New Chapter 13, 'The Second Summit: A Hash-Based Pyramid' — SLH-DSA
(FIPS 205) as the transfer experiment for the whole method:
- opens on leaf 18 as the anomaly; correctness-vs-security across the
quantum divide ('a correct implementation of a broken lock is still a
broken lock')
- Lamport -> Winternitz chains with the checksum see-saw run twice on
real w=16 numbers, including a concrete failed forgery (480 -> 479,
digit 14 -> 13)
- FORS worked at napkin scale (k=2, a=2, one reuse = one forgery) and
real scale (28 of 57,344, exponent 14)
- the virtual hypertree: digest split 21/7/2 to the bit, the 54-bit
meter peeled 9 bits per layer, verification priced exactly (254 fixed
oracle calls; the see-saw itself caps a layer at 510, so worst case
3,824 — the naive 525*35 bound is unreachable, and the chapter says
why); ~2^72 to build vs ~2^12 to check
- the eleven certificates, the loop-to-fold bridges, the honest
'visible, not correct' boundary (no second semantics — and why the
natural move fails), the cone-growth table, the t_l/t_len naming
inversion told as the war story it was, the apex as an audit
invitation with the verbatim theorem named
- 'The leaf, live': leaf-vs-head precision ('plausible, and wrong
twice'), the three-clause self-reference ledger (attested machinery /
attested scheme / honest gap), one-command tryit
- six exercises with pathway'd solutions; checkpoint hands the
who-checks-them question to the finale
Structural: attestation renamed ch14 and now carries the book's single
ending (where-to-go, further reading, final reframe, prospective
checkpoint — moved from ch12); its two interior checkpoints demoted to
bigidea/tryit so the terminal checkpoint stands alone; opening now
receives ch13's baton. ch12 ends as a chapter. Front matter: three-summit
arc, fourteen-week plan, honest discussion-exercise count; ch01 promise
ladder extended to Chapters 13/14; glossary +5 entries (and the
pre-existing Hasse-bound misordering fixed); README fourteen chapters +
build.sh recipe.
Every constant verified against fips205-slhdsa-verified and
lean-transparency-log by four adversarial checkers; arithmetic
independently recomputed; didactic panel scored the chapter 9/8 —
the book's high-water mark. Build: 128 pages, zero unresolved refs.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
From the 7-reader didactic audit (control/BOOK-OVERHAUL-PLAN.md). The two
highest-leverage moves per the cold-open reader and the panel's most-repeated
finding.
MOVE 1 — the reader touches the real thing in minute one. The panel's single
loudest note: a book that teaches "demand verification" gave the reader
nothing to verify for twelve chapters. Now: the title page names
ltl.zkdefi.org (19 entries, one post-quantum, "verify every entry yourself by
the last chapter"); the preface opens on that page instead of a generic power
claim; ch1 gains a try-it box after the pyramid pointing at entries 13-16 and
18. And ch7's broken promise is honored — it invited "check one leaf" while
never printing the 71-digit Q; the exact Q from P25519.lean is now on the
page, no hidden digits (render-verified against the repo).
MOVE 2 — ch1 cold open. Per the cold reader who hooked at line 13 and wobbled
by line 31: the first worked box (a log10 re-derivation of a punch the prose
already landed) collapses to four lines, the mechanics pushed to Exercise 1.1
— getting the reader ~30 lines sooner to the headroom box, the genuinely novel
bit. The vague "In 2014, researchers…" opener becomes the actual bug: a
two-line diff captioned as the entire defect, anchored to the real Fiat-Crypto
S&P 2019 lineage (no fabricated CVE). Competitor roll-call → footnote.
Syllabus roadmap → a second-person promise ("by Chapter 7 you will have handed
a kernel a certificate…"). "Why Lean" vendor bullets → reader-inheritance
voice ("you start on a million lines of proved mathematics").
Builds here: tectonic, 116 pages, zero errors.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
The owner's requirement, now the book's explicit contract (new "ratchet
rule" box in chapter 1): every load-bearing idea is worked at least
twice - once at napkin scale (mod 13, inverses by scanning) and once at
REAL scale, the actual 77-digit Ed25519 constants printed in full with
no digits hidden and no artificial zeros; where raw size genuinely
exceeds paper (a 77-digit square root), the book says so and teaches
witness-auditing instead of pretending.
Socratic audit result: chapters 1-11 already honor the rule (verified
rung by rung - e.g. ch6 pairs the Z/12 clock with 19^-1 mod the real p;
ch7 pairs Pratt-for-97 with costing the real certificate; ch8 runs the
extracted model at the real envelope edge). The gaps were ch12's three
summit rungs, which had NO numeric examples at all. Filled:
- Group law: "running the addition law by hand - napkin curve, then the
real one". Doubling (2,4)->(10,11) mod 13 in full; then the real base
point with x1, y1 printed in 5-digit groups, the first machine step
certified as x1*y1 = q*p + u with the 77-digit witness q printed, and
the student auditing it by casting out nines AND elevens (both clocks
close: 3=3, 1=1). Lands on the real 2B coordinates.
- Scalars: the cycle felt on the napkin curve first (order 16, so
21P = 5P) before the real prime ell.
- Apex: "decompression, run twice". Encode/decode (10,11) as "(11,
even)" mod 13 - x^2 = 3/9 = 9, roots {3,10}, parity picks 10; then
the real compressed base point: all 32 bytes printed (58 66...66),
byte 31 = 0x66 sign-bit read, y_B printed in full, and the
no-shortcuts full-size hand verification 5*y_B - 4 = 4*p, both
78-digit sides printed for digit-by-digit comparison. The square
root honestly declared machine territory, with the witness-checked
certificate named.
- New paper exercise 12.4 (+pathway/solution): encode & decompress
3P = (6,10) solo - the wrong root lands on -3P, one bit doing real
cryptographic work.
Every printed constant machine-verified before typesetting (base point
on-curve, q*p+u exact, 5y-4 = 4p exact, 2B on-curve, toy order 16).
PDF rebuilt: 109 pages, zero errors. Honesty ledger records the
revision.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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>
- 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>
- 53-page LaTeX/TikZ book (main.pdf + full sources): from zero background
to reading the real Ed25519/Pasta verification projects
- runnable exercises with sorry-holes + complete solutions for chapters
2-7, 9, 12; every solution file compiles clean (zero errors, no sorry)
against Lean v4.30.0-rc2 + Mathlib 5450b53e
- lake project pinned to the same toolchain/Mathlib the solutions were
verified with; students fetch the Mathlib cache, never build it
- honesty ledger in README: what was machine-checked and how
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
