Re-derive dARSdS and correct the apparent mean open and shut times

[remislp]

exact_mean_open_shut_time was too large by exactly twice the dead time, and HJC_adjacent_mean_open_to_shut_time_pdf by once.

The cause is one sign in qmatlib.dARSdS.

The derivation

HJC give the Laplace transform as

AR*(s) = [sI - QAA - QAF M(s) QFA]^-1 ,
M(s)   = (I - exp(-(sI - QFF) tres)) (sI - QFF)^-1

Factorising as CHS96 eqn (3.6) does, pulling out (sI - QAA):

AR*(s) = inv(VA(s)) inv(U(s)) ,  U(s) = sI - QAA ,
VA(s)  = I - inv(U(s)) QAF M(s) QFA

Differentiating the product of two inverses reproduces exactly the DARS formula already in the docstring, so the outer structure was never in question — only dVAds.

With N(s) = sI - QFF, M'(0) = -tres expQFF inv(QFF) - SFF inv(QFF)^2, and therefore

dVAds = -inv(QAA) GAF SFF GFA
        - tres GAF expQFF GFA
        - GAF SFF inv(QFF) GFA

Two of those three terms were right. The dead-time term was coded positive. That made dVAds too large by 2 tres GAF expQFF GFA, and every apparent mean duration built on it too long by 2 tres.

What changes

With the sign fixed, the three call sites add tres rather than subtracting it — which is what the theory says, because the density is written in u = t - tres and integrates to 1 (phi inv(VA) GAF expQFF u = 1, tested).

The numbers do not change. The correction now lives where the error was, instead of being cancelled three times downstream — and anyone calling dARSdS directly gets a correct answer for the first time.

How it was checked

Against references that owe nothing to the implementation:

• A numerical derivative of AR*(s), formed straight from its definition using nothing else in the library, at three dead times. A flipped sign fails it. This is the test that pins the root cause.
• Colquhoun & Hawkes (1995b), eqns (121) and (122). For a two-state channel the values reproduce the closed form exactly, at five dead times.
• The asymptotic HJC pdf. For CH82 and the AChR mechanism the result agrees with tres + sum(area * tau) — a different route through the library.
• A long simulation, and tres = 0, where the apparent means must become the ideal ones.
• On a mechanism with one open state the conditional mean open time must be flat against adjacent shut time, and is only with the correction.

Also in this PR

HJC_adjacent_mean_open_to_shut_range_mean — the mean apparent open time for openings whose adjacent shut time falls in a given range. This is what is superimposed on the observed conditional means in Fig. 6D of Colquhoun, Hatton & Hawkes (2003), and is not the continuous relationship, which cannot be compared with data directly because the data must be binned. It needs the apparent shut time density as a weight, so HJC_shut_time_pdf is exposed on its own.

Test changes

The finite-dead-time reference values in test_real_dtype.py move with the correction, and for a second, smaller reason recorded there: popen.EC50 now converges on the concentration rather than stopping as soon as Popen is within 0.001 of half maximal. Nothing about the real-dtype cast those tests guard has changed.

tests/test_apparent_means.py is new and carries the checks above.

Verification

590 passed, 1 skipped.

Found while reproducing Colquhoun, Hatton & Hawkes (2003), where the corrected means are needed for Fig. 6D; that reproduction's own step checks pass against this branch.

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