<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Reexpress MCP Server Output</title>
<style>
body {
background-color: #f5f5f5;
color: #212529;
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Helvetica Neue", Arial, sans-serif;
margin: 0;
padding: 20px;
line-height: 1.6;
}
.container {
max-width: 1200px;
margin: 0 auto;
background-color: #ffffff;
border-radius: 8px;
padding: 20px;
box-shadow: 0 2px 10px rgba(0, 0, 0, 0.1);
}
.header {
font-size: 24px;
font-weight: 600;
margin-bottom: 20px;
color: #1a1a1a;
display: flex;
align-items: baseline;
gap: 10px;
}
.section {
margin-bottom: 25px;
}
.section-title {
font-size: 14px;
color: #6c757d;
margin-bottom: 8px;
text-transform: uppercase;
letter-spacing: 0.5px;
font-weight: 600;
}
.field-grid {
display: grid;
grid-template-columns: repeat(auto-fit, minmax(300px, 1fr));
gap: 15px;
margin-bottom: 20px;
}
.field-box {
background-color: #f8f9fa;
border: 1px solid #dee2e6;
border-radius: 6px;
padding: 12px 16px;
}
.field-label {
font-size: 13px;
color: #6c757d;
margin-bottom: 4px;
display: flex;
align-items: center;
gap: 5px;
font-weight: 500;
}
.field-value {
font-size: 15px;
color: #212529;
font-weight: 600;
}
.icon {
width: 16px;
height: 16px;
display: inline-block;
vertical-align: middle;
}
.tag {
display: inline-block;
padding: 3px 10px;
border-radius: 4px;
font-size: 12px;
margin-right: 5px;
font-weight: 600;
}
.tag-positive {
background-color: #d4edda;
color: #155724;
border: 1px solid #c3e6cb;
}
.tag-caution {
background-color: #fff3cd;
color: #856404;
border: 1px solid #ffeaa7;
}
.tag-near-random-chance {
background-color: #f8d7da;
color: #721c24;
border: 1px solid #f5c6cb;
}
.tag-negative {
background-color: #f8d7da;
color: #721c24;
border: 1px solid #f5c6cb;
}
.tag-neutral {
background-color: #e2e3e5;
color: #383d41;
border: 1px solid #d6d8db;
}
.tag-highest {
background-color: #d1ecf1;
color: #0c5460;
border: 1px solid #bee5eb;
}
.prompt-box, .document-box {
background-color: #f8f9fa;
border: 1px solid #dee2e6;
border-radius: 6px;
padding: 16px;
font-family: "Consolas", "Monaco", monospace;
font-size: 14px;
line-height: 1.5;
overflow-x: auto;
white-space: pre-wrap;
word-wrap: break-word;
color: #212529;
}
.mcp-server-version {
font-family: "Consolas", "Monaco", monospace;
font-size: 12px;
color: #6c757d;
font-weight: 300;
}
.model-name {
font-family: "Consolas", "Monaco", monospace;
font-size: 12px;
color: #6c757d;
font-weight: 300;
}
.highlight {
background-color: #fff3cd;
padding: 2px 4px;
border-radius: 3px;
border: 1px solid #ffeaa7;
}
.resize-button {
float: right;
background: none;
border: none;
color: #0056b3;
cursor: pointer;
font-size: 14px;
padding: 4px 8px;
font-weight: 500;
}
.resize-button:hover {
color: #004085;
text-decoration: underline;
}
.nearest-match-box {
border-left: 4px solid #dee2e6;
}
.explanation-box {
background-color: #e7f3ff;
border-left: 4px solid #0066cc;
padding: 12px 16px;
margin-bottom: 10px;
border-radius: 0 6px 6px 0;
}
.explanation-title {
font-weight: 700;
color: #004085;
margin-bottom: 4px;
}
.explanation-box-positive {
background-color: #f8f9fa;
border: 1px solid #dee2e6;
border-left: 4px solid #155724;
padding: 12px 16px;
margin-bottom: 10px;
border-radius: 0 6px 6px 0;
}
.explanation-title-positive {
font-weight: 700;
color: #155724;
margin-bottom: 4px;
}
.explanation-box-negative {
background-color: #f8f9fa;
border: 1px solid #dee2e6;
border-left: 4px solid #721c24;
padding: 12px 16px;
margin-bottom: 10px;
border-radius: 0 6px 6px 0;
}
.explanation-title-negative {
font-weight: 700;
color: #721c24;
margin-bottom: 4px;
}
.separator {
border-top: 2px solid #dee2e6;
margin: 30px 0;
}
.info-icon {
color: #0056b3;
}
.checkmark {
color: #28a745;
font-weight: bold;
}
.cross {
color: #dc3545;
font-weight: bold;
}
.math-operator {
font-family: 'Times New Roman', serif;
font-style: italic;
display: inline-block;
}
.math-tilde {
position: relative;
}
.math-superscript {
position: absolute;
top: -0.5em;
right: -0.2em;
font-size: 0.75em;
}
.math-subscript {
font-size: 0.75em;
font-style: normal;
vertical-align: sub;
}
.math-qtilde {
display: inline-block;
position: relative;
font-style: italic;
width: 0.7em;
text-align: center;
}
.math-qtilde::after {
content: "~";
position: absolute;
top: -0.3em;
left: 0;
right: 0;
font-style: normal;
}
.math-operator-m {
font-family: 'Times New Roman', serif;
display: inline-block;
position: relative;
padding-right: 1.2em; /* Space for super/subscripts */
}
.math-superscript-hat-y {
position: absolute;
top: -0.5em;
left: 1.2em;
font-size: 0.75em;
}
.math-subscript-floor {
position: absolute;
bottom: -0.3em;
left: 1.2em;
font-size: 0.75em;
white-space: nowrap;
}
.qtilde-small {
display: inline-block;
position: relative;
width: 0.6em;
font-style: italic;
}
.qtilde-small::after {
content: "~";
position: absolute;
top: -0.2em;
left: 0;
right: 0;
text-align: center;
font-style: normal;
font-size: 0.9em;
}
.math-parens {
font-family: 'Times New Roman', serif;
}
.math-parens > .paren {
font-size: 1.3em;
vertical-align: -0.1em;
}
/* For Legend */
.legend-content {
background-color: #f8f9fa;
padding: 15px;
border-radius: 5px;
margin-top: 10px;
}
.legend-content p {
margin-bottom: 15px;
line-height: 1.6;
color: #555;
}
.legend-items {
display: flex;
flex-direction: column;
gap: 10px;
}
.legend-item {
display: flex;
align-items: center;
padding: 8px 12px;
background-color: white;
border-radius: 4px;
border: 1px solid #e0e0e0;
}
.legend-label {
font-weight: 600;
color: #333;
margin-right: 10px;
min-width: 60px;
}
.legend-value {
color: #666;
font-family: 'Courier New', monospace;
}
</style>
</head>
<body>
<div class="container">
<div class="header">
Reexpress MCP Server Output <span class="mcp-server-version">(v2.1.0)</span>
</div>
<div class="section">
<div class="section-title">Verification Results</div>
<div class="field-box" style="margin-bottom: 20px;">
<div class="field-label">Successfully Verified (Prediction)</div>
<div class="field-value">
<div class="field-value"><span class="tag tag-positive">True</span></div>
</div>
</div>
<div class="field-box" style="margin-bottom: 20px;">
<div class="field-label">Confidence</div>
<div class="field-value"><span class="tag tag-positive">>= 90%</span></div>
</div>
<div class="explanation-box-positive">
<div class="explanation-title-positive">Model 1 Summary <span class="model-name">(gpt-5.2-2025-12-11)</span></div>
<div>The question asks for the derivative of ln(x). The AI response states it is 1/x (for x>0) and provides that as the final answer.</div>
</div>
<div class="explanation-box-positive">
<div class="explanation-title-positive">Model 1 Explanation <span class="model-name">(gpt-5.2-2025-12-11)</span></div>
<div>The derivative of ln(x) is a standard, objective calculus result: d/dx ln(x) = 1/x (on its real-domain x>0). The response directly answers the question correctly, is not subjective, and does not depend on recent information; it relies on established mathematical knowledge.</div>
</div>
<div class="explanation-box-positive">
<div class="explanation-title-positive">Model 2 Explanation <span class="model-name">(gemini-3-pro-preview)</span></div>
<div>The derivative of ln(x) being 1/x is a fundamental rule in calculus, making the response factually correct and easy to verify.</div>
</div>
<div class="explanation-box-positive">
<div class="explanation-title-positive">Model 3 Agreement <span class="model-name">(granite-3.3-8b-instruct)</span></div>
<div>Do the model explanations agree that the response is correct?</div>
<div><span class="tag tag-positive">Yes</span></div>
</div>
</div>
<div class="separator"></div>
<div class="section">
<div class="section-title">Additional Information</div>
<div class="field-grid">
<div class="field-box">
<div class="field-label">File Access</div>
<div class="field-value">The verification model did not have access to any external files.</div>
</div>
<div class="field-box">
<div class="field-label">Date</div>
<div class="field-value">2026-01-11 22:09:23</div>
</div>
</div>
</div>
<div class="section">
<div class="section-title">Uncertainty (instance-level) Details</div>
<div class="field-box" style="margin-bottom: 20px;">
<div class="field-label">p(y | x)</div>
<div class="field-value">[7.182933359217714e-07, 0.9999992847442627]</div>
</div>
<div class="field-grid">
<div class="field-box">
<div class="field-label">High-Reliability Region</div>
<div class="field-value">
<span class="tag tag-positive">True</span>
</div>
</div>
<div class="field-box">
<div class="field-label">Out-of-Distribution</div>
<div class="field-value">
<span class="tag tag-positive">False</span>
</div>
</div>
<div class="field-box">
<div class="field-label">Rescaled Similarity (q')</div>
<div class="field-value">363.0</div>
</div>
</div>
<div class="field-grid">
<div class="field-box">
<div class="field-label">
Similarity to Training (q)
</div>
<div class="field-value">363</div>
</div>
<div class="field-box">
<div class="field-label">
Distance to Training Quantile (d)
</div>
<div class="field-value">0.44391030073165894</div>
</div>
<div class="field-box">
<div class="field-label">
Magnitude
</div>
<div class="field-value">[-2.5087058544158936, 2.8926875591278076]</div>
</div>
</div>
</div>
<div class="section" style="margin-left: 40px;">
<div class="section-title">Analysis of the Effective Sample Size</div>
<div class="field-box" style="margin-bottom: 20px;">
<div class="field-label">p(y | x)_lower</div>
<div class="field-value">[8.938391715673788e-07, 0.9999991655349731]</div>
</div>
<div class="field-box" style="margin-bottom: 20px;">
<div class="field-label">p(y | x)_upper</div>
<div class="field-value">[5.772249664914852e-07, 0.9999994039535522]</div>
</div>
<div class="field-grid">
<div class="field-box">
<div class="field-label">Effective Sample Size (by class)</div>
<div class="field-value">[31819.0, 50783.0]</div>
</div>
</div>
<div class="field-grid">
<div class="field-box">
<div class="field-label">
Distance to Training Lower Quantile (d_lower)
</div>
<div class="field-value">0.4370492100715637</div>
</div>
<div class="field-box">
<div class="field-label">
Distance to Training Upper Quantile (d_upper)
</div>
<div class="field-value">0.45077139139175415</div>
</div>
</div>
</div>
<div class="section">
<div class="section-title">SDM Estimator (Model-level) Details</div>
<div class="field-grid">
<div class="field-box">
<div class="field-label">
α
</div>
<div class="field-value">0.9</div>
</div>
<div class="field-box">
<div class="field-label">
Minimum Rescaled Similarity (q'_min)
</div>
<div class="field-value">6.207298755645752</div>
</div>
<div class="field-box">
<div class="field-label">
Class-wise Output Thresholds (ψ)
</div>
<div class="field-value">[0.9000474810600281, 0.9008400440216064]</div>
</div>
<div class="field-box">
<div class="field-label">
Support/training size
</div>
<div class="field-value">120158</div>
</div>
</div>
</div>
<div class="section">
<div class="section-title">Prompt</div>
<div class="prompt-box">What is the derivative of ln(x)?</div>
</div>
<div class="section">
<div class="section-title">AI Response</div>
<div class="document-box">Reference [1, internal knowledge]: The derivative of the natural logarithm function ln(x) is 1/x, which is a standard result in differential calculus. This derivative is valid for x > 0 since the natural logarithm is only defined for positive real numbers. Answer: The derivative of ln(x) is 1/x.</div>
</div>
<div class="separator"></div>
<div class="nearest-match-box">
<div class="section" style="margin-left: 40px;">
<div class="section-title">Nearest Match in Training</div>
<div class="field-grid">
<div class="field-box" style="margin-bottom: 20px;">
<div class="field-label">Successfully Verified (Prediction)</div>
<div class="field-value">
<div class="field-value"><span class="tag tag-positive">True</span></div>
</div>
</div>
<div class="field-box" style="margin-bottom: 20px;">
<div class="field-label">True Label</div>
<div class="field-value"><span class="tag tag-positive">Verified</span></div>
</div>
</div>
<div class="explanation-box-positive">
<div class="explanation-title-positive">Model 1 Summary <span class="model-name">(gpt-5.2-2025-12-11)</span></div>
<div>The question asks for the imaginary part of a complex number z satisfying z(1+i)=2. The AI response solves for z (finding z=1−i) and concludes the imaginary part is −1.</div>
</div>
<div class="explanation-box-positive">
<div class="explanation-title-positive">Model 1 Explanation <span class="model-name">(gpt-5.2-2025-12-11)</span></div>
<div>The algebra is correct: z=2/(1+i)=1−i, so Im(z)=−1. The task is objective and does not depend on any external or recent information.</div>
</div>
<div class="explanation-box-positive">
<div class="explanation-title-positive">Model 2 Explanation <span class="model-name">(gemini-3-pro-preview)</span></div>
<div>The math is standard and easy to verify algebraically. The AI correctly solved the equation z = 2/(1+i) to find z = 1 - i, and correctly identified the imaginary part as -1.</div>
</div>
<div class="explanation-box-positive">
<div class="explanation-title-positive">Model 3 Agreement <span class="model-name">(granite-3.3-8b-instruct)</span></div>
<div>Do the model explanations agree that the response is correct?</div>
<div><span class="tag tag-positive">Yes</span></div>
</div>
<div class="section">
<div class="section-title">Prompt</div>
<div class="prompt-box">If the complex number $z$ satisfies $z(1+i)=2$ (where $i$ is the imaginary unit), then the imaginary part of $z$ is ______.</div>
</div>
<div class="section">
<div class="section-title">AI Response</div>
<div class="document-box">Given the complex number \( z \) satisfies \( z(1 + i) = 2 \), we need to find the imaginary part of \( z \).
First, express \( z \) as \( a + bi \), where \( a \) is the real part and \( b \) is the imaginary part. The equation becomes:
\[
(a + bi)(1 + i) = 2
\]
Expanding the left-hand side using the distributive property:
\[
(a + bi)(1 + i) = a + ai + bi + bi^2
\]
Since \( i^2 = -1 \), this simplifies to:
\[
a + ai + bi - b = (a - b) + (a + b)i
\]
Equating the real and imaginary parts to the right-hand side \( 2 + 0i \), we get the system of equations:
1. Real part: \( a - b = 2 \)
2. Imaginary part: \( a + b = 0 \)
From the second equation, \( a + b = 0 \), we find \( a = -b \). Substituting \( a = -b \) into the first equation:
\[
-b - b = 2 \implies -2b = 2 \implies b = -1
\]
Thus, the imaginary part of \( z \) is \( -1 \).
To verify, solve for \( z \) by dividing both sides by \( 1 + i \):
\[
z = \frac{2}{1 + i} \times \frac{1 - i}{1 - i} = \frac{2(1 - i)}{2} = 1 - i
\]
The imaginary part of \( z = 1 - i \) is indeed \( -1 \).
Therefore, the imaginary part of \( z \) is \boxed{-1}.</div>
</div>
<div class="field-grid">
<div class="field-box" style="margin-bottom: 20px;">
<div class="field-label">Document ID</div>
<div class="field-value">pos_585252_bf312529-3afa-432f-b8a3-aca35c8f2c19</div>
</div>
<div class="field-box" style="margin-bottom: 20px;">
<div class="field-label">Document Source</div>
<div class="field-value">OpenVerification1: openthoughts</div>
</div>
</div>
</div>
</div>
<div class="separator"></div>
<div class="section">
<div class="section-title">Legend</div>
<div class="legend-content">
<p>An ensemble of models 1, 2, and 3 (including the hidden states of model 3) is taken as the input to the SDM estimator that determines the verification classification.</p>
<p>The classification is in the High-Reliability region when the rescaled Similarity (q') is at least the minimum rescaled Similarity (q'_min) AND the predictive uncertainty, p(y | x), for the predicted class is at least the corresponding class-wise output threshold (ψ) for the predicted class.</p>
<p>The estimates in the section 'Analysis of the Effective Sample Size' are based on the DKW inequality applied to the distance quantiles.</p>
<div class="legend-items">
<div class="legend-item">
<span class="legend-label">Class 0:</span>
<span class="legend-value">NOT Verified</span>
</div>
<div class="legend-item">
<span class="legend-label">Class 1:</span>
<span class="legend-value">Verified</span>
</div>
</div>
</div>
</div>
</div>
</body>
</html>
