| % common.sty -- single style for all 24 notes (series 01xx, 02xx, 03xx). |
| % Replaces common-m1/-m2/-m3 (kept as thin shims for old build logs; see STYLE_ALIGNMENT.md). |
| \ProvidesPackage{common} |
| \RequirePackage[margin=2.2cm]{geometry} |
| \RequirePackage[utf8]{inputenc} |
| \RequirePackage[T1]{fontenc} |
| \RequirePackage{amsmath,amssymb,amsthm,mathtools,bm} |
| \RequirePackage{booktabs,array,enumitem,longtable} |
| \RequirePackage[dvipsnames]{xcolor} |
| \RequirePackage[most]{tcolorbox} |
| \RequirePackage{listings} |
| \RequirePackage[hidelinks]{hyperref} |
| \RequirePackage{microtype} |
| \newcolumntype{P}[1]{>{\raggedright\arraybackslash}p{#1}} |
| \setlength{\emergencystretch}{3em} |
| \setlength{\parindent}{0pt} |
| \setlength{\parskip}{0.55em} |
| \setlist{itemsep=2pt,topsep=3pt} |
| \renewcommand{\arraystretch}{1.15} |
| % ---- theorem-like environments ------------------------------------------ |
| \newtheorem{lemma}{Lemma} |
| \newtheorem{proposition}{Proposition} |
| \newtheorem{theorem}{Theorem} |
| \theoremstyle{definition} |
| \newtheorem{definition}{Definition} |
| \newtheorem{example}{Example} |
| \theoremstyle{remark} |
| \newtheorem*{remark}{Remark} |
| % ---- the house skeleton: problem -> notation -> derivation -> result -> what breaks -> next |
| \newtcolorbox{problem}{colback=gray!6,colframe=gray!60,title={The problem}, |
| fonttitle=\bfseries\small,boxrule=0.5pt,arc=1pt} |
| \newcommand{\question}[1]{\textbf{The question.} #1\par\smallskip} |
| \newtcolorbox{result}[1][Boxed result]{colback=Cerulean!6,colframe=Cerulean!70!black, |
| boxrule=0.9pt,arc=2pt,title={#1},fonttitle=\bfseries\small} |
| \newtcolorbox{breaks}[1][]{colback=BrickRed!5,colframe=BrickRed!70!black, |
| boxrule=0.6pt,arc=2pt,title={Failure modes and the assumption each one violates}, |
| fonttitle=\bfseries\small,#1} |
| \newcommand{\nextnote}[1]{\begin{tcolorbox}[colback=blue!4,colframe=blue!50!black, |
| title={Next},fonttitle=\bfseries\small,boxrule=0.5pt,arc=1pt]#1\end{tcolorbox}} |
| \newcommand{\notehead}[3]{% |
| {\raggedright\Large\bfseries Note #1 \,--\, #2}\\[2pt] |
| {\raggedright\small\itshape #3\par}\vspace{2pt}\hrule\vspace{4pt}} |
| \newcommand{\nbref}[1]{\texttt{notebooks/#1}} |
| \newcommand{\ver}[1]{\textcolor{green!40!black}{\small[\textsf{verified}: #1]}} |
| % ---- shared notation ------------------------------------------------------ |
| \DeclareMathOperator*{\argmax}{arg\,max} |
| \DeclareMathOperator*{\argmin}{arg\,min} |
| \DeclareMathOperator{\Var}{Var} |
| \DeclareMathOperator{\Cov}{Cov} |
| \DeclareMathOperator{\Bern}{Bern} |
| \DeclareMathOperator{\Bin}{Bin} |
| \DeclareMathOperator{\KL}{KL} |
| \DeclareMathOperator{\clip}{clip} |
| \DeclareMathOperator{\sg}{sg} |
| \DeclareMathOperator{\TV}{TV} |
| \DeclareMathOperator{\FV}{FV} |
| \DeclareMathOperator{\imax}{imax} |
| \newcommand{\ESS}{\mathrm{ESS}} |
| \newcommand{\E}{\mathbb{E}} |
| \renewcommand{\Pr}{\mathbb{P}} |
| \newcommand{\R}{\mathbb{R}} |
| \newcommand{\N}{\mathbb{N}} |
| \newcommand{\Z}{\mathbb{Z}} |
| \newcommand{\ind}{\mathbb{1}} % bare indicator symbol (02xx notes) |
| \newcommand{\indb}[1]{\mathbb{1}\!\left[#1\right]} % bracketed indicator (01xx notes) |
| \newcommand{\pa}{\pi_\theta} |
| \newcommand{\pth}{\pi_\theta} |
| \newcommand{\pold}{\pi_{\theta_{\mathrm{old}}}} |
| \newcommand{\score}{\nabla_\theta\log\pi_\theta} |
| \newcommand{\given}{\,\middle|\,} |
| \newcommand{\pk}{\mathrm{pass@}k} |
| \newcommand{\hatpk}{\widehat{\mathrm{pass@}k}} |
| % ---- formal-methods notation and Lean listings (03xx notes) --------------- |
| \newcommand{\Prop}{\mathsf{Prop}} |
| \newcommand{\Type}{\mathsf{Type}} |
| \newcommand{\Sort}{\mathsf{Sort}} |
| \newcommand{\bool}{\mathsf{Bool}} |
| \newcommand{\wpc}{\mathrm{wp}} |
| \newcommand{\hoare}[3]{\{#1\}\;#2\;\{#3\}} |
| \newcommand{\sem}[1]{[\![#1]\!]} |
| \newcommand{\lean}[1]{\texttt{#1}} |
| % Lean listings (unicode-safe: declare the few glyphs we use) |
| \lstdefinelanguage{Lean}{ |
| morekeywords={theorem,lemma,def,example,by,fun,match,with,if,then,else,let,in, |
| fun,intro,exact,apply,induction,cases,simp,omega,decide,rfl,have,show,from, |
| inductive,structure,class,instance,where,open,import,namespace,axiom,partial, |
| termination_by,decreasing_by,at,using,rw,unfold,split,rcases,obtain}, |
| sensitive=true, morecomment=[l]{--}, morestring=[b]"} |
| \lstset{language=Lean,basicstyle=\ttfamily\footnotesize,breaklines=true, |
| columns=fullflexible,keepspaces=true,frame=single,rulecolor=\color{black!25}, |
| keywordstyle=\color{Blue}\bfseries,commentstyle=\color{OliveGreen}\itshape, |
| xleftmargin=0.5em,xrightmargin=0.5em,aboveskip=0.4em,belowskip=0.2em, |
| literate={→}{{$\to$}}1 {←}{{$\leftarrow$}}1 {↔}{{$\leftrightarrow$}}1 |
| {∀}{{$\forall$}}1 {∃}{{$\exists$}}1 {¬}{{$\neg$}}1 {∧}{{$\wedge$}}1 {∨}{{$\vee$}}1 |
| {≤}{{$\le$}}1 {≥}{{$\ge$}}1 {≠}{{$\ne$}}1 {ℕ}{{$\mathbb{N}$}}1 {ℤ}{{$\mathbb{Z}$}}1 |
| {ℝ}{{$\mathbb{R}$}}1 {λ}{{$\lambda$}}1 {⟨}{{$\langle$}}1 {⟩}{{$\rangle$}}1 |
| {α}{{$\alpha$}}1 {β}{{$\beta$}}1 {σ}{{$\sigma$}}1 {₀}{{$_0$}}1 {₁}{{$_1$}}1 |
| {₂}{{$_2$}}1 {₃}{{$_3$}}1 {∑}{{$\sum$}}1 {∣}{{$\mid$}}1 {×}{{$\times$}}1 |
| {⊥}{{$\bot$}}1 {∈}{{$\in$}}1 {∘}{{$\circ$}}1 {↑}{{$\uparrow$}}1 {·}{{$\cdot$}}1 |
| {≡}{{$\equiv$}}1 {⊢}{{$\vdash$}}1 {∅}{{$\emptyset$}}1 {∩}{{$\cap$}}1 {π}{{$\pi$}}1 |
| {⁻}{{$^-$}}1 {¹}{{$^1$}}1 {²}{{$^2$}}1 {ι}{{$\iota$}}1 {τ}{{$\tau$}}1 {Σ}{{$\Sigma$}}1 {Π}{{$\Pi$}}1 {⇒}{{$\Rightarrow$}}1 {⟹}{{$\Longrightarrow$}}1 {▸}{{$\triangleright$}}1 {⁅}{{[}}1 {≈}{{$\approx$}}1 {∘}{{$\circ$}}1} |
| % unicode that may appear in running text / \texttt |
| \DeclareUnicodeCharacter{2264}{\ensuremath{\le}} |
| \DeclareUnicodeCharacter{2265}{\ensuremath{\ge}} |
| \DeclareUnicodeCharacter{2260}{\ensuremath{\ne}} |
| \DeclareUnicodeCharacter{2115}{\ensuremath{\mathbb{N}}} |
| \DeclareUnicodeCharacter{2124}{\ensuremath{\mathbb{Z}}} |
| \DeclareUnicodeCharacter{211D}{\ensuremath{\mathbb{R}}} |
| \DeclareUnicodeCharacter{2080}{\ensuremath{_0}} |
| \DeclareUnicodeCharacter{2081}{\ensuremath{_1}} |
| \DeclareUnicodeCharacter{2082}{\ensuremath{_2}} |
| \DeclareUnicodeCharacter{2083}{\ensuremath{_3}} |
| \DeclareUnicodeCharacter{2084}{\ensuremath{_4}} |
| \DeclareUnicodeCharacter{00AC}{\ensuremath{\neg}} |
| \DeclareUnicodeCharacter{2200}{\ensuremath{\forall}} |
| \DeclareUnicodeCharacter{2203}{\ensuremath{\exists}} |
| \DeclareUnicodeCharacter{00B7}{\ensuremath{\cdot}} |
| \DeclareUnicodeCharacter{27E8}{\ensuremath{\langle}} |
| \DeclareUnicodeCharacter{27E9}{\ensuremath{\rangle}} |
| \DeclareUnicodeCharacter{2192}{\ensuremath{\to}} |
| \DeclareUnicodeCharacter{21D2}{\ensuremath{\Rightarrow}} |
| \DeclareUnicodeCharacter{2227}{\ensuremath{\wedge}} |
| \DeclareUnicodeCharacter{2228}{\ensuremath{\vee}} |
| \DeclareUnicodeCharacter{2208}{\ensuremath{\in}} |
| \DeclareUnicodeCharacter{03BB}{\ensuremath{\lambda}} |
| \DeclareUnicodeCharacter{03C3}{\ensuremath{\sigma}} |
| \DeclareUnicodeCharacter{2223}{\ensuremath{\mid}} |
| |
