Major didactic overhaul: pen-and-paper worked examples + in-book solution pathways, 2x volume (53 -> 106 pages)
- 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>
2026-07-03 08:55:00 +00:00
|
|
|
\chapter{A Guided Tour of the Real Repositories}
|
|
|
|
|
\label{app:tour}
|
|
|
|
|
|
|
|
|
|
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
|
|
|
|
|
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 \\
|
Accuracy sweep: bring the book to the proven four-tier apex state
The companion repos completed their signature apex (phases 1+2: four
button-enforced tiers up to "accept <=> decompress(R) = [k](-A)+[s]B as
points") and the scalar layer long ago crossed the kernel frontier - but
the book still taught the pre-campaign state, including one real
inaccuracy of the class coherence pass 3 purged from the repo READMEs:
ch12's apex section and audit-drill solution described the COFACTORED
equation (8sB = 8R + 8kA) with SIMD backends in the trusted base -
neither matches the proven certificates (canonical-R byte equality,
serial path pinned and proven, SHA-512 an oracle with NO assumed
properties).
Fixed:
- ch12: pyramid status diagram (scalar + signature rows now "done"),
the scalar-frontier paragraph (the wall was crossed, and how), the
apex section (future tense -> the proven four-tier statement, honest
trusted base), the "extend the pyramid" bullet (scalar -> pasta curve
layer; CONTRIBUTING files never existed - now points at the control
repo's METHOD/TIERS), exercise 12.2(c) solution (which lineage the
cofactored robustness belongs to), exercise 12.3 + solution (audit
the REAL certificate).
- ch01: framing diagram states the equation actually proven
(sB = R + kA from raw bytes, not the cofactored form).
- glossary: Cofactor entry says which verifiers check which equation.
- ch11: the companion repos' posture is stronger than the ideal-hash
example - no hash properties assumed at all, backend question
eliminated rather than assumed.
- ch08: extraction notes (one merged universe; extract-scalar.sh was
retired in coherence pass 3; SIMD scoped out, not assumed).
- repo tour appendix: floor plan, reading order (item 5 now tours the
apex capstone), Phase 3b described.
- README: companion table rows say "the complete pyramid" with the
four-tier apex; honesty ledger records this 2026-07-06 re-audit.
main.pdf rebuilt from the updated sources (106 pages, zero errors,
build-pass4.log retained).
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-06 05:46:27 +00:00
|
|
|
\code{verification/extract.sh} & the extraction recipe (Charon $\to$
|
|
|
|
|
LLBC $\to$ Aeneas): ONE merged universe per repo --- field, curve,
|
|
|
|
|
scalar, and the verify path --- plus the signature glue \\
|
Major didactic overhaul: pen-and-paper worked examples + in-book solution pathways, 2x volume (53 -> 106 pages)
- 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>
2026-07-03 08:55:00 +00:00
|
|
|
\code{verification/gen/} & the extracted model. \textbf{Never
|
|
|
|
|
hand-edited} (Chapter~\ref{ch:rust}); regenerated or left alone \\
|
|
|
|
|
\code{verification/Proofs/} & the human-written theorems ---
|
|
|
|
|
denotations, bounds lemmas, layer certificates. \textbf{No \lean{axiom}
|
|
|
|
|
may appear here} (the check script enforces it) \\
|
|
|
|
|
\code{verification/check.sh} & THE button: recompiles every shipped
|
|
|
|
|
file in dependency order and axiom-audits every certificate; if a file
|
|
|
|
|
is in the repo, this script checks it \\
|
|
|
|
|
\code{verification/lean-guard} & the resource-capped \lean{lean}
|
|
|
|
|
wrapper every compile routes through --- the postmortem-hardened
|
|
|
|
|
tooling mentioned in Chapters~\ref{ch:automation}
|
|
|
|
|
and~\ref{ch:field} \\
|
|
|
|
|
\bottomrule
|
|
|
|
|
\end{tabular}
|
|
|
|
|
\end{center}
|
|
|
|
|
|
|
|
|
|
\section{A reading order that works}
|
|
|
|
|
|
|
|
|
|
\begin{enumerate}[leftmargin=1.6em]
|
|
|
|
|
\item \textbf{\code{TRUSTED-BASE.md}} (five minutes). Count the
|
|
|
|
|
entries; for each, ask the Chapter~\ref{ch:honesty} question ---
|
|
|
|
|
``declared debt or smuggled axiom?'' --- and notice each has its
|
|
|
|
|
justification attached.
|
|
|
|
|
\item \textbf{The denotation} (in \code{Proofs/}, near the top of the
|
|
|
|
|
field spec file). One definition; confirm it is
|
|
|
|
|
Chapter~\ref{ch:denotation}'s radix-51 sum, mapping the \emph{extracted}
|
|
|
|
|
type.
|
|
|
|
|
\item \textbf{One two-clause spec end to end} --- \code{sub} is the
|
|
|
|
|
best first read: bounds hypotheses, \lean{.ok} clause, bounds
|
|
|
|
|
propagation, value equation, and inside the proof, the $16p$ constant
|
|
|
|
|
you audited in Chapter~\ref{ch:field}'s worked example.
|
|
|
|
|
\item \textbf{The certificate} --- the conjunction theorem
|
|
|
|
|
(\code{fieldImplementation}) and its \lean{\#print axioms} line. This
|
|
|
|
|
is the artifact all the marketing language ultimately refers to; note
|
|
|
|
|
how unglamorous it looks.
|
Accuracy sweep: bring the book to the proven four-tier apex state
The companion repos completed their signature apex (phases 1+2: four
button-enforced tiers up to "accept <=> decompress(R) = [k](-A)+[s]B as
points") and the scalar layer long ago crossed the kernel frontier - but
the book still taught the pre-campaign state, including one real
inaccuracy of the class coherence pass 3 purged from the repo READMEs:
ch12's apex section and audit-drill solution described the COFACTORED
equation (8sB = 8R + 8kA) with SIMD backends in the trusted base -
neither matches the proven certificates (canonical-R byte equality,
serial path pinned and proven, SHA-512 an oracle with NO assumed
properties).
Fixed:
- ch12: pyramid status diagram (scalar + signature rows now "done"),
the scalar-frontier paragraph (the wall was crossed, and how), the
apex section (future tense -> the proven four-tier statement, honest
trusted base), the "extend the pyramid" bullet (scalar -> pasta curve
layer; CONTRIBUTING files never existed - now points at the control
repo's METHOD/TIERS), exercise 12.2(c) solution (which lineage the
cofactored robustness belongs to), exercise 12.3 + solution (audit
the REAL certificate).
- ch01: framing diagram states the equation actually proven
(sB = R + kA from raw bytes, not the cofactored form).
- glossary: Cofactor entry says which verifiers check which equation.
- ch11: the companion repos' posture is stronger than the ideal-hash
example - no hash properties assumed at all, backend question
eliminated rather than assumed.
- ch08: extraction notes (one merged universe; extract-scalar.sh was
retired in coherence pass 3; SIMD scoped out, not assumed).
- repo tour appendix: floor plan, reading order (item 5 now tours the
apex capstone), Phase 3b described.
- README: companion table rows say "the complete pyramid" with the
four-tier apex; honesty ledger records this 2026-07-06 re-audit.
main.pdf rebuilt from the updated sources (106 pages, zero errors,
build-pass4.log retained).
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-06 05:46:27 +00:00
|
|
|
\item \textbf{The apex} --- \code{verify\_accepts\_iff\_decompress}
|
|
|
|
|
in \code{Proofs/DecompressMain.lean}, the top of the four-tier stack,
|
|
|
|
|
and the check script's boundary phase that guards its axiom cone. Note
|
|
|
|
|
how short the capstone proof is: every hard fact was certified below it.
|
|
|
|
|
This is where Chapter~\ref{ch:pyramid}'s invitation points.
|
Major didactic overhaul: pen-and-paper worked examples + in-book solution pathways, 2x volume (53 -> 106 pages)
- 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>
2026-07-03 08:55:00 +00:00
|
|
|
\end{enumerate}
|
|
|
|
|
|
|
|
|
|
\section{Running the machinery}
|
|
|
|
|
|
|
|
|
|
With the toolchain installed (the repos pin exact versions ---
|
|
|
|
|
Chapter~\ref{ch:rust}'s reproducibility discipline):
|
|
|
|
|
|
|
|
|
|
\begin{lstlisting}
|
|
|
|
|
$ ./verification/check.sh
|
|
|
|
|
=== Phase 1: stub audit ===
|
|
|
|
|
clean: no trivial stubs, no True targets, no axioms outside gen/
|
|
|
|
|
=== Phase 2: compile ===
|
|
|
|
|
[gen] CurveField/Funs ... ok
|
|
|
|
|
[proofs] FieldSpec ... ok (no 'sorry' warnings -- enforced)
|
|
|
|
|
=== Phase 3: axiom audit ===
|
|
|
|
|
fieldImplementation: [propext, Classical.choice, Quot.sound] OK
|
|
|
|
|
ALL CHECKS PASSED
|
|
|
|
|
\end{lstlisting}
|
|
|
|
|
|
|
|
|
|
Three details make this script worth imitating in your own projects.
|
|
|
|
|
\emph{Phase 1 runs before compilation}: trivial-stub patterns
|
|
|
|
|
(\lean{by trivial} specs, \lean{True} targets) and \lean{axiom}
|
|
|
|
|
declarations under \code{Proofs/} are cheap textual gates --- the
|
|
|
|
|
mechanical half of the Chapter~\ref{ch:honesty} field guide, automated.
|
|
|
|
|
\emph{Phase 2 treats warnings as failures}: the string
|
|
|
|
|
\lean{uses 'sorry'} in compiler output fails the build --- warnings,
|
|
|
|
|
unlike source text, cannot be hidden in comments. \emph{Phase 3 is the
|
|
|
|
|
one-command audit}, run on every certificate, every time, so the
|
|
|
|
|
axiom-clean property is continuously enforced rather than occasionally
|
Accuracy sweep: bring the book to the proven four-tier apex state
The companion repos completed their signature apex (phases 1+2: four
button-enforced tiers up to "accept <=> decompress(R) = [k](-A)+[s]B as
points") and the scalar layer long ago crossed the kernel frontier - but
the book still taught the pre-campaign state, including one real
inaccuracy of the class coherence pass 3 purged from the repo READMEs:
ch12's apex section and audit-drill solution described the COFACTORED
equation (8sB = 8R + 8kA) with SIMD backends in the trusted base -
neither matches the proven certificates (canonical-R byte equality,
serial path pinned and proven, SHA-512 an oracle with NO assumed
properties).
Fixed:
- ch12: pyramid status diagram (scalar + signature rows now "done"),
the scalar-frontier paragraph (the wall was crossed, and how), the
apex section (future tense -> the proven four-tier statement, honest
trusted base), the "extend the pyramid" bullet (scalar -> pasta curve
layer; CONTRIBUTING files never existed - now points at the control
repo's METHOD/TIERS), exercise 12.2(c) solution (which lineage the
cofactored robustness belongs to), exercise 12.3 + solution (audit
the REAL certificate).
- ch01: framing diagram states the equation actually proven
(sB = R + kA from raw bytes, not the cofactored form).
- glossary: Cofactor entry says which verifiers check which equation.
- ch11: the companion repos' posture is stronger than the ideal-hash
example - no hash properties assumed at all, backend question
eliminated rather than assumed.
- ch08: extraction notes (one merged universe; extract-scalar.sh was
retired in coherence pass 3; SIMD scoped out, not assumed).
- repo tour appendix: floor plan, reading order (item 5 now tours the
apex capstone), Phase 3b described.
- README: companion table rows say "the complete pyramid" with the
four-tier apex; honesty ledger records this 2026-07-06 re-audit.
main.pdf rebuilt from the updated sources (106 pages, zero errors,
build-pass4.log retained).
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-06 05:46:27 +00:00
|
|
|
asserted. A fourth phase arrived with the signature layer: \emph{3b pins
|
|
|
|
|
the apex tiers' cones to the documented hash/wire-format boundary
|
|
|
|
|
EXACTLY} --- an unexpected addition \emph{or removal} fails the build.
|
Major didactic overhaul: pen-and-paper worked examples + in-book solution pathways, 2x volume (53 -> 106 pages)
- 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>
2026-07-03 08:55:00 +00:00
|
|
|
|
|
|
|
|
\section{The control repository}
|
|
|
|
|
|
|
|
|
|
\code{formal-verification-control} is the method distilled --- written
|
|
|
|
|
for the next person (or the next automated agent) to extend the
|
|
|
|
|
pyramid without relearning its lessons:
|
|
|
|
|
|
|
|
|
|
\begin{itemize}[leftmargin=1.4em]
|
|
|
|
|
\item \code{INVARIANTS.md} --- the non-negotiables (honesty, safety,
|
|
|
|
|
rigor); the source of house rules this book has been quoting.
|
|
|
|
|
\item \code{TERRAIN.md} --- the map: pipeline, toolchain, layer status,
|
|
|
|
|
representation costs.
|
|
|
|
|
\item \code{METHOD.md} --- ways of thinking that worked, stated as
|
|
|
|
|
practices rather than commandments.
|
|
|
|
|
\item \code{FAILURES.md} --- mapped dead ends \emph{with their tells}:
|
|
|
|
|
the memory-exhausting tactic patterns, the extraction scopes that drag
|
|
|
|
|
in the world, the kernel-capacity wall. Chapter~\ref{ch:field} told two
|
|
|
|
|
of these stories; the file has the rest, and reading failure maps
|
|
|
|
|
before starting work is the cheapest experience money can't buy.
|
|
|
|
|
\end{itemize}
|
|
|
|
|
|
|
|
|
|
A closing observation to carry out of the tour: nothing in these
|
|
|
|
|
repositories asks to be trusted. The claims are in the READMEs, the
|
|
|
|
|
assumptions in the ledgers, the checks in a script anyone can run, the
|
|
|
|
|
axioms in a one-command audit. That shape --- \emph{auditability as the
|
|
|
|
|
default posture} --- is the real deliverable of the whole verification
|
|
|
|
|
enterprise, and the standard this book hopes you now hold everything
|
|
|
|
|
else to.
|