feat!: Gaussian's EP operations stop wearing arithmetic's clothes

`Gaussian` publicly implemented `Mul`, `Div`, `Add` and `Sub`. They were
the EP product, cavity and variance-space convolutions, and every one of
them lies to a reader who takes the operator at face value:

    a = N(10, 2)   b = N(4, 3)   c = N(1, 1)

    a * b        N(8.15, 1.66)   not 40
    a - b        sigma GREW, 2 -> sqrt(4 + 9)
    a * N(1, 0)  mu = NaN        "multiply by one"
    a / c        pi = -0.75      mu() prints a confident 0

The last is this crate's signature defect on a public operator. `Div` is
the cavity and can legitimately leave a negative precision, which is not
a distribution — and `mu()`/`sigma()` guard `pi <= 0` and report `0.0`
and `inf`, so it comes back as a plausible number with no panic, no
`Debug` marker and nothing to test against.

The four impls are now `pub(crate)` inherent methods that say what they
do: `ep_product`, `cavity`, `convolve`, `convolve_diff`, plus `scale`
for the one operation that genuinely is arithmetic. Nothing in a user's
workflow needed operator syntax; inference did, and it still has it.

`pi()` and `tau()` follow. Storing natural parameters is a performance
decision — it makes message passing two adds — not a contract. The
public surface is now exactly: `from_ms`, `from_mv`, `mu`, `sigma`,
`variance`, `probability_below`, `probability_above`. `from_mv` and
`variance` are promoted from `pub(crate)`; they are the honest pair for
callers who already hold a variance and should not pay a round trip
through the square root.

Four integration tests asserted bit-identity on `(pi, tau)`. They assert
it on `(mu, variance)` instead — still `assert_eq!`, still exact, and
`1/pi` and `tau/pi` are deterministic, so bit-equal natural parameters
give bit-equal moments. `a_nan_sigma_passes_through_from_ms` drops its
`|| g.pi().is_nan()` half: `sigma()` substitutes for `pi <= 0` and
`pi == inf`, so NaN survives to it only from a NaN precision.

`benches/gaussian.rs` is deleted. It timed two f64 additions through the
public operators, and keeping those public solely to feed it is the same
thing #73 objected to when a benchmark was dictating five public types.
The paths it covered are exercised by `batch` and `history_converge`
through the real call chain.

Closes #71.

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

benches/gaussian.rs

@@ -1,53 +0,0 @@
-use criterion::{Criterion, criterion_group, criterion_main};
-use trueskill_tt::gaussian::Gaussian;
-
-fn benchmark_gaussian_arithmetic(criterion: &mut Criterion) {
-    // Define test Gaussians
-    let g1 = Gaussian::from_ms(25.0, 25.0 / 3.0);
-    let g2 = Gaussian::from_ms(0.0, 1.0);
-    let g3 = Gaussian::from_ms(1.0, 1.0);
-
-    // Benchmark addition
-    criterion.bench_function("Gaussian::add", |bencher| {
-        bencher.iter(|| g1 + g2);
-    });
-
-    // Benchmark subtraction
-    criterion.bench_function("Gaussian::sub", |bencher| {
-        bencher.iter(|| g1 - g3);
-    });
-
-    // Benchmark multiplication
-    criterion.bench_function("Gaussian::mul", |bencher| {
-        bencher.iter(|| g1 * g2);
-    });
-
-    // Benchmark division
-    // NOTE: numerator must have higher precision (smaller sigma) than the
-    // denominator in this representation; g2 (sigma=1) / g1 (sigma=8.33) is
-    // well-defined, whereas g1 / g2 underflows and panics in mu_sigma.
-    criterion.bench_function("Gaussian::div", |bencher| {
-        bencher.iter(|| g2 / g1);
-    });
-
-    // Benchmark natural parameter conversions
-    criterion.bench_function("Gaussian::pi", |bencher| {
-        bencher.iter(|| g1.pi());
-    });
-
-    criterion.bench_function("Gaussian::tau", |bencher| {
-        bencher.iter(|| g1.tau());
-    });
-
-    // Benchmark combined pi/tau operations (used in mul/div)
-    criterion.bench_function("Gaussian::pi_tau_combined", |bencher| {
-        bencher.iter(|| {
-            let pi = g1.pi();
-            let tau = g1.tau();
-            (pi, tau)
-        });
-    });
-}
-
-criterion_group!(benches, benchmark_gaussian_arithmetic);
-criterion_main!(benches);