test: calibrate the marginals against the exact posterior

Investigation for #46 and #47, before touching either.

A scored history is linear-Gaussian, so its true joint posterior has a
closed form and the crate can be checked against ground truth. Measured
on five competitors:

                    means      marginal sd (crate / exact)
    tree (star)     exact      1.000
    loopy (robin)   exact      0.502

On a tree the crate is exact in both. With cycles the means stay exact —
the standard Gaussian-BP result, and the property ratings rely on —
while marginal variances come out about half the true width.

That is the opposite direction from what #47 reports, so whatever is
happening in that consumer's model, the crate being conservative is not
it.

It also means #46 cannot be implemented as an added covariance accessor.
The exact correlation between two nodes here is +0.857, so ignoring it
overstates the width of a difference — but the too-narrow marginals
partially cancel that, leaving 1.327x rather than 2.646x. Adding true
correlations to these marginals without correcting them would give 0.765
against a true 1.524: overconfident, which is the direction the reporter
specifically called unsafe.

Pins the two real invariants (exactness on a tree, exact means with
cycles) and deliberately only records the variance gap, since closing it
is what #46 proposes.

Also records the working rules this project has converged on: investigate
before implementing, fix the root issue, and scout crates.io on measured
accuracy rather than adoption.

Refs #46, #47

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011hcFjNDmHXZF8URGLku5zZ

CLAUDE.md

@@ -24,6 +24,20 @@ is where several defects have hidden — a debug-only run is not evidence.
 - `approx` — `approx::AbsDiffEq` etc. for `Gaussian`. Most numerical goldens need it.
 - `rayon` — opt-in parallel within-slice sweep and per-slice query passes.
 
+## Working rules
+
+- **Investigate before implementing.** Measure the actual behaviour first —
+  against an analytic reference where one exists. Several "obvious" fixes in
+  this repo turned out to be wrong in sign or unnecessary, and the measurement
+  is what caught them.
+- **Fix the root issue, not the symptom.** A clamp that hides an underflow, or
+  a tolerance loosened to make a test pass, is a defect deferred.
+- **Scout crates.io before hand-rolling numerics.** Check accuracy against an
+  independent reference rather than trusting downloads: `puruspe` has 1.4M
+  downloads and is 346 ULP off in the tail, where `libm` is 1. Fewer
+  dependencies is preferable, not mandatory — take the dependency when it is
+  measurably better.
+
 ## Architecture
 
 A Rust port of [TrueSkillThroughTime.py](https://github.com/glandfried/TrueSkillThroughTime.py):