A GVar's moments are exact only when each operation is at most quadratic
over the spread of its input and the input really is Gaussian. Neither
holds in general. GVar now carries two fields that accumulate through
arithmetic and say how far the result has drifted from a Gaussian:

  κ3   the third cumulant, exposed standardized as `skewness`
  err  an estimate of the absolute error in `center`, exposed as
       `moment_error`, tracking the leading Taylor term each operation
       neglects

`distrust` combines them into one dimensionless number: the displacement
of the quantiles in units of `rad`. It is zero for an exact Gaussian and
grows without bound as the description degrades. The two components are
complementary. `exp` of a Gaussian is exactly lognormal, so its
`moment_error` is zero while its skewness is large; a quadratic has
neither.

Two fixes fall out of the same derivation:

Var[f(x)] = f'^2 σ^2 + f''^2 σ^4/2 + f' f''' σ^4 + O(σ^6). The third term
was omitted although it is the same order as the second, and it is
positive for `inv`, `log`, `sqrt` and `x^p`, so σ was systematically
understated: `log(3 ± 0.5)` was low by 3.1%, now 0.5%.

ThickNumbers builds the result of `hull`, `intersect`, `typemin` and
`typemax` with the two-argument call `TN(lo, hi)`, but `GVar(center, σ)`
is a different parametrization; those four now have GVar methods. The
generic versions produced a hull spanning [-2.5, 6.5] for operands
spanning [2, 4] and [2.5, 4.5], and an intersection wider than either
operand.

Integer powers use exact Gaussian raw moments, which terminate for a
polynomial, rather than an asymptotic correction to the variance. Mean,
variance and third cumulant are then all exact, and SpecialFunctions is
no longer needed. Exponents above 20 overflow the moment sum and throw.

Assisted-by: Claude Opus 4.8 <noreply@anthropic.com>