diff --git a/.github/agent-instructions/chapter-author-agent.md b/.github/agent-instructions/chapter-author-agent.md
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+++ b/.github/agent-instructions/chapter-author-agent.md
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+# Chapter Author Agent Instructions
+
+## Mission
+Create or update the chapter notebook from the chapter PDF, open/update the PR, and iterate until review agents report no blocking concerns.
+
+## Workflow
+1. Read chapter PDF and draft notebook structure that follows chapter flow.
+2. Add initial explanations, derivations, examples, and exercises.
+3. Submit PR with chapter PDF + notebook pair.
+4. Wait for review comments from:
+   - Content Coverage Agent
+   - Interactivity Agent
+5. Apply requested updates with high educational value.
+6. Push revisions and re-run review cycle.
+7. Repeat until both agents pass.
+8. Mark PR ready for human review.
+
+## Completion gate
+Proceed to human review only when:
+- No unresolved missing-concept findings from content review.
+- No unresolved high-impact interactivity recommendations.
diff --git a/.github/agent-instructions/content-coverage-agent.md b/.github/agent-instructions/content-coverage-agent.md
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+++ b/.github/agent-instructions/content-coverage-agent.md
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+# Content Coverage Agent Instructions
+
+## Mission
+Review a chapter PR and verify that notebook content fully covers chapter concepts from the paired PDF.
+
+## Inputs
+- Chapter PDF path from workflow output (`chapter_pdf`)
+- Notebook path from workflow output (`chapter_notebook`)
+- PR diff
+
+## Review rules
+1. Build a chapter concept checklist from the PDF section/headings/examples.
+2. Map each concept to where it appears in the notebook.
+3. Flag concepts as **missing** when they are absent or only insufficiently covered in the notebook.
+4. Do **not** flag extra material if it is relevant and pedagogically useful.
+5. Prioritize mathematically meaningful omissions over formatting/editorial details.
+6. A concept is considered covered only when the notebook includes explicit explanation, derivation, or a worked example.
+7. Mentions only in variable names, comments, or section titles without explanatory text count as insufficient coverage and should be flagged.
+8. Treat insufficient coverage as missing in output comments, and state why the current treatment is not enough for learner understanding.
+
+## Output format for PR comment
+- Missing concept: `<name>`
+  - Why it matters: `<learning impact>`
+  - Evidence from chapter: `<section/page>`
+  - Suggested notebook placement: `<where to add>`
+
+If no meaningful omissions exist, post: `Coverage review passed: all core chapter concepts are present.`
diff --git a/.github/agent-instructions/interactivity-agent.md b/.github/agent-instructions/interactivity-agent.md
new file mode 100644
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+++ b/.github/agent-instructions/interactivity-agent.md
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+# Interactivity Agent Instructions
+
+## Mission
+Review a chapter PR and propose notebook improvements that use visualization and interactivity to improve understanding.
+
+## Inputs
+- Chapter PDF path from workflow output (`chapter_pdf`)
+- Notebook path from workflow output (`chapter_notebook`)
+- PR diff
+
+## Review rules
+1. Identify concepts in the chapter where plots, sliders, animations, or parameter sweeps would improve comprehension.
+2. Propose additions that are concrete and notebook-friendly.
+3. Prefer additions tied directly to chapter learning goals.
+4. Skip cosmetic-only suggestions unless they directly improve conceptual clarity.
+5. Keep recommendations concise and prioritized by educational impact.
+6. Rank educational impact by: (a) concept difficulty in the chapter, (b) likelihood of student misconceptions, and (c) how strongly interactivity clarifies parameter effects or geometric intuition.
+
+## Output format for PR comment
+- Suggested interactive section: `<title>`
+  - Concept supported: `<concept>`
+  - Why interactivity helps: `<learning value>`
+  - Suggested implementation direction: `<plot/widget idea>`
+  - Suggested location in notebook: `<where to insert>`
+
+If notebook interactivity is already strong for all major concepts, post: `Interactivity review passed: no high-impact additions identified.`
diff --git a/.github/workflows/chapter-pr-agent-cycle.yml b/.github/workflows/chapter-pr-agent-cycle.yml
new file mode 100644
index 0000000..4a0c059
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+++ b/.github/workflows/chapter-pr-agent-cycle.yml
@@ -0,0 +1,178 @@
+name: Chapter PR Agent Cycle
+
+on:
+  pull_request:
+    types: [opened, synchronize, reopened, ready_for_review]
+    paths:
+      - "NLPDE/**"
+      - ".github/agent-instructions/**"
+      - ".github/workflows/chapter-pr-agent-cycle.yml"
+
+permissions:
+  contents: read
+  pull-requests: write
+
+jobs:
+  chapter-context-check:
+    name: Verify chapter ↔ notebook mapping
+    runs-on: ubuntu-latest
+    outputs:
+      chapter_pdf: ${{ steps.detect.outputs.chapter_pdf }}
+      chapter_notebook: ${{ steps.detect.outputs.chapter_notebook }}
+      skip_review: ${{ steps.detect.outputs.skip_review }}
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+        with:
+          fetch-depth: 0
+
+      - name: Detect changed chapter assets
+        id: detect
+        shell: bash
+        run: |
+          set -euo pipefail
+          if [[ ! -d NLPDE ]]; then
+            echo "NLPDE directory not found in this checkout; skipping chapter review jobs."
+            echo "skip_review=true" >> "$GITHUB_OUTPUT"
+            echo "chapter_pdf=" >> "$GITHUB_OUTPUT"
+            echo "chapter_notebook=" >> "$GITHUB_OUTPUT"
+            exit 0
+          fi
+
+          BASE_SHA="${{ github.event.pull_request.base.sha }}"
+          HEAD_SHA="${{ github.event.pull_request.head.sha }}"
+          DIFF_OUTPUT="$(git diff --name-only "$BASE_SHA" "$HEAD_SHA" -- NLPDE)" || {
+            echo "Failed to compute NLPDE file diff for base=$BASE_SHA head=$HEAD_SHA."
+            exit 1
+          }
+          mapfile -t CHANGED <<< "$DIFF_OUTPUT"
+
+          if [[ ${#CHANGED[@]} -eq 0 ]]; then
+            echo "No files changed in NLPDE/. Workflow triggered by agent instruction or workflow updates only."
+            echo "skip_review=true" >> "$GITHUB_OUTPUT"
+            echo "chapter_pdf=" >> "$GITHUB_OUTPUT"
+            echo "chapter_notebook=" >> "$GITHUB_OUTPUT"
+            exit 0
+          fi
+          echo "skip_review=false" >> "$GITHUB_OUTPUT"
+
+          mapfile -t PDF_FILES < <(printf '%s\n' "${CHANGED[@]}" | grep -E '^NLPDE/[^/]*\.pdf$' || true)
+          mapfile -t IPYNB_FILES < <(printf '%s\n' "${CHANGED[@]}" | grep -E '^NLPDE/[^/]*\.ipynb$' || true)
+
+          if [[ ${#PDF_FILES[@]} -eq 0 && ${#IPYNB_FILES[@]} -eq 0 ]]; then
+            echo "No chapter PDF or notebook files found in NLPDE/ changes."
+            echo "Update the chapter PDF and notebook pair in the same PR."
+            exit 1
+          fi
+
+          if [[ ${#PDF_FILES[@]} -ne 1 || ${#IPYNB_FILES[@]} -ne 1 ]]; then
+            echo "Expected exactly one chapter PDF and one notebook update per PR."
+            echo "Found ${#PDF_FILES[@]} PDF file(s):"
+            if [[ ${#PDF_FILES[@]} -eq 0 ]]; then
+              echo "<none>"
+            else
+              printf '%s\n' "${PDF_FILES[@]}"
+            fi
+            echo "Found ${#IPYNB_FILES[@]} notebook file(s):"
+            if [[ ${#IPYNB_FILES[@]} -eq 0 ]]; then
+              echo "<none>"
+            else
+              printf '%s\n' "${IPYNB_FILES[@]}"
+            fi
+            exit 1
+          fi
+
+          PDF="${PDF_FILES[0]}"
+          IPYNB="${IPYNB_FILES[0]}"
+
+          PDF_BASE="$(basename "$PDF" .pdf)"
+          IPYNB_BASE="$(basename "$IPYNB" .ipynb)"
+          if [[ "$PDF_BASE" != "$IPYNB_BASE" ]]; then
+            echo "Expected 1:1 chapter naming, but found:"
+            echo "PDF: $PDF_BASE"
+            echo "Notebook: $IPYNB_BASE"
+            echo "Use matching base names, for example: NLPDE_Ch2.pdf and NLPDE_Ch2.ipynb"
+            exit 1
+          fi
+
+          echo "chapter_pdf=$PDF" >> "$GITHUB_OUTPUT"
+          echo "chapter_notebook=$IPYNB" >> "$GITHUB_OUTPUT"
+
+  content-coverage-agent:
+    name: Content coverage review
+    needs: chapter-context-check
+    if: needs.chapter-context-check.outputs.skip_review != 'true'
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - name: Load content agent instructions
+        id: content_prompt
+        shell: bash
+        run: |
+          {
+            echo "prompt<<EOF"
+            cat .github/agent-instructions/content-coverage-agent.md
+            echo "EOF"
+          } >> "$GITHUB_OUTPUT"
+
+      - name: Review chapter coverage (placeholder)
+        env:
+          CONTENT_AGENT_PROMPT: ${{ steps.content_prompt.outputs.prompt }}
+        run: |
+          echo "Integrate your preferred PR review agent here."
+          echo "Context PDF: ${{ needs.chapter-context-check.outputs.chapter_pdf }}"
+          echo "Context notebook: ${{ needs.chapter-context-check.outputs.chapter_notebook }}"
+          echo "Goal: report missing concepts from chapter in notebook (additional relevant material is allowed)."
+          echo "Instruction payload size: ${#CONTENT_AGENT_PROMPT} characters"
+
+  interactivity-agent:
+    name: Interactivity and visualization review
+    needs: chapter-context-check
+    if: needs.chapter-context-check.outputs.skip_review != 'true'
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - name: Load interactivity agent instructions
+        id: interactivity_prompt
+        shell: bash
+        run: |
+          {
+            echo "prompt<<EOF"
+            cat .github/agent-instructions/interactivity-agent.md
+            echo "EOF"
+          } >> "$GITHUB_OUTPUT"
+
+      - name: Suggest interactive improvements (placeholder)
+        env:
+          INTERACTIVITY_AGENT_PROMPT: ${{ steps.interactivity_prompt.outputs.prompt }}
+        run: |
+          echo "Integrate your preferred PR review agent here."
+          echo "Context PDF: ${{ needs.chapter-context-check.outputs.chapter_pdf }}"
+          echo "Context notebook: ${{ needs.chapter-context-check.outputs.chapter_notebook }}"
+          echo "Goal: suggest concrete plot/interactivity additions that improve learning outcomes."
+          echo "Instruction payload size: ${#INTERACTIVITY_AGENT_PROMPT} characters"
+
+  author-revision-loop:
+    name: Author agent revision loop guidance
+    needs: [chapter-context-check, content-coverage-agent, interactivity-agent]
+    if: needs.chapter-context-check.outputs.skip_review != 'true'
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - name: Load author agent instructions
+        run: cat .github/agent-instructions/chapter-author-agent.md
+
+  config-only-update:
+    name: Config-only update notice
+    needs: chapter-context-check
+    if: needs.chapter-context-check.outputs.skip_review == 'true'
+    runs-on: ubuntu-latest
+    steps:
+      - name: Explain skip
+        run: echo "Skipping chapter review jobs because no NLPDE chapter files changed."
diff --git a/docs/agent-workflow.md b/docs/agent-workflow.md
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+++ b/docs/agent-workflow.md
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+# Chapter PR Agent Workflow
+
+This repository uses a PR-centered multi-agent loop for chapter development in `NLPDE/`.
+
+## Agents
+1. **Chapter Author Agent**
+   - Creates or updates a chapter notebook from the chapter PDF.
+   - Opens/updates the PR and applies agent feedback.
+2. **Content Coverage Agent**
+   - Uses the chapter PDF as source-of-truth context.
+   - Verifies notebook concept coverage and reports missing concepts only.
+3. **Interactivity Agent**
+   - Uses the chapter PDF and notebook to propose high-impact visualization/interactivity additions.
+
+## PR trigger
+Workflow file: `.github/workflows/chapter-pr-agent-cycle.yml`
+
+On PR updates affecting `NLPDE/**`, the workflow:
+- Enforces a 1:1 chapter mapping by requiring exactly one changed PDF and one changed notebook in `NLPDE/`, with identical filenames before the extension (case-sensitive), e.g., `NLPDE/NLPDE_Ch2.pdf` ↔ `NLPDE/NLPDE_Ch2.ipynb`.
+- Runs content coverage review stage.
+- Runs interactivity review stage.
+- Runs author revision-loop guidance stage.
+
+## Preprocessing recommendation (shared chapter context)
+Yes—preprocessing is recommended because multiple agents reuse the same chapter context.
+
+Recommended pattern:
+1. Extract chapter PDF text once in a preprocessing step.
+2. Chunk by section/subsection with page metadata.
+3. Create embeddings and index chunks in a vector store.
+4. Expose retrieval output to each agent so all reviews use consistent chapter evidence.
+
+This reduces repeated parsing costs, improves consistency across agent comments, and helps produce page/section-cited feedback.