Fix callout type mismatches, enhance deep-explanation agent

- Fix 8 fun-note callouts with Hands-On title to exercise class
- Update deep-explanation agent (02): add missing mathematical
  formalization check (only when math clarifies inner workings)
- Add algorithm-without-formula to audit compliance checks

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: apartsin

agents/book-skills/agents/02-deep-explanation.md

@@ -59,6 +59,12 @@ Flag any concept that fails one or more of these questions.
 - Algorithms described as steps without explaining the reasoning behind the design
 - Architecture choices presented without explaining the alternative that was rejected
 
+### Missing Mathematical Formalization (only when math clarifies)
+- Add formulas only when they make a concept or its inner workings clearer than prose alone. Do not add math for decoration or rigor for its own sake.
+- Loss functions, optimization objectives, scoring mechanisms, and distance metrics should always have formal notation since these are inherently mathematical
+- When prose says "computes a weighted sum" or "minimizes the divergence", the formula makes the operation unambiguous; add it with LaTeX notation and a term-by-term explanation
+- Skip formalization for high-level workflow descriptions, API usage patterns, or architectural decisions where math would not add clarity
+
 ### Missing Numeric Grounding
 - Formulas or operations presented without a concrete numeric trace showing actual values flowing through them
 - Tensor operations described without showing example shapes (e.g., "input (2, 10, 512) becomes (2, 10, 8, 64) after splitting into 8 heads")
@@ -155,8 +161,9 @@ When deepening explanations, check whether the concept connects to material in o
 - [ ] No concept is introduced without a motivating problem or question preceding it
 - [ ] No claim of the form "X is better than Y" appears without an explanation of conditions and reasoning
 - [ ] No formula appears without an intuitive explanation of what each term represents
+- [ ] No algorithm or computational concept is described only in prose; each has a corresponding formula or equation
 - [ ] Every fix includes draft replacement text (not just "needs more depth")
-- [ ] The report covers all five categories: problem statements, claims, intuition, shallow explanations, mental models
+- [ ] The report covers all six categories: problem statements, claims, intuition, shallow explanations, mental models, missing formalization
 
 ### Quality Levels
 | Aspect | Poor | Adequate | Good | Excellent |
@@ -180,3 +187,4 @@ When deepening explanations, check whether the concept connects to material in o
 - **Shallow claim persists**: A reviewer flags "300 dimensions is optimal" but the Writer does not add evidence. Detection: search for numeric thresholds or comparative claims without citations or reasoning. Fix: add the source, the methodology, and the conditions under which the claim holds.
 - **Formula without intuition**: An equation is presented with variable definitions but no explanation of why the formula has its particular structure. Detection: check for math blocks followed only by variable definitions. Fix: add a paragraph explaining the intuition behind the formula's design.
 - **Name-drop without mechanism**: A technique is mentioned by name but its core idea is never explained. Detection: search for technique names that appear only once or twice without an accompanying "how it works" paragraph. Fix: add at least 3 sentences explaining the core mechanism.
+- **Algorithm without formula (when math would clarify)**: A computational procedure is described in prose (e.g., "the model computes a weighted sum") but no mathematical notation is given, and the formula would make the operation clearer. Detection: search for verbs like "computes", "calculates", "optimizes", "minimizes", "scores" near algorithm names without a nearby `$$` or `\[` math block. Fix: add a LaTeX formula with term-by-term explanation and a worked numeric example. Skip if the concept is purely procedural (API calls, configuration) where math would not add clarity.

part-6-agentic-ai/module-22-ai-agents/section-22.5.html

@@ -27,8 +27,8 @@ <h3>Prerequisites</h3>
         <p>This section builds on all previous sections in this chapter and assumes familiarity with <a class="cross-ref" href="../../part-7-multimodal-applications/module-28-llm-applications/section-28.1.html">code generation</a> from <a class="cross-ref" href="../module-25-specialized-agents/section-25.1.html">Section 25.1</a>.</p>
     </div>
 
-    <div class="callout fun-note">
-              <div class="callout-title">Hands-On</div>
+    <div class="callout exercise">
+              <div class="callout-title">Hands-On Lab</div>
         <p>This section includes a hands-on lab: <strong>Lab: Evaluate an Agent on SWE-bench Lite</strong>. Look for the lab exercise within the section content.</p>
     </div>
 

part-6-agentic-ai/module-23-tool-use-protocols/section-23.2.html

@@ -27,8 +27,8 @@ <h3>Prerequisites</h3>
         <p>This section builds on agent foundations from <a class="cross-ref" href="../module-22-ai-agents/index.html">Chapter 22</a> and <a class="cross-ref" href="../../part-3-working-with-llms/module-10-llm-apis/section-10.1.html">LLM API</a> basics from <a class="cross-ref" href="../../part-3-working-with-llms/module-10-llm-apis/index.html">Chapter 10</a>.</p>
     </div>
 
-    <div class="callout fun-note">
-              <div class="callout-title">Hands-On</div>
+    <div class="callout exercise">
+              <div class="callout-title">Hands-On Lab</div>
         <p>This section includes a hands-on lab: <strong>Lab: Build an MCP Server and Client</strong>. Look for the lab exercise within the section content.</p>
     </div>
 

part-6-agentic-ai/module-24-multi-agent-systems/section-24.1.html

@@ -27,8 +27,8 @@ <h3>Prerequisites</h3>
         <p>This section builds on <a class="cross-ref" href="../module-22-ai-agents/section-22.3.html">tool use</a> and protocols from <a class="cross-ref" href="../module-23-tool-use-protocols/index.html">Chapter 23</a> and agent foundations from <a class="cross-ref" href="../module-22-ai-agents/index.html">Chapter 22</a>.</p>
     </div>
 
-    <div class="callout fun-note">
-              <div class="callout-title">Hands-On</div>
+    <div class="callout exercise">
+              <div class="callout-title">Hands-On Lab</div>
         <p>This section includes a hands-on lab: <strong>Lab: Build the Same Agent in Three Frameworks</strong>. Look for the lab exercise within the section content.</p>
     </div>
 

part-6-agentic-ai/module-25-specialized-agents/section-25.1.html

@@ -27,8 +27,8 @@ <h3>Prerequisites</h3>
         <p>This section builds on agent foundations from <a class="cross-ref" href="../module-22-ai-agents/index.html">Chapter 22</a>, <a class="cross-ref" href="../module-22-ai-agents/section-22.3.html">tool use</a> from <a class="cross-ref" href="../module-23-tool-use-protocols/index.html">Chapter 23</a>, and <a class="cross-ref" href="../module-24-multi-agent-systems/section-24.1.html">multi-agent</a> patterns from <a class="cross-ref" href="../module-24-multi-agent-systems/index.html">Chapter 24</a>.</p>
     </div>
 
-    <div class="callout fun-note">
-              <div class="callout-title">Hands-On</div>
+    <div class="callout exercise">
+              <div class="callout-title">Hands-On Lab</div>
         <p>This section includes a hands-on lab: <strong>Lab: Build a Code Generation Agent with Self-Debugging</strong>. Look for the lab exercise within the section content.</p>
     </div>
 

part-6-agentic-ai/module-25-specialized-agents/section-25.2.html

@@ -27,8 +27,8 @@ <h3>Prerequisites</h3>
         <p>This section builds on agent foundations from <a class="cross-ref" href="../module-22-ai-agents/index.html">Chapter 22</a>, <a class="cross-ref" href="../module-22-ai-agents/section-22.3.html">tool use</a> from <a class="cross-ref" href="../module-23-tool-use-protocols/index.html">Chapter 23</a>, and <a class="cross-ref" href="../module-24-multi-agent-systems/section-24.1.html">multi-agent</a> patterns from <a class="cross-ref" href="../module-24-multi-agent-systems/index.html">Chapter 24</a>.</p>
     </div>
 
-    <div class="callout fun-note">
-              <div class="callout-title">Hands-On</div>
+    <div class="callout exercise">
+              <div class="callout-title">Hands-On Lab</div>
         <p>This section includes a hands-on lab: <strong>Lab: Browser Automation Agent with Playwright MCP</strong>. Look for the lab exercise within the section content.</p>
     </div>
 

part-6-agentic-ai/module-25-specialized-agents/section-25.6.html

@@ -27,8 +27,8 @@ <h3>Prerequisites</h3>
         <p>This section builds on <a class="cross-ref" href="section-25.1.html">code generation agents</a> from Section 25.1, <a class="cross-ref" href="../../part-8-evaluation-production/module-29-evaluation-observability/section-29.2.html">evaluation metrics</a> from Section 29.2, and <a class="cross-ref" href="../module-22-ai-agents/section-22.2.html">ReAct agent loops</a> from Section 22.2.</p>
     </div>
 
-    <div class="callout fun-note">
-        <div class="callout-title">Hands-On</div>
+    <div class="callout exercise">
+        <div class="callout-title">Hands-On Lab</div>
         <p>This section includes a hands-on lab: <strong>Lab: Build a Minimal Coding Agent for SWE-bench Verified</strong>. Look for the lab exercise within the section content.</p>
     </div>
 

part-6-agentic-ai/module-26-agent-safety-production/section-26.5.html

@@ -27,8 +27,8 @@ <h3>Prerequisites</h3>
         <p>This section builds on all previous chapters in Part VI, especially <a class="cross-ref" href="../module-22-ai-agents/section-22.3.html">tool use</a> (<a class="cross-ref" href="../module-23-tool-use-protocols/index.html">Chapter 23</a>) and <a class="cross-ref" href="../module-24-multi-agent-systems/section-24.1.html">multi-agent</a> systems (<a class="cross-ref" href="../module-24-multi-agent-systems/index.html">Chapter 24</a>).</p>
     </div>
 
-    <div class="callout fun-note">
-              <div class="callout-title">Hands-On</div>
+    <div class="callout exercise">
+              <div class="callout-title">Hands-On Lab</div>
         <p>This section includes a hands-on lab: <strong>Lab: Chaos Test a Multi-Agent Pipeline</strong>. Look for the lab exercise within the section content.</p>
     </div>
 

part-8-evaluation-production/module-31-production-engineering/section-31.7.html

@@ -27,8 +27,8 @@ <h3>Prerequisites</h3>
         <p>This section builds on <a class="cross-ref" href="../../part-2-understanding-llms/module-09-inference-optimization/index.html">inference optimization</a> from Chapter 9, <a class="cross-ref" href="section-31.1.html">deployment architecture</a> from Section 31.1, and <a class="cross-ref" href="../../part-4-training-adapting/module-16-distillation-merging/index.html">quantization fundamentals</a> from Chapter 16.</p>
     </div>
 
-    <div class="callout fun-note">
-        <div class="callout-title">Hands-On</div>
+    <div class="callout exercise">
+        <div class="callout-title">Hands-On Lab</div>
         <p>This section includes a hands-on lab: <strong>Lab: Run a Quantized Model Locally and Measure Quality vs. Latency</strong>. Look for the lab exercise within the section content.</p>
     </div>