Ch 1 · The Names It Already Has

A scan on 2026-09-17 found pytorch in one tracked file and reinforcement learning in none. Part of that zero is a real gap. Part of it is that the corpus renamed things that already had names, and a grep for the standard vocabulary counted the renaming as ignorance.

1 · The table

what the corpus calls it	the standard name	where
the fold F, “rank-1 Jacobian loss”	the Jacobian of a vector-valued map, and its rank	D p. 140
transverse eigenvalue μ_max	eigenvalue of the linearisation at a fixed point	D §4.2 · H p. 412
“the linearisation at Γ”	first-order Taylor expansion	D p. 140
curvature at the threshold κ*	the Hessian	D p. 136
G = U∘F∘K∘C	the chain rule for composite maps	D p. 146
descent on the potential Φ	gradient descent	D p. 226
stochastic forcing along the orbit	stochastic gradient descent	D p. 226 ff
constrained basin conditions	Lagrange multipliers	D p. 226 ff
kernel-checked derivative chains	automatic differentiation	D p. 164
“same normal form, different parameters”	similarity of matrices	H p. 274
diagonal normal form	diagonalizability	H p. 270

D = Deisenroth · H = Hefferon. Printing-specific; the script re-locates them against your copy and exits non-zero if a row moves.

2 · The same move, further up

level	what the corpus has	the standard object
discrete	the g-series 0, 2, 6, 33, 64; rfl on numerals	recurrences; what a definitional equality is worth
probability	“the basin”, “converges to Γ”	convergence — and in which sense
dynamics	Γ, T* = 2π, μ_max, ε₀ = 1/3	limit cycle, period, Floquet multiplier, Grönwall radius
verification	sorry, “0 sorry”, “domain axiom”	five words for one hole, not interchangeable
rung 28	“an index”; e^−4π proposed as one	K-theory classes and the index pairing
rung 33	spectral triples — 31 mentions	the spectral triple, with its floor under it

The row that already cost money WP-94 censused 3,207,496 running words and found five verification communities with five names for one object — sorry, Admitted, axiom, trust — and concluded they are not interchangeable. Two weeks later a live page of this corpus printed “0 sorry” as though it meant nothing assumed, with three axioms open and one never named.

Do not read the top of that table as settled The rows are ordered by where a subject is taught, not where it is known. Under a total-function kernel the elementary rows are the ones that surprise — (3 : ℕ) - 5 = 0, x / 0 = 0, 0⁰ = 1, √(−1) = 0, and (-7 : ℤ) / 2 = -4, which is not what C or a rounded-down Python int() gives. Each is a theorem in Book17Core.lean or Book17Mathlib.lean, closed by the kernel, reported by #print axioms, and gated by tools/axiom_gate.py. [VERIFIED 2026-09-19] The corpus's own case is checked: GateScreen.lean generalised WP-39's T2(i) from one loss to every layer-local map fixing zero, and the proof never used the squaring the prose had carried for two years. [VERIFIED 2026-09-15]

3 · One row is an identity, and it has a test

The rest are correspondences of practice. Similarity is not: two matrices are similar exactly when they represent one linear map in different bases (H p. 274). That is what the Coherence Bridge means to claim, stated in a standard term with a decision procedure attached — so it was run.

The test returns zero

tools/coherence_similarity.py parses the table out of book4/hub.html — not transcribed — and finds eleven rows carrying both μ and ω. Near Γ each is a 2×2 system with eigenvalues μ ± iω.

test	invariant	matching pairs
linear similarity (same map, new basis)	the eigenvalue pair	0 of 55
similarity up to time-rescaling	the ratio μ/ω	0 of 55
topological conjugacy [standard]	being a spiral sink	11 of 11

The closest pair under the most generous reading is Immune adaptation and Market volatility, μ/ω = −2.4444 against −2.3929 — near, and not equal. Nothing else is within 0.11.

So the claim is true at the level where it carries no information, and false at every level where it would. Every 2D linear spiral sink is topologically conjugate to every other; eleven of eleven rows qualify, and so would any eleven damped oscillators picked at random. The moment the test asks for anything finer — the same map in a new basis, or even the same map after rescaling the clock — the count is zero.

Ch 20 already says the honest version: “six systems have been shown to admit the same normal form with different invariants … it is not yet a categorical equivalence, and the difference matters.” This adds the number. Four other pages still carry the unhedged form — vol2-dashboard.html, ch-e-gtct.html, ch24-seed-sentences.html and the TO deploy — and are not edited here. [OPEN]

4 · Open

(i) Correct the pages carrying “exact mathematical identities” unhedged. Done, and the count was wrong: “four” came from one grep, the corpus holds eleven files and thirteen occurrences. Two of the four named were not among them. The page the similarity test parses its own data from — book4/hub.html — was one of the seven unnamed. [CLOSED 2026-09-19]
(ii) “Descent on Φ” is asserted in Vol I and never written as an update rule; Deisenroth §7.1 gives the rule. One page of work, not done. [OPEN]
(iii) reinforcement learning and program synthesis remain at zero and are not a naming problem. [OPEN]

5 · References

Deisenroth, Faisal & Ong, Mathematics for Machine Learning, CUP 2020 · Hefferon, Linear Algebra 4e. sha256 in docs/floor-texts.tsv.
tools/book17_ch01_verify.py — eleven rows located, exit 0, 2026-09-19.
WP-82 · WP-94 · WP-122