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- pen-and-paper worked examples in all 12 chapters, using the REAL constants throughout: 2^-64 waiting-time arithmetic, headroom budgets, hand type-checking, rfl traces, full goal-state boards, the column-sum audit at 2^54, inverting 19 mod p via Euclid, the x19 fold at real weights, denoting p itself (telescope), the 16p audit (8 fails by 151), the 254+11 inversion-chain bookkeeping, the substitution test, sizing the 28-vs-1000 extraction, cofactor/torsion arithmetic, and the full Bernstein-Lange completeness derivation - CORRECTNESS FIX: ch7 asserted a false factorization of p-1; replaced with the computationally verified p-1 = 2^2 * 3 * 65147 * Q (Q 71-digit prime), witness w=2 verified for all four Pratt conditions - every chapter's exercises now followed immediately by 'Solutions and pathways' (pathway first, then answer), incl. new exercises - NEW Interlude: a complete two-clause verification done entirely by hand, then mapped line-by-line onto the compiled Lean proof - NEW appendices: A pen-and-paper toolkit (8 recipe cards + drills + answers), B guided walkthroughs of every exercise-file hole, C tour of the real repositories; plus glossary, instructor notes, 13-week plan - preamble: worked-example box, solution macros, math-safe inline code Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
122 lines
5.5 KiB
TeX
122 lines
5.5 KiB
TeX
\chapter{A Guided Tour of the Real Repositories}
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\label{app:tour}
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The companion projects are working code, laid out for auditors rather
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than tourists. This appendix is the tourist map: what lives where, what
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to read first, and how to run the machinery yourself. Everything below
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names \code{dalek-ed25519-verified}; the other three ed25519 forks are
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structured identically, and \code{pasta-pallas-verified} differs only
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where Montgomery form demands it.
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\section{The floor plan}
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\begin{center}
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\small
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\begin{tabular}{@{}lp{0.62\linewidth}@{}}
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\toprule
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\textbf{Path} & \textbf{What it is, and the rule that governs it} \\
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\midrule
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\code{README.md} & the claims: what is proven, what is frontier ---
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the honest-boundary statements of Chapter~\ref{ch:honesty} \\
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\code{TRUSTED-BASE.md} & the ledger: every assumption, each with its
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reason --- read this \emph{before} being impressed by anything \\
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\code{verification/extract.sh} & extraction roots for the field layer
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(Charon $\to$ LLBC $\to$ Aeneas); \code{extract-scalar.sh} likewise for
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scalars \\
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\code{verification/gen/} & the extracted model. \textbf{Never
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hand-edited} (Chapter~\ref{ch:rust}); regenerated or left alone \\
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\code{verification/Proofs/} & the human-written theorems ---
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denotations, bounds lemmas, layer certificates. \textbf{No \lean{axiom}
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may appear here} (the check script enforces it) \\
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\code{verification/check.sh} & THE button: recompiles every shipped
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file in dependency order and axiom-audits every certificate; if a file
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is in the repo, this script checks it \\
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\code{verification/lean-guard} & the resource-capped \lean{lean}
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wrapper every compile routes through --- the postmortem-hardened
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tooling mentioned in Chapters~\ref{ch:automation}
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and~\ref{ch:field} \\
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\bottomrule
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\end{tabular}
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\end{center}
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\section{A reading order that works}
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\begin{enumerate}[leftmargin=1.6em]
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\item \textbf{\code{TRUSTED-BASE.md}} (five minutes). Count the
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entries; for each, ask the Chapter~\ref{ch:honesty} question ---
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``declared debt or smuggled axiom?'' --- and notice each has its
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justification attached.
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\item \textbf{The denotation} (in \code{Proofs/}, near the top of the
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field spec file). One definition; confirm it is
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Chapter~\ref{ch:denotation}'s radix-51 sum, mapping the \emph{extracted}
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type.
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\item \textbf{One two-clause spec end to end} --- \code{sub} is the
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best first read: bounds hypotheses, \lean{.ok} clause, bounds
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propagation, value equation, and inside the proof, the $16p$ constant
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you audited in Chapter~\ref{ch:field}'s worked example.
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\item \textbf{The certificate} --- the conjunction theorem
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(\code{fieldImplementation}) and its \lean{\#print axioms} line. This
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is the artifact all the marketing language ultimately refers to; note
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how unglamorous it looks.
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\item \textbf{The frontier} --- the scalar layer's in-progress files,
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clearly marked. Read one open lemma statement and recognize its shape
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(it is 9.B with bigger constants). This is where
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Chapter~\ref{ch:pyramid}'s invitation points.
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\end{enumerate}
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\section{Running the machinery}
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With the toolchain installed (the repos pin exact versions ---
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Chapter~\ref{ch:rust}'s reproducibility discipline):
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\begin{lstlisting}
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$ ./verification/check.sh
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=== Phase 1: stub audit ===
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clean: no trivial stubs, no True targets, no axioms outside gen/
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=== Phase 2: compile ===
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[gen] CurveField/Funs ... ok
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[proofs] FieldSpec ... ok (no 'sorry' warnings -- enforced)
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=== Phase 3: axiom audit ===
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fieldImplementation: [propext, Classical.choice, Quot.sound] OK
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ALL CHECKS PASSED
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\end{lstlisting}
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Three details make this script worth imitating in your own projects.
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\emph{Phase 1 runs before compilation}: trivial-stub patterns
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(\lean{by trivial} specs, \lean{True} targets) and \lean{axiom}
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declarations under \code{Proofs/} are cheap textual gates --- the
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mechanical half of the Chapter~\ref{ch:honesty} field guide, automated.
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\emph{Phase 2 treats warnings as failures}: the string
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\lean{uses 'sorry'} in compiler output fails the build --- warnings,
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unlike source text, cannot be hidden in comments. \emph{Phase 3 is the
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one-command audit}, run on every certificate, every time, so the
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axiom-clean property is continuously enforced rather than occasionally
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asserted.
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\section{The control repository}
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\code{formal-verification-control} is the method distilled --- written
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for the next person (or the next automated agent) to extend the
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pyramid without relearning its lessons:
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\begin{itemize}[leftmargin=1.4em]
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\item \code{INVARIANTS.md} --- the non-negotiables (honesty, safety,
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rigor); the source of house rules this book has been quoting.
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\item \code{TERRAIN.md} --- the map: pipeline, toolchain, layer status,
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representation costs.
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\item \code{METHOD.md} --- ways of thinking that worked, stated as
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practices rather than commandments.
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\item \code{FAILURES.md} --- mapped dead ends \emph{with their tells}:
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the memory-exhausting tactic patterns, the extraction scopes that drag
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in the world, the kernel-capacity wall. Chapter~\ref{ch:field} told two
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of these stories; the file has the rest, and reading failure maps
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before starting work is the cheapest experience money can't buy.
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\end{itemize}
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A closing observation to carry out of the tour: nothing in these
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repositories asks to be trusted. The claims are in the READMEs, the
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assumptions in the ledgers, the checks in a script anyone can run, the
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axioms in a one-command audit. That shape --- \emph{auditability as the
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default posture} --- is the real deliverable of the whole verification
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enterprise, and the standard this book hopes you now hold everything
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else to.
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