print-quality pass: the book gets looked at, and the looking becomes a gate

The operator caught what no check had ever tested: nobody had LOOKED at
the rendered pages. A ten-inspector visual audit of all 129 pages (every
page opened as an image) found 40 defects, including didactic
correctness bugs invisible to the text layer:

BAD, fixed:
- ch03 printed WRONG Lean operators: \lean{P /\ Q} lost its backslash
  ('P / Q') and \lean{P \/ Q} lost the operator entirely ('P  Q') —
  TeX ate them inside the non-verbatim macro. Now the unicode ∧/∨ the
  book uses everywhere else.
- ch12: the doubling display overflowed its box border, slicing the
  math; stacked on two lines.
- toolkit Card 6: the headroom-audit display was clipped by the page
  edge; now an align* stack.

UGLY, fixed:
- title page: the 'pyramid motif' at 5% white opacity on near-black
  rendered as smudge artifacts, plus a clipped ∀ glyph in the corner
  — redrawn with solid mixed colors (no transparency), glyph removed;
  the footer's mid-word paragraph gap was a \vspace landing inside
  horizontal mode; fixed with \par
- ch06: both clock diagrams' wrap-around arrows ran counterclockwise,
  retracing over earlier arcs — target position expressed as 12 (one
  revolution) so the arc continues clockwise, landing on 0 (mod 12)
  and 1 (mod 11) correctly
- ch04: two_mul'' printed as two_mul" (quote ligature)
- one-line orphaned box fragments and stranded solution headings
  throughout: bigidea/tryit/pitfall/aha/checkpoint are now unbreakable
  (none exceeds half a page), worked boxes announce '(continued)' after
  a break, \solhead keeps four lines with \Needspace
- --all/--receipt flags printed as one merged dash: \ddash macro
- inline code no longer hyphen-breaks at underscores (codeguards)
- ch09's 2^{...} smudge, glossary margin overflow, ch08 orphaned
  listing line, ch13 command-line layout, three >10pt overfulls

THE STRUCTURAL LESSON, encoded: the two worst clipping bugs had been
announced as 80pt/73pt overfull warnings in every build log and ignored.
check-book.sh now FAILS on any overfull box past 10pt — the machine was
telling us; now it is allowed to stop us.

132 pages; publication-history and README counts synced; every fixed
page re-rendered and verified by eye. Button: ALL GREEN (96 checks).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

README.md

@@ -25,7 +25,7 @@ Lean 4 against models extracted from the actual Rust sources:
 **[`main.pdf`](main.pdf)** — fourteen chapters + interlude + three
 appendices, full color, built with LaTeX/TikZ from the sources in this
 repo (`./build.sh`, tectonic, no root needed). **Second edition,
-published August 8, 2026** (129 pages; the full publication history is
+published August 8, 2026** (132 pages; the full publication history is
 printed in the book's front matter). No prior Lean or formal
 methods assumed; high-school algebra and a little programming suffice.
 

chapters/appendix-repo-tour.tex

@@ -108,7 +108,7 @@ phase catches it and what the failure actually says. Then try to be
 sneakier: weaken a theorem's \emph{statement} instead of its proof, or
 plant an \lean{axiom} in a \code{Proofs/} file, and see the stub-audit
 phase refuse before the compiler even starts. Restore with
-\code{git checkout -- .} when done. Ten minutes of vandalism buys you
+\code{git checkout \ddash\ .} when done. Ten minutes of vandalism buys you
 something reading cannot: the difference between believing the button
 because it is green and believing it because you have personally failed
 to fool it.

chapters/appendix-toolkit.tex

@@ -91,12 +91,12 @@ which is itself a toolkit skill.
 \section{Card 6: the headroom audit}
 
 For any limb design, three lines locate the overflow cliff:
-\[
+\begin{align*}
-\text{headroom} = \text{word bits} - \text{radix bits}; \qquad
+\text{headroom} &= \text{word bits} - \text{radix bits};\\
-\text{add budget} = 2^{\text{headroom}}; \qquad
+\text{add budget} &= 2^{\text{headroom}};\\
-\text{mul check: } (\text{limb count}) \cdot 2^{2\cdot\text{bound bits}}
+\text{mul check: } &(\text{limb count}) \cdot 2^{2\cdot\text{bound bits}}
 \overset{?}{<} 2^{\text{wide word}} .
-\]
+\end{align*}
 Run all three whenever anyone shows you a limb representation ---
 Chapter~\ref{ch:why} (budget), Chapter~\ref{ch:automation} (mul check),
 and Chapter~\ref{ch:field}'s $16p$ audit are all instances.

chapters/appendix-walkthroughs.tex

@@ -140,8 +140,12 @@ addition must happen \emph{on the clock face}, not in \lean{Nat}).
 this proof on paper. Bounds clause: \lean{simp only [add]; omega}.
 Value clause --- the one genuine difficulty in the file --- state the
 exact integer identity with its correction term:
-\lean{have key : (add a b).1 + 4 * (add a b).2 + 15 * ((a.2 + b.2 +
+\begin{lstlisting}[language=Lean]
-(a.1 + b.1) / 4) / 4) = (a.1 + 4*a.2) + (b.1 + 4*b.2)}, discharge with
+have key : (add a b).1 + 4 * (add a b).2
+    + 15 * ((a.2 + b.2 + (a.1 + b.1) / 4) / 4)
+    = (a.1 + 4*a.2) + (b.1 + 4*b.2)
+\end{lstlisting}
+discharge it with
 \lean{simp only [add]; omega}, then cast
 (\lean{push_cast}), kill the modulus
 (\lean{rw [show (15 : ZMod 15) = 0 by decide]}), and close with
@@ -149,9 +153,9 @@ exact integer identity with its correction term:
 correction term is wrong --- recompute $c_2$ on paper (Interlude Step
 2); \lean{omega}'s refusal is, as always, a counterexample pointing at
 the boundary. \textbf{9.C \code{mulVal_spec}}: same cast-and-kill
-scaffold, but the integer identity is pure algebra ---
+scaffold, but the integer identity is pure algebra,
-\lean{mulVal a b + 15 * (a.2 * b.2) = (a.1 + 4*a.2) * (b.1 + 4*b.2)}
+\lean{mulVal a b + 15*(a.2*b.2) = (a.1 + 4*a.2)*(b.1 + 4*b.2)}
-by \lean{ring} --- and \emph{no bounds hypotheses are needed}, a fact
+by \lean{ring}, and \emph{no bounds hypotheses are needed} --- a fact
 worth noticing (denotation does not care about digit discipline; only
 machine words do).
 

chapters/ch03-propositions-as-types.tex

@@ -35,8 +35,8 @@ Chapter~\ref{ch:lean} \emph{is} the proof checker.
 proposition $P$        & type            & \lean{P : Prop} \\
 proof of $P$           & value/program of that type & \lean{h : P} \\
 $P \to Q$ (implication)& function type   & \lean{P -> Q} \\
-$P \land Q$ (and)      & pair type       & \lean{P /\ Q} \\
+$P \land Q$ (and)      & pair type       & \lean{P ∧ Q} \\
-$P \lor Q$ (or)        & tagged union    & \lean{P \/ Q} \\
+$P \lor Q$ (or)        & tagged union    & \lean{P ∨ Q} \\
 $\lnot P$ (not)        & \lean{P -> False} & \lean{Not P} \\
 ``true''               & type with one trivial value & \lean{True} \\
 ``false''              & \emph{empty} type & \lean{False} \\
@@ -246,8 +246,9 @@ structure of $n$, induction (Chapter~\ref{ch:tactics}) is how a recipe
 consults structure.
 \end{worked}
 
-Dually, \lean{exists n, P n} is proved by handing over a concrete witness
+Dually, \lean{exists n, P n} is proved by handing over a concrete
-together with evidence: \lean{Exists.intro 4 pf}. And remember the
+witness together with the evidence for it: \lean{Exists.intro 4 pf}.
+And remember the
 \lean{Rational} exercise from last chapter --- the denominator you could not
 keep nonzero? Dependent types fix it by letting data carry proofs:
 
@@ -279,17 +280,17 @@ coffee.
 
 \begin{tryit}
 Open \code{exercises/Ch03.lean} and prove, as programs (no tactics yet!):
-\lean{P -> Q -> P}; \ \lean{(P /\ Q) -> (P \/ Q)}; \ and modus ponens
+\lean{P -> Q -> P}; \ \lean{(P ∧ Q) -> (P ∨ Q)}; \ and modus ponens
 \lean{P -> (P -> Q) -> Q}. Each is a one-liner. Feel free to be delighted
 when the pieces click together like typed Lego.
 \end{tryit}
 
 \section*{Exercises}
 
-\exercise{Prove \lean{and_assoc : (P /\ Q) /\ R -> P /\ (Q /\ R)} as a
+\exercise{Prove \lean{and_assoc : (P ∧ Q) ∧ R -> P ∧ (Q ∧ R)} as a
 term-mode program using \lean{h.1}, \lean{h.2}, and \lean{And.intro}.}
 
-\exercise{Prove \lean{or_swap : P \/ Q -> Q \/ P}. You will need case
+\exercise{Prove \lean{or_swap : P ∨ Q -> Q ∨ P}. You will need case
 analysis on which side holds: \lean{match h with | Or.inl p => ... | Or.inr q => ...}}
 
 \exercise{\lean{Not P} is \emph{defined} as \lean{P -> False}. Using only

chapters/ch04-tactics.tex

@@ -377,8 +377,9 @@ theorem two_mul' (n : Nat) : 2 * n = n + n := by
   | zero      => rfl
   | succ k ih => rw [Nat.mul_succ, ih, Nat.succ_add, Nat.add_succ]
 \end{lstlisting}
-Library: \lean{exact?} finds \lean{Nat.two_mul}, so
+Library: \lean{exact?} finds \lean{Nat.two_mul}, giving
-\lean{theorem two_mul'' (n : Nat) : 2 * n = n + n := Nat.two_mul n}. Both
+\lean{theorem two_mul\textquotesingle\textquotesingle\ (n : Nat) : 2 * n = n + n}
+proved by \lean{Nat.two_mul n}. Both
 are legitimate craft: the first when you are building the ecosystem, the
 second when you are using it. Mathlib has over 200{,}000 lemmas ---
 searching \emph{is} a proof technique, and \lean{exact?} is its tactic.

chapters/ch06-modular-arithmetic.tex

@@ -67,7 +67,7 @@ is the entry ticket to division.
   \begin{scope}
     \draw[ink2,thick] (0,0) circle (2.2);
     \foreach \i in {0,...,11} \node[color=ink] at ({90-\i*30}:1.8) {\i};
-    \foreach \s/\t in {0/4, 4/8, 8/0}
+    \foreach \s/\t in {0/4, 4/8, 8/12}
       \draw[-{Stealth},accent,thick] ({90-\s*30}:2.55) arc ({90-\s*30}:{90-\t*30+8}:2.55);
     \node[color=accent,align=center] at (0,-3.4) {$\Zmod{12}$: stepping by $4$\\ visits only $\{0,4,8\}$ --- never $1$};
   \end{scope}
@@ -75,7 +75,7 @@ is the entry ticket to division.
   \begin{scope}[xshift=9.5cm]
     \draw[ink2,thick] (0,0) circle (2.2);
     \foreach \i in {0,...,10} \node[color=ink] at ({90-\i*32.72}:1.8) {\i};
-    \foreach \s/\t in {0/4, 4/8, 8/1}
+    \foreach \s/\t in {0/4, 4/8, 8/12}
       \draw[-{Stealth},proven,thick] ({90-\s*32.72}:2.55) arc ({90-\s*32.72}:{90-\t*32.72+8}:2.55);
     \node[color=proven,align=center] at (0,-3.4) {$\Zmod{11}$: stepping by $4$\\ reaches $1$ in three steps: $4^{-1}=3$};
   \end{scope}

chapters/ch08-rust-to-lean.tex

@@ -103,11 +103,13 @@ returns a \lean{Result} that is an error unless the mathematical sum fits.
 So the innocent theorem ``add returns the right field element'' \emph{cannot
 even be stated} without first proving \emph{add returns at all}:
 
+\noindent\begin{minipage}{\linewidth}
 \begin{lstlisting}[language=Lean]
 theorem add_spec (a b : Array U64 5)
     (ha : LimbsBounded a) (hb : LimbsBounded b) :
     ∃ c, fieldElement51_add a b = .ok c ∧ LimbsBounded c ∧ ...
 \end{lstlisting}
+\end{minipage}
 
 That hypothesis \lean{LimbsBounded} --- each limb below $2^{54}$, say --- is
 the bounds invariant promised in Chapters~\ref{ch:pat}

chapters/ch09-denotation-bridge.tex

@@ -69,7 +69,7 @@ diagram, instantiated.
 \section{Why redundancy is freedom (and where bugs hide)}
 
 A subtlety with consequences: denotation is \textbf{many-to-one}. The limb
-arrays $(19, 0, 0, 0, 0)$ and $(p + 19 \bmod 2^{\cdots}, \dots)$ --- or more
+arrays $(19, 0, 0, 0, 0)$ and $(19 + (2^{51}-19),\; 2^{51}-1,\; \dots)$ --- i.e.\ $p$ itself added limb-wise --- --- or more
 mundanely, unreduced sums whose limbs exceed $2^{51}$ --- can denote the
 \emph{same} field element. The representation has slack, and the
 implementation \emph{exploits} it: the fast \code{add} from

chapters/ch10-verifying-a-field.tex

@@ -237,7 +237,8 @@ good fast code turn out to obey the same engineering aesthetics. This is not
 a coincidence; both are fighting combinatorial growth with structure.
 \end{aha}
 
-\textbf{Four forks, one method, real divergence.} The companion projects
+\Needspace{4\baselineskip}
+\noindent\textbf{Four forks, one method, real divergence.} The companion projects
 verify not just upstream \code{curve25519-dalek} but three production forks
 (Solana's, RISC~Zero's, Betrusted's) --- each against \emph{its own}
 extraction. Worth it? The audit found the forks implement the same

chapters/ch12-the-pyramid.tex

@@ -63,7 +63,8 @@ Then
 \[
 x_3 \;=\; \frac{2xy}{1 + 11} \;=\; \frac{16}{12} \;\equiv\; 3 \cdot 12^{-1}
 \;=\; 3\cdot 12 \;=\; 36 \;\equiv\; 10,
-\qquad
+\]
+\[
 y_3 \;=\; \frac{y^2\!+\!x^2}{1 - 11} \;=\; \frac{20}{3} \;\equiv\; 7\cdot 3^{-1}
 \;=\; 7 \cdot 9 \;=\; 63 \;\equiv\; 11
 \]
@@ -75,10 +76,10 @@ want it.
 
 \emph{Run 2 --- the real base point, full digits.} The same doubling, on
 Ed25519's base point $B = (x_1, y_1)$:
-\par\noindent{\footnotesize $x_1 \;=$}\\[-2pt]
+\par\noindent{\footnotesize $x_1 \;=$}\\[1pt]
 {\footnotesize\ttfamily\begin{tabular}{@{}l@{}}15\,11222\,13495\,35400\,77250\,11514\,09588\,53151\,14540\\
 12693\,04185\,72060\,46113\,28394\,98477\,62202\end{tabular}}\par\smallskip
-\par\noindent{\footnotesize $y_1 \;=$}\\[-2pt]
+\par\noindent{\footnotesize $y_1 \;=$}\\[1pt]
 {\footnotesize\ttfamily\begin{tabular}{@{}l@{}}46\,31683\,56949\,26478\,16942\,83940\,03475\,16314\,13079\\
 93866\,25622\,56157\,83033\,60316\,52518\,55960\end{tabular}}\par\smallskip
 The machine's first step is the product $u = x_1 y_1 \bmod p$. Nobody
@@ -88,10 +89,10 @@ remainder $u$ it claims, turning the step into one integer equation
 \[
 x_1 \cdot y_1 \;=\; q \cdot p + u ,
 \]
-\par\noindent{\footnotesize $q \;=$}\\[-2pt]
+\par\noindent{\footnotesize $q \;=$}\\[1pt]
 {\footnotesize\ttfamily\begin{tabular}{@{}l@{}}12\,08977\,70796\,28320\,61800\,09211\,27670\,82520\,91632\\
 10154\,43348\,57648\,36890\,62715\,98782\,09761\end{tabular}}\par\smallskip
-\par\noindent{\footnotesize $u \;=$}\\[-2pt]
+\par\noindent{\footnotesize $u \;=$}\\[1pt]
 {\footnotesize\ttfamily\begin{tabular}{@{}l@{}}46\,82740\,38508\,23179\,24507\,22166\,30277\,19756\,51442\\
 05554\,12565\,49766\,74165\,82953\,38171\,01731\end{tabular}}\par\smallskip
 which Chapter~\ref{ch:modular}'s shadow arithmetic audits on two
@@ -105,10 +106,10 @@ each is two careful minutes over the blocks printed above; that labor
 \emph{is} the pen-and-paper content at this size. Five more certified
 steps of exactly this shape (square, multiply by $d$, the two inversions
 via Fermat chains) complete the doubling, landing on
-\par\noindent{\footnotesize $x_{2B} =$}\\[-2pt]
+\par\noindent{\footnotesize $x_{2B} =$}\\[1pt]
 {\footnotesize\ttfamily\begin{tabular}{@{}l@{}}24\,72741\,32351\,06541\,00255\,45745\,71675\,58883\,46227\\
 68167\,39763\,84567\,26423\,68252\,12336\,08206\end{tabular}}\par\smallskip
-\par\noindent{\footnotesize $y_{2B} =$}\\[-2pt]
+\par\noindent{\footnotesize $y_{2B} =$}\\[1pt]
 {\footnotesize\ttfamily\begin{tabular}{@{}l@{}}15\,54967\,55802\,80190\,17635\,26687\,10449\,54225\,15495\\
 72066\,44506\,05805\,07079\,59306\,26430\,49417\end{tabular}}\par\smallskip
 --- the coordinates of $2B$ that every Ed25519 stack on earth agrees on.
@@ -329,7 +330,7 @@ little-endian):
 bytes, nothing elided).
 Byte 31 is $\code{0x66} = 01100110_2$: its top bit is $0$, so the sign
 bit says ``$x$ even.'' The remaining 255 bits, read little-endian, are
-\par\noindent{\footnotesize $y_B \;=$}\\[-2pt]
+\par\noindent{\footnotesize $y_B \;=$}\\[1pt]
 {\footnotesize\ttfamily\begin{tabular}{@{}l@{}}46\,31683\,56949\,26478\,16942\,83940\,03475\,16314\,13079\\
 93866\,25622\,56157\,83033\,60316\,52518\,55960\end{tabular}}\par\smallskip
 The design claim behind this constant: $y_B = 4/5$ in $\Fp$, i.e.\
@@ -340,10 +341,10 @@ $5\,y_B \equiv 4 \pmod p$. At full size that is one integer equation,
 and this one you can verify with \emph{no} shortcuts and \emph{no}
 witnesses: multiply $y_B$ by $5$ yourself (one right-to-left carry pass),
 multiply $p$ by $4$, subtract $4$, compare every digit:
-\par\noindent{\footnotesize $5\,y_B - 4 \;=$}\\[-2pt]
+\par\noindent{\footnotesize $5\,y_B - 4 \;=$}\\[1pt]
 {\footnotesize\ttfamily\begin{tabular}{@{}l@{}}231\,58417\,84746\,32390\,84714\,19700\,17375\,81570\,65399\\
 69331\,28112\,80789\,15168\,01582\,62592\,79796\end{tabular}}\par\smallskip
-\par\noindent{\footnotesize $4\,p \;=\;\;\;\;\;\;\;$}\\[-2pt]
+\par\noindent{\footnotesize $4\,p \;=\;\;\;\;\;\;\;$}\\[1pt]
 {\footnotesize\ttfamily\begin{tabular}{@{}l@{}}231\,58417\,84746\,32390\,84714\,19700\,17375\,81570\,65399\\
 69331\,28112\,80789\,15168\,01582\,62592\,79796\end{tabular}}\par\smallskip
 An honest fifteen minutes, and you have hand-checked a constant that

chapters/ch13-second-summit.tex

@@ -466,9 +466,11 @@ self-reference keeps its books honest.
 
 \begin{tryit}
 Touch the second summit yourself; it costs one command. Clone
-\code{github.com/saymrwulf/lean-transparency-log} and run
+\code{github.com/saymrwulf/lean-transparency-log} and run:
-\code{python3 verify.py --receipt
+\begin{center}
-receipts/fips205-slhdsa-verified.receipt.json} --- the receipt binds
+\code{python3 verify.py \ddash receipt receipts/fips205-slhdsa-verified.receipt.json}
+\end{center}
+The receipt binds
 leaf~18 by inclusion proof to the size-$19$ signed head. Then open
 \code{entries/000018.json} and find, with your own eyes: the eleven
 certificate names, the five oracle axioms in the apex's observed cone,

chapters/ch14-attestation-protocol.tex

@@ -243,7 +243,7 @@ The fifteen-minute exercise, and the best return on time in this book: clone
 the mirror and run the verifier.
 
 \begin{itemize}
-\item \code{python3 verify.py --all} --- plain Python for the hashing, the
+\item \code{python3 verify.py \ddash all} --- plain Python for the hashing, the
   \code{openssl} binary for signatures, and it \emph{fails closed} without
   them (this chapter taught you why ``couldn't check'' must
   never print as a pass). It recomputes every leaf hash, every historical
@@ -288,7 +288,7 @@ its trusted base; read a leaf's exclusions before believing anything beyond
 them. Second: the estate's paper about this log is frozen under journal
 review and describes the thirteen-leaf snapshot of July 2026. Nothing it
 describes was altered --- the paper-era leaves and heads sit byte-identical
-inside today's history, and \code{verify.py --all} checks both eras in one
+inside today's history, and \code{verify.py \ddash all} checks both eras in one
 run. A document that ages honestly inside a system that keeps moving is not
 a defect; it is what append-only means.
 

chapters/glossary.tex

@@ -5,8 +5,8 @@
 \newcommand{\gloss}[1]{\par\smallskip\noindent{\bfseries #1.}\ }
 
 \gloss{Axiom-clean} Of a theorem: \lean{\#print axioms} reports exactly
-Lean's standard trio \lean{[propext, Classical.choice, Quot.sound]} and
+Lean's standard trio --- \lean{propext}, \lean{Classical.choice},
-nothing else. The gold standard for shipped certificates
+\lean{Quot.sound} --- and nothing else. The gold standard for shipped certificates
 (Chapter~\ref{ch:honesty}).
 
 \gloss{Bounds invariant} A predicate limiting how large limbs may grow

check-book.sh

@@ -96,10 +96,25 @@ selftest() {
 [ "${1:-}" = "--selftest" ] && selftest
 
 echo "=== Phase 1: build ==="
-./build.sh
+BUILDLOG="$(mktemp)"
+./build.sh 2>&1 | tee "$BUILDLOG"
 command -v pdfinfo >/dev/null && command -v pdftotext >/dev/null || {
   echo "FAIL: poppler-utils (pdfinfo/pdftotext) required"; exit 1; }
 
+# Print-quality gate: an overfull box past 10pt is text visibly leaving the
+# margin or a border slicing through content. The 2026-08-08 visual audit
+# found the two worst rendering defects in the book had been announced in
+# every build log as 80pt/73pt overfull warnings — and ignored. Never again.
+if grep -oE "Overfull \\\\hbox \([0-9]+\.[0-9]+pt" "$BUILDLOG" \
+   | grep -oE "[0-9]+\.[0-9]+" | awk '$1 > 10 {bad=1} END {exit bad}'; then
+  echo "  ok    no overfull box exceeds 10pt (print-quality gate)"
+else
+  echo "  FAIL  overfull boxes past 10pt — text is leaving the page:"
+  grep -E "Overfull \\\\hbox \([0-9]{2,}" "$BUILDLOG" | sort -u | head -5
+  rm -f "$BUILDLOG"; exit 1
+fi
+rm -f "$BUILDLOG"
+
 python3 "$HERE/check-book.py" "$HERE"
 
 echo

main.tex

@@ -7,13 +7,13 @@
 \begin{titlepage}
 \pagecolor{ink}\color{paper}
 \begin{tikzpicture}[remember picture,overlay]
-  % faint pyramid motif — the proof pyramid the book builds toward
+  % the proof pyramid the book climbs — drawn in solid mixed colors, never
+  % transparency: low-opacity fills on a dark ground render as smudge and
+  % vary by viewer. Crisp thin outlines make it read as intentional.
   \foreach \i/\w in {0/5.4, 1/4.2, 2/3.0, 3/1.8}{
-    \fill[paper,opacity=0.05] ($(current page.center)+(-\w/2,{-2.2+\i*0.95})$)
+    \draw[paper!30!ink, line width=0.5pt, fill=paper!8!ink]
-      rectangle ++(\w,0.8);
+      ($(current page.center)+(-\w/2,{-3.0+\i*0.95})$) rectangle ++(\w,0.8);
   }
-  \node[anchor=south west,paper,opacity=0.06,scale=6,font=\ttfamily]
-    at ($(current page.south west)+(0.5,0.4)$) {$\forall$};
 \end{tikzpicture}
 \vspace*{3.2cm}
 {\fontsize{15}{18}\selectfont\scshape\color{accent} a hands-on course in\par}
@@ -21,18 +21,21 @@
 {\fontsize{40}{44}\selectfont\bfseries Verifying Cryptography\\[2pt] with Lean 4\par}
 \vspace{0.8cm}
 {\fontsize{15}{20}\selectfont\color{paper}
-From \code{1+1=2} to a machine-checked proof that\\ real elliptic-curve code is correct.\par}
+From {\ttfamily 1+1=2} to a machine-checked proof that\\ real elliptic-curve code is correct.\par}
 \vfill
 {\large\color{paper} A curriculum for the curious undergraduate ---\\
 no prior formal-verification or Lean experience assumed.\par}
 \vspace{0.8cm}
-{\color{ink2}\rule{\linewidth}{0.6pt}}
+{\color{paper!40!ink}\rule{\linewidth}{0.6pt}\par}
-\vspace{0.3cm}
+\vspace{0.15cm}
-{\small\color{paper} Companion to a public transparency log of machine-checked
+{\small\color{paper}\raggedright
-proofs --- \textbf{\code{ltl.zkdefi.org}}, 19 entries and counting, one of them
+Companion to a public transparency log of machine-checked proofs ---
-post-quantum. Open it on your phone now; by the last chapter you will be able
+\textbf{\code{ltl.zkdefi.org}}, 19 entries and counting, one of them
-to verify every entry yourself. \\ Every code snippet in this book runs. Every
+post-quantum. Open it on your phone now; by the last chapter you will be
-claim it makes about a proof, a proof assistant has checked.\par}
+able to verify every entry yourself.\par
+\smallskip
+Every code snippet in this book runs. Every claim it makes about a proof,
+a proof assistant has checked.\par}
 \end{titlepage}
 \restoregeometry
 \pagecolor{paper}\color{ink}
@@ -45,7 +48,7 @@ claim it makes about a proof, a proof assistant has checked.\par}
 \vspace*{2cm}
 {\small
 \noindent\textbf{Second edition} --- published August 8, 2026: fourteen
-chapters, 129 pages.
+chapters, 132 pages.
 
 \medskip
 \noindent\emph{Publication history}

preamble.tex

@@ -18,7 +18,8 @@
 \usepackage{fancyhdr}
 \usepackage{titlesec}
 \usepackage{booktabs}
-\usepackage[strings]{underscore} % plain _ works in text; math subscripts unaffected
+\usepackage[strings]{underscore}
+\usepackage{needspace} % plain _ works in text; math subscripts unaffected
 \usepackage{hyperref}
 
 % ---- palette -------------------------------------------------------------
@@ -105,7 +106,12 @@
 % Inline code: plain styled text (robust in tables/footnotes, unlike lstinline).
 % Also safe inside math mode (wraps itself in \text there).
 % Unicode symbols in inline code are handled by the declarations below.
-\newcommand{\inlinecode}[1]{\ifmmode\text{\ttfamily\small #1}\else{\ttfamily\small #1}\fi}
+% Inside code: never break at an underscore with a hyphen — a hyphen inside
+% a printed identifier is a lie in a book that teaches exact names.
+\newcommand{\codeguards}{\let\BreakableUnderscore\textunderscore\relax}
+% command-line double dash, kept visibly TWO hyphens in tt (they touch otherwise)
+\newcommand{\ddash}{-\kern0.10em-}
+\newcommand{\inlinecode}[1]{\ifmmode\text{\ttfamily\small\codeguards#1}\else{\ttfamily\small\codeguards#1}\fi}
 \newcommand{\lean}[1]{\inlinecode{#1}}
 \newcommand{\rust}[1]{\inlinecode{#1}}
 \newcommand{\code}[1]{\inlinecode{#1}}
@@ -195,23 +201,23 @@
 
 % ---- pedagogical boxes: each means ONE thing ----------------------------
 % BIG IDEA — the load-bearing concept of a section.
-\newtcolorbox{bigidea}[1][]{enhanced,breakable,colback=accentsoft,
+\newtcolorbox{bigidea}[1][]{enhanced,colback=accentsoft,
   colframe=accent,boxrule=0.4pt,arc=3pt,left=10pt,right=10pt,top=8pt,bottom=8pt,
   fonttitle=\bfseries\color{paper},coltitle=paper,title={\faLightbulb\ The big idea},#1}
 % TRY IT — a hands-on invitation to run something.
-\newtcolorbox{tryit}[1][]{enhanced,breakable,colback=codebg,colframe=ink2,
+\newtcolorbox{tryit}[1][]{enhanced,colback=codebg,colframe=ink2,
   boxrule=0.4pt,arc=3pt,left=10pt,right=10pt,top=8pt,bottom=8pt,
   fonttitle=\bfseries\color{paper},coltitle=paper,title={\faTerminal\ Try it yourself},#1}
 % PITFALL — a trap, with its tell.
-\newtcolorbox{pitfall}[1][]{enhanced,breakable,colback=warnsoft,colframe=warn,
+\newtcolorbox{pitfall}[1][]{enhanced,colback=warnsoft,colframe=warn,
   boxrule=0.4pt,arc=3pt,left=10pt,right=10pt,top=8pt,bottom=8pt,
   fonttitle=\bfseries\color{paper},coltitle=paper,title={\faExclamationTriangle\ Pitfall},#1}
 % AHA — an intuition that clicks.
-\newtcolorbox{aha}[1][]{enhanced,breakable,colback=provensoft,colframe=proven,
+\newtcolorbox{aha}[1][]{enhanced,colback=provensoft,colframe=proven,
   boxrule=0.4pt,arc=3pt,left=10pt,right=10pt,top=8pt,bottom=8pt,
   fonttitle=\bfseries\color{paper},coltitle=paper,title={\faStar\ Aha},#1}
 % CHECKPOINT — end-of-chapter self-check.
-\newtcolorbox{checkpoint}[1][]{enhanced,breakable,colback=white,colframe=ink,
+\newtcolorbox{checkpoint}[1][]{enhanced,colback=white,colframe=ink,
   boxrule=0.6pt,arc=3pt,left=10pt,right=10pt,top=8pt,bottom=8pt,
   fonttitle=\bfseries\color{paper},coltitle=paper,title={\faFlagCheckered\ Checkpoint},#1}
 
@@ -236,7 +242,8 @@
 \newtcolorbox{worked}[1]{enhanced,breakable,colback=white,colframe=ink2,
   boxrule=0.4pt,leftrule=2.6pt,arc=1pt,left=10pt,right=10pt,top=8pt,bottom=8pt,
   colbacktitle=codebg,coltitle=ink,
-  fonttitle=\bfseries,title={\pennib\ Pen and paper: #1}}
+  fonttitle=\bfseries,title={\pennib\ Pen and paper: #1},
+  title after break={\pennib\ Pen and paper: #1 \emph{(continued)}}}
 \providecommand{\pennib}{\raisebox{-1pt}{\small$\angle$}}
 
 % exercises
@@ -246,7 +253,7 @@
 
 % solutions — immediately after each chapter's exercises.
 % Every solution leads with the PATHWAY (how to find it), then the answer.
-\newcommand{\solhead}[1]{\medskip\noindent%
+\newcommand{\solhead}[1]{\Needspace{4\baselineskip}\medskip\noindent%
   {\bfseries\color{proven}Solution #1.}\ }
 \newcommand{\pathway}{\par\smallskip\noindent{\itshape\color{ink2}Pathway.}\ }
 \newcommand{\answer}{\par\smallskip\noindent{\itshape\color{ink2}Answer.}\ }