Add reliability diagnostics to GVar

[timholy]

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

[codecov]

Codecov Report

❌ Patch coverage is 75.22936% with 27 lines in your changes missing coverage. Please review.
✅ Project coverage is 66.66%. Comparing base (eb09203) to head (ce246b6).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/GaussianRandomVariables.jl	75.22%	27 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##             main       #8       +/-   ##
===========================================
+ Coverage   38.70%   66.66%   +27.95%     
===========================================
  Files           1        1               
  Lines         124      168       +44     
===========================================
+ Hits           48      112       +64     
+ Misses         76       56       -20     

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