Vignette: drop non-standard terminology

Remove the "fool's convergence" and "sampling-density cliff/blind
spot" labels from the robust-error section; these are not standard
terms in the quadrature literature and the surrounding prose already
describes the failure mode plainly.

Author: bnaras

vignettes/cubature.Rmd

@@ -164,18 +164,16 @@ hcubature(f2, 0, pi / 2, fDim = 2)$integral
 The default error estimator in `hcubature` uses a single "null rule"
 difference between the degree-7 Genz–Malik rule and its embedded
 degree-5 companion on each region. For smooth integrands this is
-reliable and cheap. For integrands with **localized support** — a
-thin hinge, a near-step sigmoid, a very narrow Gaussian inside an
-oversized bounding box — it can fail in a particular way: the rule's
-sample points miss the integrand's support entirely, all sample values
-are zero, the rule estimate is zero with zero estimated error, and
-the algorithm confidently reports "converged" on a completely wrong
-answer. This is sometimes called **fool's convergence** or a
-**sampling-density blind spot**. It is distinct from ordinary
-numerical error — the algorithm is internally consistent; it has
-just never evaluated the function at a point where it's nonzero.
-`pcubature` can fail the same way because its Clenshaw–Curtis tensor
-grid is also a fixed sample geometry.
+reliable and cheap. For integrands with **localized support** — a thin
+hinge, a near-step sigmoid, a very narrow Gaussian inside an oversized
+bounding box — it can fail in a particular way: the rule's sample
+points miss the integrand's support entirely, all sample values are
+zero, the rule estimate is zero with zero estimated error, and the
+algorithm confidently reports "converged" on a completely wrong
+answer. This is distinct from ordinary numerical error — the algorithm
+is internally consistent; it has just never evaluated the function at
+a point where it's nonzero.  `pcubature` can fail the same way because
+its Clenshaw–Curtis tensor grid is also a fixed sample geometry.
 
 A small reproducible example: a hinge-squared times a steep logistic
 times a standard Gaussian over `[-10, 10]²`. With default settings
@@ -227,21 +225,19 @@ integrators already use more conservative error estimators.
 
 ### When robust is not enough: the sampling-density cliff
 
-Neither robust path is a complete cure. The safeguards work on
-regions where the rule has *seen some signal* and needs a better
-estimate of it. If the integrand's support is so narrow that every
-sample point of the base rule misses it entirely, the safeguards
-have nothing to work with. This failure mode — what we call the
-**sampling-density cliff** — is located at a parameter value
-determined by the rule's sample geometry. For `hcubature`'s
-Genz–Malik rule on `[-h, h]^d`, the cliff for hinge-line integrands
-sits at `t₁ = -√(9/70)·h ≈ -0.3586·h`; for `pcubature`'s robust
-(m = 2) Clenshaw–Curtis grid it's at
-`t₁ = -cos(3π/8)·h ≈ -0.3827·h`. For parameters on one side of the
-cliff every sample point fires and the algorithm converges
-correctly; for parameters on the other side every sample point
-evaluates to zero and the algorithm silently reports zero. No
-combination of error-estimator tweaks can detect this.
+Neither robust path is a complete cure. The safeguards work on regions
+where the rule has *seen some signal* and needs a better estimate of
+it. If the integrand's support is so narrow that every sample point of
+the base rule misses it entirely, the safeguards have nothing to work
+with. This failure mode is determined by the rule's sample
+geometry. For `hcubature`'s Genz–Malik rule on `[-h, h]^d`, the cliff
+for hinge-line integrands sits at `t₁ = -√(9/70)·h ≈ -0.3586·h`; for
+`pcubature`'s robust (m = 2) Clenshaw–Curtis grid it's at `t₁ =
+-cos(3π/8)·h ≈ -0.3827·h`. For parameters on one side of the cliff
+every sample point fires and the algorithm converges correctly; for
+parameters on the other side every sample point evaluates to zero and
+the algorithm silently reports zero. No combination of error-estimator
+tweaks can detect this.
 
 The only way to address the cliff is a **denser base rule**, which
 is exactly what Cuba's Cuhre provides: it uses a degree-13 rule with