beamer

name	beamer
description	Beamer LaTeX slide workflow: create, compile, review, and polish academic presentations. Use this skill whenever the user works on Beamer .tex slide decks, or asks to create slides, make a presentation, prepare a lecture, build a talk, or generate Beamer slides from a paper. Covers: creation, editing, compilation, proofreading, visual audit, pedagogical review, TikZ diagrams, figure extraction, and comprehensive quality checks. Trigger on: beamer, slides, lecture, presentation, seminar talk, conference talk, defense slides, tikz, compile latex, proofread slides, slide review, 讨论班, 论文讲解. Do NOT trigger on: powerpoint, pptx, PPT, 做PPT — use the powerpoint-slides skill instead.
argument-hint	[action] [file] — actions: create, compile, review, audit, pedagogy, tikz, excellence, devils-advocate, visual-check, validate, extract-figures
allowed-tools	["Read","Write","Edit","Bash","Grep","Glob","Agent","AskUserQuestion","TaskCreate","TaskUpdate","TaskList","TaskGet"]

Beamer Slide Workflow

Universal skill for academic Beamer presentations. Full lifecycle: create → compile → review → polish → verify.

---

0. REFERENCE PREAMBLE

When creating new slides, use this as the default preamble unless the user has a custom template.

\documentclass[aspectratio=169,10pt]{beamer}

\usetheme{Madrid}
\usecolortheme{default}
\setbeamertemplate{navigation symbols}{}
\setbeamertemplate{footline}[frame number]

\usepackage{amsmath,amssymb,amsthm,booktabs,mathtools}
\usepackage{stmaryrd}  % for \llbracket, \rrbracket
\usepackage{graphicx}  % for \includegraphics (extracted figures)
\usepackage{hyperref}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,positioning,decorations.pathreplacing}

% Semantic colors — use in BOTH text and TikZ for global consistency
\definecolor{positive}{HTML}{0173B2}       % blue (correct, advantage)
\definecolor{negative}{HTML}{DE8F05}       % orange (limitation, drawback)
\definecolor{emphasis}{HTML}{029E73}        % green (highlight, key finding)
\definecolor{neutral}{gray}{0.55}          % muted context
\definecolor{cbPurple}{HTML}{CC78BC}        % additional accent
\newcommand{\pos}[1]{\textcolor{positive}{#1}}
\newcommand{\con}[1]{\textcolor{negative}{#1}}
\newcommand{\HL}[1]{\textcolor{emphasis}{#1}}

Rules:

• Always 10pt — 11pt or 12pt produces oversized, sparse slides.
• Always aspectratio=169 — modern projectors are 16:9.
• Default presenter: \author{Presenter: [name]} and \institute{Shanghai Jiao Tong University}. Override only if user specifies otherwise.
• If user provides a custom preamble, header file, or theme: use theirs.
• Add domain-specific macros (e.g. \newcommand{\F}{\mathbb{F}}) as needed.
• Algorithm/code packages (add only when needed):
  • Algorithms: \usepackage[ruled,lined]{algorithm2e} — set \SetAlgoLined, \DontPrintSemicolon
  • Code listings: \usepackage{listings} — set basicstyle=\ttfamily\small, keywordstyle=\bfseries\color{positive}, commentstyle=\color{neutral}. Max 10 lines of code per slide; highlight key lines with escapeinside={(*@}{@*)} and \colorbox.
  • Pseudocode: \usepackage{algorithmic} — simpler than algorithm2e, suitable for short procedures.
• Data plotting (add only when needed):
  • \usepackage{pgfplots} + \pgfplotsset{compat=1.18} — data-driven plots (bar, scatter, error bars, histograms). Far more efficient than manual TikZ coordinate plots for data visualization.
  • \usepackage{subcaption} — multiple subfigures in one frame via \begin{subfigure}{0.48\textwidth}.
• Theorem environments: Beamer provides theorem, lemma, corollary, definition, example, proof out of the box (styled by the theme). Use them for formal statements — they get automatic numbering and consistent styling. Customize with \setbeamertemplate{theorems}[numbered] or [ams style].

---

1. HARD RULES (Non-Negotiable)

1. No overlays — never use \pause, \onslide, \only, \uncover. Use multiple slides for progressive builds, color emphasis for attention. Common replacement patterns:
   • Progressive formula build-up: slide A shows the base equation, slide B copies it and adds the next term (grayed-out terms from slide A stay as context). Copy-paste the full frame and extend.
   • Step-by-step list reveal: slide A shows items 1-2, slide B shows 1-4 (items 1-2 repeated). Use \textcolor{neutral}{} on previously-shown items to mute them.
   • Diagram incremental build: slide A shows the base structure, slide B adds annotations/edges. Duplicate the tikzpicture and append new elements — never delete prior elements.
2. Max 2 colored boxes per slide — more dilutes emphasis. Demote transitional remarks to plain italic.
3. Motivation before formalism — every concept starts with "Why?" before "What?".
4. Worked example within 2 slides of every definition.
5. XeLaTeX only — never pdflatex.
6. Beamer .tex is the single source of truth — TikZ diagrams, content, notation all originate here.
7. Verify after every task — compile, check warnings, open PDF.
8. Telegraphic style — keyword phrases, not full sentences. Slides are speaker prompts, not manuscripts. Exception: framing sentences that set up a definition or transition. Each bullet item should be ≤2 lines (~15 words) — if longer, split into sub-items or rewrite more concisely.
9. Every slide earns its place — each slide must contain at least one substantive element (formula, diagram, table, theorem, or algorithm). A slide with only 3 short bullets and nothing else must be merged or enriched.
10. Box-interior overflow guard — alertblock, exampleblock, and block environments add internal padding (~15% less width, ~12-16pt extra height for title bar + vertical padding). Content that fits on a bare slide can overflow inside a box in both directions. Rules:
    • Vertical overflow (most common, hardest to detect): display math (\[ \]) + text below it inside a single box easily exceeds vertical capacity. Limit box content to one display equation OR 2-3 short bullet items — not both. Never use aggressive \vspace{-Xpt} inside a box; it pulls bottom content past the border.
    • Horizontal overflow: never use \qquad inside a box; use \quad or ,. If a display equation is wider than ~70% of \textwidth on a bare slide, reformat before placing inside a box.
    • Beamer suppresses overfull warnings inside blocks — zero compile warnings does NOT guarantee no visual overflow. Always visually verify every box in the PDF.
11. Reference slide — the second-to-last slide (before Thank You) must be a References slide listing key cited works. Use \begin{thebibliography}{9} with \small. Include the primary paper and 3-5 most relevant references.
12. Color and contrast standards — text-background contrast ratio ≥ 4.5:1 (WCAG AA). Never use red+green for binary contrasts (color blindness affects ~8% of men). Prefer blue+orange. Semantic color commands defined in preamble: \pos{} = positive/correct (blue), \con{} = negative/limitation (orange), \HL{} = emphasis/key finding (green), \textcolor{neutral}{} = de-emphasized. These are color-blind safe. Limit total palette to 3-5 colors.
13. Visual hierarchy in font sizes — slide title: 20-24pt (beamer default), key findings/theorems: normal size with \textbf, supporting text: normal, labels/captions: \small minimum. Never use \tiny for any user-facing content.
14. Backup slides — after the Thank You slide, include 3-5 backup slides for anticipated questions. Use \appendix before backup section. Separate from main deck with a \begin{frame}{Backup Slides}\end{frame} divider. Backup slides should NOT count toward the timing allocation. Content to include (derive from Phase 0 material analysis):
    • Full proof of the main theorem (if only a sketch was shown in the main deck)
    • Parameter choices / security analysis details (for crypto/protocol papers)
    • Extended comparison table with additional baselines
    • Experimental setup details (hardware, hyperparameters, datasets)
    • Definitions of prerequisites that were assumed known (in case someone asks)
15. Columns layout — use \begin{columns}[T] + \column{W\textwidth} for side-by-side content. Rules:
    • Comparison / parallel content: two columns at 0.48\textwidth each (leave 0.04 gap).
    • Figure + text: figure column 0.45-0.55, text column 0.40-0.50, gap 0.05.
    • Three columns maximum: each ≤ 0.30\textwidth, only for short items (icons, stats, one-liners).
    • Never nest columns inside columns.
    • Always use [T] (top-align) unless deliberately centering.
    • Columns content follows the same density constraints as regular slides.

---

2. ACTIONS

Parse $ARGUMENTS to determine which action to run. If no action specified, ask.

2.1 compile [file]

3-pass XeLaTeX + bibtex for full citation resolution.

# Adapt TEXINPUTS/BIBINPUTS to your project's preamble/bib locations
xelatex -interaction=nonstopmode FILE.tex
bibtex FILE
xelatex -interaction=nonstopmode FILE.tex
xelatex -interaction=nonstopmode FILE.tex

Post-compile checks:

• Grep log for Overfull \\hbox warnings (count and locations)
• Grep for Undefined control sequence or undefined citations
• Grep for Label(s) may have changed
• Open PDF for visual verification
• Report: success/failure, overfull count, undefined items, page count

2.2 create [topic]

Collaborative, iterative lecture creation. Strict phase gates — never skip ahead.

Phase 0: Material Analysis (if papers/materials provided)

Read first, ask later. Must understand the content before asking meaningful questions.

• Read the full paper/materials thoroughly
• Extract: core contribution, key techniques, main theorems, comparison with prior work
• Map notation conventions
• Identify the paper's logical structure and which parts are slide-worthy
• Internally note: prerequisite knowledge, natural section boundaries, what could be skipped or expanded

Do NOT present results or ask questions yet — proceed directly to Phase 1.

Phase 1: Needs Interview (MANDATORY — informed by Phase 0)

Conduct a content-driven interview via AskUserQuestion. The questions below are the minimum required set — you MUST also add paper-specific questions derived from Phase 0.

Minimum required questions (always ask):

1. Duration: How long is the presentation?
2. Audience level: Who are the listeners?

Optional question (ask when the talk is a journal club, defense, or user seems to want rehearsal support): 3. Speaker notes: Would you like speaker notes in the Presenter View? If yes, \note{} blocks will be added per frame with telegraphic talking points (key message, transition cue, anticipated questions). Requires adding \setbeameroption{show notes on second screen=right} to the preamble for dual-screen display.

Content-driven questions (derive from Phase 0, ask as many as needed):

• Prerequisite knowledge: List concrete technical dependencies identified in Phase 0. Ask which ones the audience knows. E.g., "The paper builds on sumcheck and polynomial commitments. Should I review these?" — not "familiar with basic algebra?".
• Content scope: Offer the paper's actual components as options. Ask which to emphasize, skip, or briefly mention.
• Depth vs. breadth: If the paper has both intuitive overview and detailed constructions, ask which the user prefers.
• Paper-specific decisions: E.g., if the paper compares two constructions, ask whether to present both equally or focus on one.

Guidelines:

• Options should come from the paper's actual content, not generic templates.
• 3-6 questions total; don't over-ask, don't under-ask.
• If something is obvious from context (e.g., user said "讨论班"), infer rather than ask.

Slide count heuristic: ~1 slide per 1.5-2 minutes.

Timing allocation table:

Duration	Total slides	Intro/Motivation	Methods/Background	Core content	Summary/Conclusion
5min (lightning)	5-7	1-2	0-1	2-3	1
10min (short)	8-12	2	1-2	4-5	1
15min (conference)	10-15	2-3	2-3	5-7	1-2
20min (seminar)	13-18	3	2-3	6-9	2
45min (keynote)	22-30	4-5	5-7	10-14	2-3
90min (lecture)	45-60	5-6	8-12	25-35	3-4

Talk-type specific tips:

Talk type	Key emphasis	Common mistake
Lightning (5min)	One core message, no background review	Cramming a full talk into 5 minutes
Conference (10-20min)	1-2 key results, fast methods overview	Too much technical detail, no big picture
Seminar (45min)	Deep dive OK, but need visual rhythm	Wall-to-wall formulas without examples
Defense/Thesis	Demonstrate mastery, systematic coverage	Skipping motivation, rushing results
Journal club	Critical analysis, facilitate discussion	Summarizing without evaluating
Grant pitch	Significance → feasibility → impact	Too technical, not enough "why it matters"

Time distribution principle: Spend 40-50% of time on core content (results/techniques). Max 3-4 consecutive theory-heavy slides before a worked example or visual break.

Phase 2: Structure Plan (GATE — user must approve before drafting)

Produce a detailed outline. For each section:

• Section title
• Number of slides allocated
• Key content points per slide (1-2 lines each)
• TikZ diagrams or figures planned (brief description)
• Notation to introduce

Present the plan to the user. Ask: structure OK? Expand/shrink/cut anything?

Do NOT proceed to drafting until user approves.

Phase 3: Draft (iterative, batched)

This phase is the most critical. Follow all sub-rules strictly.

3a. Writing Style

• Telegraphic keywords, not full sentences. Exception: one framing sentence per slide to set context.
• Formulas and analysis interleave tightly — define a quantity, then immediately state its cost/property/implication on the same slide. Never isolate a formula on one slide and its analysis on the next.
• No conversational hedging — never write "wait, not exactly", "actually, let me clarify", or similar. If a point needs qualification, state it precisely from the start.
• Use \textbf{} for key terms on first introduction; use \pos{...} for positive properties, \con{...} for drawbacks/limitations, \HL{...} for key findings (defined in preamble).

3a-2. Opening and Closing Strategies

Opening slide (pick one strategy):

• Surprising statistic — a counter-intuitive number that challenges assumptions
• Provocative question — something the audience cannot immediately answer
• Real-world failure/problem — "System X failed because..." → "How do we prevent this?"
• Visual demonstration — show the phenomenon before explaining it

The opening should create tension or curiosity that the rest of the talk resolves.

Closing strategies:

• Call-back to opening — revisit the opening question/problem, now answered (circular narrative)
• 3 key takeaways — numbered, telegraphic, one slide. The audience remembers the last thing they see.
• Open question / future direction — leave the audience thinking, naturally invites Q&A
• Never end on a bare "Thank You" — the second-to-last content slide should deliver the lasting impression. The Thank You slide is a courtesy, not the conclusion.

3b. Mathematical Slide Patterns

Each math-heavy slide should follow one of these patterns:

Definition slide:

[Framing sentence: why this definition matters]
[Formal definition in display math]
[Key properties / immediate consequences as 2-3 bullet items]

Construction/Algorithm slide:

[One-line goal statement]
[Core equation / algorithm steps]
[Complexity analysis: prover cost, verifier cost, soundness]

Comparison slide:

[Side-by-side table: prior work vs this work]
[1-2 lines highlighting the key difference]

Insight/Remark slide (adds value beyond the paper):

[Observation the paper doesn't emphasize, or a comparison with related work]
[Why this matters / what it implies]

Every slide must have a clear takeaway — the one thing the audience should remember.

Theorem/Proof slide (for formal mathematical statements):

[Framing sentence: informal statement of the result]
\begin{theorem}[Optional name]
  [Formal statement in display math]
\end{theorem}
[Key implication or "why this matters" as 1-2 bullets]

• Proof on the next slide (never cramming theorem + proof on one slide).
• For long proofs: show proof sketch (key steps only), put full proof in backup slides.
• Use \begin{proof}[Proof sketch] to signal abbreviated proofs.

Cross-referencing between slides:

• Label key slides with \label{slide:construction} inside the frame.
• Reference from other slides: see Slide~\ref{slide:construction} or clickable \hyperlink{slide:construction}{\beamerbutton{Back to Construction}}.
• Especially useful for Q&A — quickly jump back to a referenced result.
• In backup slides, always hyperlink back to the main slide that motivates them.

3c. Content Density Constraints

Upper bounds (per slide):

• ≤ 7 bullet points or items
• ≤ 2 displayed equations (more → split)
• ≤ 5 new symbols introduced
• ≤ 2 colored boxes (alertblock/exampleblock)

Lower bounds (per slide):

• Each slide MUST contain at least one substantive element: a formula, diagram, table, theorem statement, or algorithm
• A slide with only ≤ 3 short text-only bullets is too sparse — merge with an adjacent slide or add a formula/diagram
• Pure text-only bullet slides should be ≤ 30% of the total deck

Density self-check after each batch:

• Count slides that have zero formulas/diagrams/tables → flag if > 30% of batch
• Count slides with ≤ 3 short items and no math → candidates for merging

3d. Batch Workflow

• Work in batches of 5-10 slides, following the approved structure
• After each batch, compile (xelatex -interaction=nonstopmode) to catch errors early — fixing 2 issues in a 10-slide batch is far cheaper than fixing 12 issues in a 40-slide deck at Phase 5
• After each batch, self-check: notation consistency, density constraints, motivation-before-formalism
• Continue to next batch only after current batch compiles cleanly and passes self-check

3e. Table Best Practices

• Always center tables — wrap every standalone table in \begin{center}...\end{center}. Left-aligned tables look misaligned on slides.
• Never place a table immediately after the frame title — themes like Madrid have a colored title bar whose bottom edge visually merges with \toprule, making the table appear embedded in the title. Always insert \vspace{4pt} (or introductory text) between the title and the first \toprule. The compiler emits zero warnings for this — it can only be caught by visual inspection.
• Always use booktabs (\toprule, \midrule, \bottomrule) — never vertical lines (|).
• Column alignment: numbers right-aligned (r), text left-aligned (l), short labels centered (c).
• Max 6-7 columns, 8-10 rows per slide. More → split across slides following these pagination rules:
  • Each continuation slide repeats the full header row (\toprule + header + \midrule).
  • Append " (cont'd)" to the frame title: \frametitle{Results (cont'd)}.
  • Split at logical row group boundaries (e.g., between algorithm families, dataset groups) — never mid-group.
  • Last page must have ≥3 data rows; if fewer, merge with the previous page.
  • Each page gets its own takeaway line below the table if the subset tells a different story.
• Use \resizebox{\textwidth}{!}{...} only as last resort — prefer reducing columns/rows first.
• Highlight key cells with \cellcolor{positive!15} or \textbf{} — draw the eye to the result.
• For comparison tables: bold the best result in each row/column.
• Caption below table in \small, or use the frame title as the implicit caption.

3f. Algorithm and Code Display

• Pseudocode ≤ 10 lines per slide. If longer, split into "high-level overview" and "key subroutine" slides.
• Highlight the critical line(s): use escapeinside in listings or \colorbox in algorithm2e.
• Input/output clearly stated at the top of the algorithm.
• Use consistent naming: variables in math italic ($x$), functions in sans-serif or typewriter.
• For code (not pseudocode): \ttfamily\small, syntax highlighting via listings. Show only the relevant fragment — never dump an entire source file.

Phase 4: Figures

• TikZ diagrams in Beamer source (single source of truth)
• Apply TikZ quality standards (see Section 2.6)
• R/Python scripts if needed

Data visualization guidelines (journal figures ≠ slide figures):

• Simplify ruthlessly — remove minor gridlines, detailed legends (label directly on plot), secondary axes. Show only data supporting the current slide's point.
• Enlarge everything — axis labels ≥ 18pt, line width 2-4pt, marker size 8-12pt. If unreadable at 2-3 feet from laptop, it fails on a projector.
• Direct labeling — label lines/bars directly instead of using a separate legend. Reduces cognitive load.
• One message per figure — split multi-panel journal figures across multiple slides. Each slide shows one comparison.
• Highlight the result — key data in bold saturated color, comparison data in muted gray. Use \textcolor{blue!70!black}{...} for the key finding, gray for reference.
• Color-blind safe palette — prefer blue (#0173B2) + orange (#DE8F05) over red + green. Add line style differences (solid/dashed/dotted) as redundant encoding. In TikZ:

  \definecolor{cbBlue}{HTML}{0173B2}
  \definecolor{cbOrange}{HTML}{DE8F05}
  \definecolor{cbGreen}{HTML}{029E73}
  \definecolor{cbPurple}{HTML}{CC78BC}
  

• Progressive disclosure — for complex figures, build incrementally: axes → first dataset → comparison → annotation with finding. Use separate slides (not \pause).
• Subfigures — use \begin{subfigure}{0.48\textwidth} (requires subcaption package) for side-by-side panels in one frame. Each subfigure gets its own \caption{(a) ...}. Preferred over raw \includegraphics side-by-side when panels need individual captions. Max 2 subfigures per slide (4 panels = split across 2 slides).

pgfplots for data-driven figures (preferred over manual TikZ for data):

Use pgfplots whenever plotting numerical data. It handles axes, legends, scaling, and data loading automatically.

% Bar chart from inline data
\begin{tikzpicture}
\begin{axis}[
  ybar, bar width=12pt,
  xlabel={Method}, ylabel={Accuracy (\%)},
  symbolic x coords={Baseline, Ours, Oracle},
  xtick=data, ymin=0, ymax=100,
  nodes near coords, every node near coord/.append style={font=\small},
  width=0.85\textwidth, height=5cm
]
  \addplot coordinates {(Baseline,72) (Ours,89) (Oracle,95)};
\end{axis}
\end{tikzpicture}

% Line plot from CSV file
\begin{tikzpicture}
\begin{axis}[
  xlabel={Epoch}, ylabel={Loss},
  legend pos=north east, grid=major,
  width=0.85\textwidth, height=5cm
]
  \addplot table[x=epoch, y=train_loss, col sep=comma] {data/results.csv};
  \addplot table[x=epoch, y=val_loss, col sep=comma] {data/results.csv};
  \legend{Train, Validation}
\end{axis}
\end{tikzpicture}

% Scatter plot with error bars
\begin{axis}[xlabel={$x$}, ylabel={$y$}]
  \addplot+[only marks, error bars/.cd, y dir=both, y explicit]
    coordinates {(1,2)+-(0,0.3) (2,3.5)+-(0,0.5) (3,5.1)+-(0,0.4)};
\end{axis}

• Always set explicit width and height to prevent overflow.
• Use \addplot table[col sep=comma]{file.csv} to load data from file — keeps .tex clean.
• For presentation: enlarge tick labels (tick label style={font=\small}), thicken lines (thick), use semantic colors (color=positive).

Phase 5: Quality Loop (MANDATORY — iterative)

After completing the full draft, enter the quality loop:

┌─→ 5a. Compile (2-pass XeLaTeX)
│   5b. Self-Review (structure + content + visual)
│   5c. Score (apply rubric)
│   5d. Fix all issues found
└── If score < 90 and round < 3: loop back to 5a
    If score ≥ 90 or round = 3: report to user

5a. Compilation

• 2-pass XeLaTeX compilation (bibtex not needed here — already resolved in Phase 3 batch compiles)
• Check: errors, overfull hbox, undefined references
• Open PDF for visual inspection

5b. Self-Review — re-read the .tex and verify:

Structure:

• Slide count matches plan (±2 tolerance)
• Logical flow: motivation → background → technique → results → summary
• No section has >4 consecutive formal slides without a worked example or visual break
• Transition sentences between major sections

Content density:

• No slide has only ≤3 short bullets with no math/diagram
• Pure text-only slides ≤ 30% of deck
• No slide exceeds upper bounds (7 bullets, 2 equations, 5 symbols, 2 boxes)

TikZ and visuals:

• No label-label or label-curve overlaps
• No content overflowing slide boundary
• No content overflowing inside colored boxes (alertblock/exampleblock/block have ~85% effective width; visually verify every box in PDF)
• TikZ diagram fits within remaining slide space — for mixed slides (text + diagram), verify the diagram's bounding box height + text height ≤ ~70mm. Common failure: large TikZ scale + multiple equations above = diagram clipped at bottom
• All marked points lie on their curves — for every \fill, \node, or \draw endpoint that should be on a plotted curve, verify the y-coordinate is computed via \pgfmathsetmacro from the same function, NOT hardcoded. Visually check in PDF that dots/markers visually sit on the curve line
• Dashed reference lines terminate at the curve — vertical/horizontal guide lines should end exactly where they meet the curve, not at arbitrary y-values
• Tables fit within slide width
• All standalone tables are centered (\begin{center}...\end{center})
• No table's \toprule visually merges with the title bar (add \vspace{4pt} or text before first table)
• Font sizes in TikZ ≥ \footnotesize
• Consistent styling across all diagrams

Notation:

• Same symbol used consistently throughout
• Every symbol defined before use

5c. Quality Score

Start at 100. Deduct:

Severity	Issue	Deduction
Critical	Compilation failure	-100
Critical	Equation overflow (slide or box-interior)	-20
Critical	TikZ diagram overflows slide boundary (clipped at bottom/right)	-15 per diagram
Critical	Undefined control sequence / citation	-15
Critical	Overfull hbox > 10pt	-10
Major	Content overflow inside colored box (vertical or horizontal, visual-only)	-10 per box
Major	TikZ marked points not on curve (hardcoded y-values instead of computed)	-8 per diagram
Major	Sparse slide (≤3 items, no math/diagram)	-5 per slide
Major	TikZ label overlap	-5
Major	Missing references slide	-5
Major	Table not centered (standalone table without \begin{center})	-3 per table
Major	Table \toprule visually merged with title bar (no spacing after frame title)	-5 per slide
Major	Notation inconsistency	-3
Minor	\vspace overuse (>3 per slide)	-1
Minor	Font size reduction (\footnotesize etc.)	-1 per slide

Thresholds:

• ≥ 90: Ready to deliver. Report to user.
• 80-89: Acceptable. Fix remaining majors if possible, report with caveats.
• < 80: Must fix. Loop back and resolve critical/major issues.

5d. Fix — fix all critical and major issues. Re-compile. If score improves to ≥ 90, exit loop. Max 3 rounds to avoid infinite loops.

Post-Creation Checklist (final gate)

[ ] Compiles without errors
[ ] No overfull hbox > 10pt
[ ] All citations resolve
[ ] Score ≥ 90
[ ] Every definition has motivation + worked example
[ ] Max 2 colored boxes per slide
[ ] No sparse slides (all slides have substantive content)
[ ] TikZ diagrams visually verified — no overlaps, no overflow, all marked points on curves
[ ] Tables fit within slide boundaries, are centered, and separated from title bar
[ ] No content overflow inside colored boxes (visual PDF check)
[ ] References slide present (second-to-last, before Thank You)

2.3 review [file] or proofread [file]

Read-only report, no file edits.

5 check categories:

Category	What to check
Grammar	Subject-verb, articles, prepositions, tense consistency
Typos	Misspellings, search-replace artifacts, duplicated words, unreplaced placeholders ([name], [TODO], [XXX], template remnants)
Overflow	Long equations without \resizebox, too many items per slide
Consistency	Citation format (\citet/\citep), notation, terminology, box usage, denominator consistency across slides
Academic quality	Informal abbreviations, missing words, claims without citations, ambiguous abbreviations (same abbreviation for different terms)

Report format per issue:

### Issue N: [Brief description]
- **Location:** [slide title or line number]
- **Current:** "[exact text]"
- **Proposed:** "[fix]"
- **Category / Severity:** [Category] / [High|Medium|Low]

2.4 audit [file]

Visual layout audit. Read-only report.

Check dimensions:

• Overflow: Content exceeding boundaries, wide tables/equations
• Font consistency: Inline size overrides, inconsistent sizes
• Box fatigue: 2+ boxes per slide, wrong box types
• Spacing: \vspace overuse, structural issues
• Layout: Missing transitions, missing framing sentences

Spacing-first fix principle (priority order):

1. Reduce vertical spacing (structural changes)
2. Consolidate lists
3. Move displayed equations inline
4. Reduce image/table size with \resizebox
5. Last resort: \footnotesize (never \tiny)

2.5 pedagogy [file]

Holistic pedagogical review. Read-only report.

13 patterns to validate:

#	Pattern	Red flag
1	Motivation before formalism	Definition without context
2	Incremental notation	5+ new symbols on one slide
3	Worked example after definition	2 consecutive definitions, no example
4	Progressive complexity	Advanced concept before prerequisite
5	Fragment reveals (problem→solution)	Dense theorem revealed all at once
6	Standout slides at pivots	Abrupt topic jump, no transition
7	Two-slide strategy for dense theorems	Complex theorem crammed in 1 slide
8	Semantic color usage	Binary contrasts in same color
9	Box hierarchy	Wrong box type for content
10	Box fatigue	3+ boxes on one slide
11	Socratic embedding	Zero questions in entire deck
12	Visual-first for complex concepts	Notation before visualization
13	Side-by-side for comparisons	Sequential slides for related definitions

Deck-level checks: Narrative arc, pacing (max 3-4 theory slides before example), visual rhythm (section dividers every 5-8 slides), notation consistency, student prerequisite assumptions.

2.6 tikz [file]

TikZ diagram review and extraction.

Quality standards:

• Labels NEVER overlap with curves, lines, dots, or other labels

• When two labels are near the same vertical position, stagger them

• Visual semantics: solid=observed, dashed=counterfactual, filled=observed, hollow=counterfactual

• Line weights: axes=thick, data=thick, annotations=thick (not very thick)

• Standard scale: [scale=1.1] for full-width diagrams

• Dot radius: 4pt for data points

• Minimum 0.2 units between any label and nearest graphical element

• Mathematical accuracy of plotted points: NEVER hardcode y-coordinates for points, markers, or dashed-line endpoints that should lie on a plotted curve. ALL such coordinates must be computed from the SAME function used to draw the curve via \pgfmathsetmacro. This applies to:

  • Points marked on a single curve (e.g., labeled special values like "BiPerm at ℓ=2")
  • Dashed vertical/horizontal lines that terminate at a curve
  • Intersections of two curves
  • Any annotation anchored to a curve position

  Common mistake (WRONG — hardcoded y that doesn't match the curve):

  \draw[thick] plot[domain=0.8:10] (\x, {0.3*\x + 2.7/\x});
  \draw[dashed] (2, 0) -- (2, 3.2);  % BAD: 3.2 is not 0.3*2+2.7/2=1.95
  \node at (2, 3.2) {BiPerm};         % BAD: label floats above the curve
  

  Correct pattern (ALWAYS compute from the function):

  \draw[thick] plot[domain=0.8:10] (\x, {0.3*\x + 2.7/\x});
  \pgfmathsetmacro{\yTwo}{0.3*2 + 2.7/2}  % = 1.95, exactly on curve
  \draw[dashed] (2, 0) -- (2, \yTwo);
  \fill (2, \yTwo) circle (2pt);
  \node[above left] at (2, \yTwo) {BiPerm};
  

  For curve intersections, solve the system algebraically first, then encode the exact formula:

  % Intersection of y=0.5x and y=2.5/x+0.3:
  % 0.5x = 2.5/x + 0.3 => x^2 - 0.6x - 5 = 0 => x = (0.6+sqrt(20.36))/2
  \pgfmathsetmacro{\xint}{(0.6 + sqrt(20.36))/2}
  \pgfmathsetmacro{\yint}{0.5*\xint}
  \fill (\xint, \yint) circle (3pt);
  

• TikZ diagram sizing on mixed-content slides: a TikZ diagram sharing a slide with text/equations MUST fit in the remaining vertical space. Beamer 16:9 at 10pt has ~70mm usable height below the title bar. Before writing the TikZ code, estimate:

  1. Text + equations above the diagram: count displayed equations (each ~12-15mm) + text lines (~5mm each) + spacing
  2. Remaining height = 70mm − text height
  3. TikZ bounding box height = (max y-coordinate − min y-coordinate) × yscale × 0.3528mm/pt
  4. If the diagram won't fit: reduce yscale, shrink coordinate ranges, or move content to a separate slide

  Safe defaults for mixed slides: xscale=0.5-0.7, yscale=0.4-0.6. For full-slide diagrams: scale=0.9-1.1.

• Edge labels on short arrows: when placing node[midway, above] labels on arrows between boxes, the label text can extend past the arrow endpoints into adjacent box borders. Prevention rules:

  1. Estimate label text width vs. arrow length (right= gap). If the label is wider than ~80% of the gap, increase the gap or shrink the label font (\scriptsize / \tiny).
  2. Use above=4pt (or more) instead of bare above to add vertical clearance between label and box border.
  3. For flow diagrams with 3+ boxes: total width = (N × box width) + ((N-1) × gap). Must stay ≤ 14cm for 16:9 beamer. Adjust box text width and gap together.
  4. When in doubt, compile and visually verify that no label overlaps any box border.

Extraction to SVG (for web/Quarto use):

xelatex -interaction=nonstopmode extract_tikz.tex
PAGES=$(pdfinfo extract_tikz.pdf | grep "Pages:" | awk '{print $2}')
for i in $(seq 1 $PAGES); do
  idx=$(printf "%02d" $((i-1)))
  pdf2svg extract_tikz.pdf tikz_exact_$idx.svg $i
done

TikZ checklist:

[ ] No label-label overlaps
[ ] No label-curve overlaps
[ ] No edge labels overlapping adjacent nodes (check label width vs. arrow length)
[ ] Diagram bounding box fits within remaining slide space (especially mixed text+diagram slides)
[ ] ALL marked points/dots/line-endpoints on curves computed via \pgfmathsetmacro from the SAME function — no hardcoded y-values
[ ] Dashed reference lines terminate exactly at the curve, not at arbitrary coordinates
[ ] Consistent dot style (solid=observed, hollow=counterfactual)
[ ] Consistent line style (solid=observed, dashed=counterfactual)
[ ] Arrow annotations: FROM label TO feature
[ ] Axes extend beyond all data points
[ ] Labels legible at presentation size
[ ] Minimum spacing between labels and graphical elements

Common TikZ diagram patterns:

Use these as starting points, then customize. All patterns assume arrows.meta, positioning, decorations.pathreplacing libraries are loaded (included in default preamble).

Flowchart (horizontal):

\begin{tikzpicture}[
  box/.style={draw, rounded corners, minimum width=2.2cm, minimum height=0.8cm,
              font=\small, fill=positive!10},
  arr/.style={-{Stealth}, thick}
]
  \node[box] (A) {Step 1};
  \node[box, right=1.5cm of A] (B) {Step 2};
  \node[box, right=1.5cm of B] (C) {Step 3};
  \draw[arr] (A) -- node[above, font=\scriptsize] {label} (B);
  \draw[arr] (B) -- (C);
\end{tikzpicture}

• Total width ≤ 14cm for 16:9. Formula: N × box_width + (N-1) × gap.
• For vertical flows: use below= instead of right=.

Timeline:

\begin{tikzpicture}
  \draw[-{Stealth}, thick] (0,0) -- (12,0) node[right] {Time};
  \foreach \x/\lab in {1.5/Event A, 5/Event B, 9/Event C} {
    \draw[thick] (\x, 0.15) -- (\x, -0.15);
    \node[above=3pt, font=\small] at (\x, 0.15) {\lab};
  }
\end{tikzpicture}

Tree diagram:

\begin{tikzpicture}[
  level distance=1.2cm, sibling distance=2.5cm,
  every node/.style={draw, rounded corners, font=\small, minimum width=1.5cm}
]
  \node {Root}
    child { node {A} child { node {A1} } child { node {A2} } }
    child { node {B} child { node {B1} } };
\end{tikzpicture}

Annotated brace:

\draw[decorate, decoration={brace, amplitude=6pt, raise=2pt}]
  (start) -- (end) node[midway, above=10pt, font=\small] {annotation};

Coordinate plot with computed intersection:

\begin{tikzpicture}[scale=1.1]
  \draw[-{Stealth}, thick] (0,0) -- (6,0) node[right] {$x$};
  \draw[-{Stealth}, thick] (0,0) -- (0,4) node[above] {$y$};
  \draw[thick, positive] plot[smooth, domain=0.5:5.5] (\x, {0.5*\x});
  \draw[thick, negative, dashed] plot[smooth, domain=0.5:5.5] (\x, {2.5/\x + 0.3});
  % Exact intersection via \pgfmathsetmacro (see quality standards above)
\end{tikzpicture}

Decision diamond (for algorithm flowcharts):

\node[diamond, draw, aspect=2, inner sep=1pt, font=\small] (D) {condition?};
\draw[arr] (D) -- node[right, font=\scriptsize] {yes} ++(0,-1.2);
\draw[arr] (D) -- node[above, font=\scriptsize] {no} ++(2.5,0);

Iterative TikZ review loop (for complex diagrams):

When a TikZ diagram has ≥ 5 nodes or involves plotted curves, run an iterative review:

┌─→ Step 1: Mentally render — trace every coordinate, compute where each element appears
│   Step 2: Check for issues — overlaps, misalignments, inconsistent semantics
│   Step 3: Classify — CRITICAL (overlap, wrong semantics, geometric error),
│                       MAJOR (poor spacing, readability), MINOR (aesthetic)
│   Step 4: Fix all CRITICAL and MAJOR issues
│   Step 5: Re-compile and visually verify in PDF
└── If CRITICAL or MAJOR remain and round < 3: loop back to Step 1
    If all clear or round = 3: declare APPROVED or report remaining issues

Verdict criteria:

• APPROVED: Zero CRITICAL, zero MAJOR → diagram is complete
• NEEDS REVISION: CRITICAL or MAJOR issues remain → list exact fixes needed
• REJECTED: Fundamental structural problems → consider redesigning the diagram

2.7 excellence [file]

Comprehensive multi-dimensional review. Use the Agent tool to dispatch review agents in parallel for maximum efficiency.

Parallel agent dispatch — launch these as concurrent Agent calls:

1. Visual audit agent — "Read [file]. Check every slide for: overflow, font consistency, box fatigue (2+ boxes), spacing issues, missing transitions. Report per slide with severity. Follow spacing-first fix principle."
2. Pedagogical review agent — "Read [file]. Validate 13 pedagogical patterns (motivation before formalism, incremental notation, worked examples, etc.) and deck-level checks (narrative arc, pacing, visual rhythm, notation consistency). Report pattern-by-pattern with status."
3. Proofreading agent — "Read [file]. Check grammar, typos, citation consistency (\citet/\citep), notation consistency, academic quality. Report per issue with location and fix."
4. TikZ review agent (if file contains \begin{tikzpicture}) — "Read [file]. For every TikZ diagram: check label overlaps, geometric accuracy, visual semantics, spacing. Be merciless — find every flaw. Report per issue with exact coordinates and fixes."
5. Domain review agent (optional) — "Read [file]. Verify substantive correctness: assumptions, derivations, citation fidelity."

After all agents return, synthesize a combined report:

# Slide Excellence Review: [Filename]

## Overall Quality Score: [EXCELLENT / GOOD / NEEDS WORK / POOR]

| Dimension | Critical | Major | Minor |
|-----------|----------|-------|-------|
| Visual/Layout | | | |
| Pedagogical | | | |
| Proofreading | | | |
| TikZ (if any) | | | |

### Critical Issues (Immediate Action Required)
### Major Issues (Next Revision)
### Recommended Next Steps

Quality score rubric (for multi-agent excellence review — complements the numeric score in Phase 5 which is used during create):

Score	Critical issues	Medium issues	Meaning
Excellent	0-2	0-5	Ready to present (≈ Phase 5 score ≥ 90)
Good	3-5	6-15	Minor refinements (≈ Phase 5 score 80-89)
Needs Work	6-10	16-30	Significant revision (≈ Phase 5 score < 80)
Poor	11+	31+	Major restructuring

2.8 devils-advocate [file]

Challenge slide design with 5-7 specific pedagogical questions.

Challenge categories:

1. Ordering — "Could students understand better if X before Y?"
2. Prerequisites — "Do students have the background for this?"
3. Gaps — "Should we include an intuitive example here?"
4. Alternative presentations — "2 other ways to present this concept"
5. Notation conflicts — "This symbol conflicts with earlier usage"
6. Cognitive load — "Too many new symbols on this slide"
7. Standalone readability — "Does this section stand alone as a book chapter?"

2.9 visual-check [file]

PDF→image systematic visual review. Converts compiled PDF to images, then reviews each slide visually. This catches issues invisible in source code and suppressed by the compiler (especially box-interior overflow).

Why this matters: Beamer suppresses overfull warnings inside block/alertblock/exampleblock environments. Zero compile warnings does NOT mean zero visual overflow. This action provides ground truth.

Workflow:

1. Compile (if not already compiled):

   xelatex -interaction=nonstopmode FILE.tex
   

2. Convert PDF to images using PyMuPDF:

   import fitz
   doc = fitz.open('FILE.pdf')
   n = doc.page_count          # cache before iterating or closing
   zoom = 200 / 72  # 200 DPI
   matrix = fitz.Matrix(zoom, zoom)
   for i in range(n):
       page = doc.load_page(i)
       pixmap = page.get_pixmap(matrix=matrix)
       pixmap.save(f'/tmp/slide-{i+1:03d}.jpg', output='jpeg')
   doc.close()
   print(f'Exported {n} slides')
   

   Or via bash: python3 -c "import fitz; ..."

   Fallback (if PyMuPDF unavailable): Use the Read tool directly on the PDF — Claude Code is multimodal and can read PDF files page by page.

3. Systematic per-slide inspection — use Read tool to view each image, checking:

   • No text overflow at any edge (top, bottom, left, right)
   • No content overflowing inside colored boxes (check every alertblock/exampleblock/block)
   • All text legible (no text smaller than readable at presentation distance)
   • Tables and equations fit within slide width
   • TikZ labels not overlapping with lines, dots, or other labels
   • Consistent font sizes across similar slide types
   • Adequate contrast between text and background
   • No visual clutter (too many elements competing for attention)

4. Report per issue:

   ### Slide N: [slide title]
   - **Issue:** [description]
   - **Severity:** Critical / Major / Minor
   - **Fix:** [specific recommendation]
   

2.10 validate [file] [duration]

Automated quantitative validation. Checks measurable properties without reading content.

Checks performed:

1. Slide count vs. duration (if duration provided):

   # Get page count
   pdfinfo FILE.pdf | grep "Pages:"
   

   Compare against timing allocation table (Section 2.2, Phase 1). Flag if outside recommended range.

2. Aspect ratio:

   pdfinfo FILE.pdf | grep "Page size:"
   

   Expected: 364.19 x 272.65 pts (16:9 at 10pt) or similar 16:9 ratio. Flag if 4:3 (old projector format).

3. File size:

   • > 50 MB: warning (slow to share/email)
   • > 100 MB: critical (likely uncompressed images)

4. Compilation health (from .log file):

   grep -c "Overfull \\\\hbox" FILE.log
   grep -c "Undefined control sequence" FILE.log
   grep -c "Citation.*undefined" FILE.log
   grep -c "multiply defined" FILE.log
   

5. Source code static checks (from .tex file):

   • Count \pause / \onslide / \only usage → must be 0 (Hard Rule 1)
   • Count slides with >2 colored boxes → flag violations (Hard Rule 2)
   • Count \tiny usage → must be 0 (Hard Rule 13)
   • Check for \begin{thebibliography} → warn if missing (Hard Rule 11)

Report format:

# Validation Report: [Filename]

| Check | Result | Status |
|-------|--------|--------|
| Slide count | N slides / Xmin duration | OK / WARNING |
| Aspect ratio | 16:9 | OK |
| File size | X.X MB | OK / WARNING |
| Overfull hbox | N warnings | OK / CRITICAL |
| Undefined references | N | OK / CRITICAL |
| Overlay commands | N found | OK / VIOLATION |
| Box fatigue violations | N slides | OK / WARNING |
| References slide | Present / Missing | OK / WARNING |

Overall: PASS / PASS WITH WARNINGS / FAIL

2.11 extract-figures [pdf] [pages]

Extract figures from a paper PDF and prepare them for inclusion in Beamer slides.

Use when the user wants to reuse figures from an existing paper (their own or a cited work) instead of redrawing in TikZ.

Workflow

1. Identify target figures — if user doesn't specify pages, use mcp__pdf-mcp__pdf_get_toc and mcp__pdf-mcp__pdf_read_pages to locate figures in the paper. Ask user which figures to extract if ambiguous.

2. Extract images from specified pages:

   mcp__pdf-mcp__pdf_extract_images(path=PDF_PATH, pages=PAGES, output_dir="figures")
   

   Uses output_dir to save images directly to figures/ as PNG files (original resolution, zero token cost). Returns {page, index, width, height, format, file_path} metadata only — no base64 data.

3. Rename to descriptive names following the naming convention:

   mv figures/page3_img0.png figures/fig-LABEL.png
   

   Naming convention: fig-<descriptive-label>.png (e.g., fig-architecture.png, fig-results-table.png).

4. Generate LaTeX snippet — output ready-to-paste code:

   Full-width figure:

   \begin{frame}{Frame Title}
     \begin{center}
       \includegraphics[width=0.85\textwidth]{figures/fig-LABEL.png}
     \end{center}
     \vspace{-6pt}
     {\small Source: \citet{author2024paper}}
   \end{frame}
   

   Figure + text side-by-side (columns layout):

   \begin{frame}{Frame Title}
     \begin{columns}[T]
       \column{0.50\textwidth}
         \includegraphics[width=\textwidth]{figures/fig-LABEL.png}
         {\small Source: \citet{author2024paper}}
       \column{0.45\textwidth}
         Key observations:
         \begin{itemize}
           \item Point 1
           \item Point 2
         \end{itemize}
     \end{columns}
   \end{frame}
   

   Two figures side-by-side (subfigure):

   \begin{frame}{Frame Title}
     \begin{figure}
       \begin{subfigure}{0.48\textwidth}
         \includegraphics[width=\textwidth]{figures/fig-LEFT.png}
         \caption{(a) Description}
       \end{subfigure}\hfill
       \begin{subfigure}{0.48\textwidth}
         \includegraphics[width=\textwidth]{figures/fig-RIGHT.png}
         \caption{(b) Description}
       \end{subfigure}
     \end{figure}
   \end{frame}
   

5. Cropping guidance — if the extracted image contains surrounding text or margins that should be removed, use the trim and clip options:

   \includegraphics[width=0.85\textwidth, trim=LEFT BOTTOM RIGHT TOP, clip]{figures/fig-LABEL.png}
   

   • Units are in bp (big points). Estimate from the image dimensions returned by pdf_extract_images.
   • Common case: trim=50 200 50 100, clip to remove page margins and surrounding text.
   • Always visually verify after compilation — cropping coordinates are estimates.

Rules

• Always attribute — include {\small Source: ...} below every extracted figure unless it's the user's own paper.
• Prefer vector — if only a single clean figure is on a page, extraction quality is usually sufficient. For complex multi-figure pages, consider redrawing the key figure in TikZ for better quality and consistency.
• Resolution check — if extracted image width < 800px, warn the user that it may appear pixelated on a projector. Suggest either finding a higher-resolution source or redrawing in TikZ.
• Don't extract tables — tables from PDF rasterize poorly. Always recreate tables in LaTeX using booktabs.
• Preamble dependency — ensure \usepackage{graphicx} is in the preamble (add if missing). If using subfigures, also ensure \usepackage{subcaption}.

2.12 from-report [json_file]

Generate a reproduction report Beamer presentation from result-analyzer output.

This action directly consumes beamer_report_data.json to auto-generate a complete Beamer .tex file.

Usage:

# Generate .tex from result-analyzer JSON
python beamer-skill/generate_beamer_report.py beamer_report_data.json -o reproduction_slides.tex

# Generate and compile to PDF
python beamer-skill/generate_beamer_report.py beamer_report_data.json -o slides.tex --compile

Integration flow:

result-analyzer (--beamer flag)
    ↓ outputs beamer_report_data.json
beamer-skill/generate_beamer_report.py
    ↓ reads JSON, generates .tex
reproduction_slides.tex → XeLaTeX → reproduction_slides.pdf

Generated slides:

1. Title slide — paper name + overall Pass/Fail status
2. Metric comparison table — color-coded (green=PASS, orange=WARN, red=FAIL)
3. Training curves — embedded figure (if plot exists)
4. Sample comparison — side-by-side figures (if generated)
5. Conclusion — overall status + score
6. Thank You — courtesy slide

Customization: After generation, you can manually edit the .tex or use other beamer-skill actions (review, audit, excellence) to polish the auto-generated slides.

---

3. VERIFICATION PROTOCOL

Every task ends with verification. Non-negotiable.

[ ] Compiled without errors (xelatex exit code 0)
[ ] No overfull hbox > 10pt
[ ] All citations resolve
[ ] PDF opens and renders correctly
[ ] Visual spot-check of modified slides

---

4. DOMAIN REVIEW (Template)

For substantive correctness (not presentation), review through 5 lenses:

1. Assumption stress test — all assumptions stated, sufficient, necessary?
2. Derivation verification — each step follows? Decomposition sums to whole?
3. Citation fidelity — slide accurately represents cited paper?
4. Code-theory alignment — code implements exact formula from slides?
5. Backward logic check — read conclusion→setup, every claim supported?

Severity: CRITICAL = math wrong. MAJOR = missing assumption. MINOR = could be clearer.

---

5. TROUBLESHOOTING

Error: ! Undefined control sequence. \llbracket Cause: Missing stmaryrd package for double brackets. Fix: Add \usepackage{stmaryrd} to preamble. Or define \newcommand{\llbracket}{[\![} as fallback.

Error: Overfull \vbox on a specific slide Cause: Too much content for the frame height. Fix priority:

1. Reduce \vspace values
2. Shorten text (telegraphic style)
3. Split into two slides
4. Use \small on one element (not the whole slide)
5. Last resort: \footnotesize (never \tiny)

Error: Font "XXX" not found with XeLaTeX Cause: System font not installed, or wrong font name. Fix: Use fc-list | grep "FontName" to check available fonts. Fall back to default Latin Modern if custom font unavailable.

Error: Equations overflow slide width Cause: Long multi-term equation. Fix priority:

1. Use \begin{align} with line breaks at natural points (=, +)
2. Introduce intermediate variables to shorten expressions
3. Use \resizebox{\textwidth}{!}{...} as last resort (degrades readability)

Error: PDF images don't render in Quarto/web Cause: Browsers cannot display PDF inline. Fix: Convert to SVG: pdf2svg input.pdf output.svg. Never use PNG for diagrams (raster = blurry).

Error: Content visually overflows inside alertblock/exampleblock/block but compiler reports 0 warnings Cause: Beamer suppresses overflow warnings inside block environments. Two distinct failure modes:

• Vertical: display math + text below it exceeds the box's vertical capacity; bottom content spills past the lower border. Aggravated by \vspace{-Xpt}.
• Horizontal: the block's internal padding reduces effective width by ~15%, so wide equations overflow sideways. Fix priority (vertical — most common):

1. Remove or reduce \vspace{-Xpt} inside the box
2. Keep box content minimal: one display equation OR a few bullet items, not both
3. Move explanatory text below the equation to outside the box (plain text after \end{...block})
4. Split into two separate boxes or slides Fix priority (horizontal):
5. Replace \qquad with \quad or ,
6. Move secondary notation (e.g., sampling arrows) to a separate line
7. Break the equation with \\ at natural points
8. Move the equation outside the box Never rely on compile warnings alone — always visually verify every colored box in the PDF.