The scan for precision defects found none in `quality()` — but it did
find that N identical teams have an exact closed form, which is a much
stronger regression net than the single two-team golden that was there.
For two identical single-player teams quality is
`sqrt(2b^2 / (2b^2 + s1^2 + s2^2))`. With the conventional parameters
that ratio is exactly 1/5, and the N-group generalisation is
`(1/5)^((n-1)/2)` — one factor per adjacent pair. Measured across
n = 2..10 the implementation matches to 1e-9, so the determinant path
that #9 rebuilt is correct over the whole range, not just at n = 2.
The n=3 and n=5 values (0.200 and 0.040) are also what the `trueskill`
Python package produces for the same configuration, which is the
cross-implementation check the README Todo has been asking for since
the redesign. Asserted separately as literals so a change to the
closed-form reasoning cannot silently carry them along.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011hcFjNDmHXZF8URGLku5zZ
logaritmiskandClaude Opus 5
564969ee5d