y="250" font-size="16" fill="#85B589" text-anchor="middle">normalized kernel T</text>
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<text x="250" y="440" font-size="18" fill="#777" text-anchor="middle">Kernel shape is the compact behavioral signature used downstream.</text>
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<text x="0" y="30" font-size="24" font-weight="bold" fill="#444">Separability into a Control Signal</text>
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<text x="0" y="115" font-family="Georgia, serif" font-style="italic" font-size="22" fill="#8C7A6B">Δ<tspan font-size="16" dy="5">A</tspan><tspan dy="-5"> = D</tspan><tspan font-size="16" dy="5">KL</tspan><tspan dy="-5">(T&#770;' || T&#772;</tspan><tspan font-size="16" dy="5">A</tspan><tspan dy="-5">)</tspan></text>
<text x="0" y="155" font-family="Georgia, serif" font-style="italic" font-size="24" fill="#8C7A6B">g = Δ<tspan font-size="16" dy="5">H</tspan><tspan dy="-5"> - Δ</tspan><tspan font-size="16" dy="5">A</tspan></text>
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<text x="180" y="235" font-family="Georgia, serif" font-style="italic" font-size="22" text-anchor="middle">g = Δ<tspan font-size="16" dy="5">H</tspan><tspan dy="-5"> - Δ</tspan><tspan font-size="16" dy="5">A</tspan></text>
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<!-- ========================================================= -->
<!-- COLUMN 3: THE SOLUTION (CONTAMINATION & DR-RL) -->
<!-- ========================================================= -->
<text x="1340" y="80" font-family="Georgia, serif" font-size="28" font-weight="bold" fill="#333333">3. Robust Control &amp; Contamination</text>
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<text x="380" y="100" font-size="18" fill="#222" text-anchor="middle">synthetic agent sessions</text>
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<text x="250" y="220" font-size="18" fill="#222" text-anchor="middle">mixed batch for training</text>
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<text x="250" y="275" font-family="Georgia, serif" font-size="20" fill="#555" text-anchor="middle">alpha = 0.33</text>
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π* = arg max<tspan font-size="16" dy="5">π</tspan> min<tspan font-size="16" dy="0">Q ∈ U<tspan font-size="12" dy="5">ε</tspan></tspan>
<tspan dy="-10"> E</tspan><tspan font-size="16" dy="5">d ~ Q</tspan>
<tspan dy="-5">[ R(p,d) - λ COI</tspan><tspan font-size="16" dy="5">leak</tspan><tspan dy="-5">(p,τ') ]</tspan>
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<text x="12" y="24" font-family="Georgia" font-style="italic" font-size="22" fill="#4EA5D9">P&#770;<tspan font-size="14" dy="5">N</tspan></text>
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<text x="-140" y="-50" font-family="Georgia" font-style="italic" font-size="18" fill="#E37862">worst-case Q*</text>
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