`time_expanded_joint` collapsed consecutive appearances only at
`drift <= 0.0` exactly. Anything smaller-but-positive got an explicit
`1.0 / drift` precision, which the matrix cannot hold: at `drift = 1e-16`
the entry is `1e16`, and `1e16 + 0.28` rounds back to `1e16`, so the
prior and the event contrasts are annihilated in the stored f64 before
the factorisation ever runs.
Measured, 8 competitors over 15 slices:
drift_scale before after
1e-6 1.3e-3 relative error exact
1e-7..1e-9 Err(JointUnavailable) exact
1e-10 12 200x TOO SMALL, as Ok exact
At 1e-10 the caller was handed sigma = 0.0055 where the truth is 0.6108
— a 111x overconfident interval, returned as a success.
This is representation, not conditioning. Solved in 200-digit precision
the same system converges smoothly onto the collapsed value and is flat
from 1e-16 to 1e-40, so the quantity is perfectly well conditioned. That
also rules out the obvious fix: symmetric (Jacobi) equilibration measured
30x WORSE, because the information is gone from the assembled matrix
before any solver sees it. The fix has to be at assembly.
The threshold balances the two errors that trade off. Ignoring a real
drift costs about `drift / V`; representing one costs about
`EPSILON * V / drift`. They cross at `V * sqrt(EPSILON)`, scaled to each
competitor's own prior variance.
Ordinary drift is far above it and unaffected — the default gamma
accumulates 0.0069 per unit time against a threshold of 1.0e-6 — and the
test asserts both halves: everything below the threshold reaches the
collapsed answer bit-identically, and a drift of 1e-2 still moves it, so
the test cannot pass by collapsing everything.
Also corrects the `JointUnavailable` message, which asserted "a
competitor has neither a proper prior nor any evidence" for a fixture
where every competitor had both.
BREAKING CHANGE: a drift variance below `prior_variance * sqrt(EPSILON)`
now collapses two appearances into one latent variable. Affected fits
previously returned a badly wrong variance or an error.
Closes#57
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011hcFjNDmHXZF8URGLku5zZ
logaritmiskandClaude Opus 5
83bdb84152