Record the issue 572 evaluation: the gate passes, and two things it turned up

[wshlavacek]

Closes the evaluation that issue #572 asked for and that ADR-0123 narrowed to two named
measurements. Both have now been taken. This is documentation only. No code change and no new
configuration key.

What the issue asked

Issue #572 proposes solving an observable's scale and offset analytically instead of searching for
them, and asks for an evaluation first, because there is a real argument on the other side. If
every candidate gets the best flat line for free, the objective might stop telling a global search
which candidates are any good.

What the measurements say

The ordering, not just the width. Earlier work on this had already shown that profiling does
not delete the landscape on a Gaussian family the way it does on a log one. It had not shown
whether the ordering that survives is any good, which is the thing a global search actually uses.
On the synthetic fixture the searched ordering is slightly worse than random and the profiled
ordering is positive. Narrow the two rate boxes from six decades to two, so that sampled points are
actual candidates, and the profiled ordering becomes strong while the searched one does not move.

A fit gets there sooner. Running the same optimizer on both sides with the same number of
simulations, the profiled side reaches the optimum in about half the simulations with the noise
scale also profiled, and in well under half without. That is the head to head the issue asked for.

How often the profile returns a flat line is a fact about the box. Narrowing those same rate
boxes takes it from 18 sampled points in 81 down to 3, with everything else unchanged. Over six
decades of rate constant most points give a trajectory that is flat or instantaneous, and for those
the flat line really is the best the observation model can do. Saying so is the profile being
right, and it does not touch the ranking of the rest. That is the answer to the issue's
counter argument.

Both benchmark models agree. On Smith the spread across the sampled box drops from nine orders
of magnitude to a factor of 3.4, and the worst sampled point still scores five times better than
having no model at all, so what was removed is noise rather than signal.

Two things nobody had spotted

The rule for which noise families can do this is that the loss has to be a sum of squares, not that
the residual has to be on a linear scale. Gaussian and Laplace noise have the same residual scale,
so no rule read off that attribute can tell them apart, and that attribute is exactly what
ADR-0123's table invites an implementer to read. Under Laplace the least squares answer is not the
best one, and it loses even at the point the data was generated from. PyBNF already has a predicate
that separates the two correctly. It was added for unrelated work and gives the right answer for
both confs.

The closed form in the issue is the unconstrained answer, and a profiled parameter still has
declared bounds. Left inert, the way a profiled noise scale is today, the solve returns a negative
scale for a parameter the user declared positive at a third of the sampled points, and scores
better for doing it. Clamping, refusing, or accepting the sign flip is a decision to make on
purpose rather than to fall into.

The question the issue said had to be decided

Which weighting the solve should use. The measurements answer it. The solve has to be the
objective's own best answer over the coefficients, which is option (a) in the issue. That is what
makes the closed form agree with a numerical minimum, and what lets the gradient stay simple. It
leaves the existing analytic scale normalization alone.

About ADR-0123

It becomes superseded in part. Its census and its refusals stand. Its family table and its reading
of the Laske slug are corrected here.

It also recorded two tools as having landed in the benchmark corpus. They were committed to a
branch that was never merged, so it has been pointing at files that are not on main. The companion
pull request merges that branch, along with the additions these measurements needed.

Reproducing

Everything is in wshlavacek/BNGL-Models, branch 572-linear-profiling-race, under
pybnf-jobs/. Each script records the failure modes that produced a plausible wrong answer while
it was being written.

What happens next

The gate is met, so building this is worth doing. ADR-0129 lists the scope, ordered as an
implementation would take it and modelled on the existing noise profiling switch. That is a
separate change and a separate decision, and a follow-up issue will track it.