Changes in version 0.3.1                        

  - al_pvalue() could return a negative probability far in the right
    tail. The Lugannani-Rice tail is an asymptotic expansion and its
    correction term overshoots there: at n = 150 on badly non-uniform
    samples the returned value was -6.5e-29 and -2.1e-89. Numerically
    zero, and no decision at any conventional level was affected, but a
    probability must lie in [0, 1] and callers comparing against a level
    must never see a negative number. The value is now clamped to [0, 1]
    in the C back-end, so both the R and the Python bindings inherit the
    fix. Found 17 September 2026 while using the test as a calibration
    instrument for a time-series language model. A regression test now
    checks the tail directly.

                 Changes in version 0.3.0 (2026-09-14)                  

  - Breaking, and it corrects a wrong answer. al_scale() now matches the
    sample band arc length to the spacing-corrected model band length
    al_band_model_star() rather than to the population band length
    al_band_model(). The old behaviour was inconsistent: order
    statistics inside the band are spaced like Q'(u)E/n with E standard
    exponential, so the polygonal sum converges to
    
    S*(sigma) = int E sqrt(f0(z)^2 + sigma^2 E^2) dz = E S(sigma E),

    and not to S(sigma). The two differ by a constant factor, because
    the square root is nonlinear and E[E^2] = 2 rather than 1, and the
    gap does NOT close as the sample grows. At the standard normal on
    the default band the old estimator returned about 1.05 when the
    scale was 1, at every sample size. al_scale() now returns 1.001 at n
    = 20000 and its bias shrinks with n.
    
    Estimates of SCALE change. Regression slopes computed from this
    estimator do not, because a multiplicative bias in the level cancels
    in a log-linear slope; interval coverage does change, and becomes
    correct.

  - New al_band_model_star(), the spacing-corrected model band arc
    length, on both fronts. Its exponential expectation uses an 80-node
    Gauss-Legendre rule under the map t = s/(1 - s), which agrees with
    adaptive double integration to 3e-13 across sigma from 0.1 to 10 and
    across four bands. A Gauss-Laguerre rule was tried first and
    rejected: it reaches only 2e-5 at sigma = 10, because the integrand
    has a kink at t of order f/sigma that falls below its first node.

  - New al_scale_raw(), the uncorrected estimator, retained only so that
    the size of the correction can be measured. It is inconsistent and
    is documented as such.

                 Changes in version 0.2.0 (2026-09-11)                  

  - Breaking. k4_fit_varpro() now searches the fourth shape parameter h
    DIRECTLY rather than on the log scale, and the sentinel asking for
    the free four-parameter fit changes from a negative hfix to NA (NaN
    in C and in Python). Column four of starts now carries h itself, not
    log h.
    
    This is not a refactor. On the log scale h was necessarily positive
    and the boundary at h = 0 lay at minus infinity, so the free fit
    could not reach the negative half-line at all and crept toward the
    boundary reporting a spurious small h instead of naming the submodel
    it had effectively chosen. The negative half-line holds real members
    -- the log-logistic at h = -1, the Burr III and five-parameter
    logistic slice at h = -1/m -- and an audit of the edible-oil traces
    found curves that genuinely prefer it. h = 0, the generalised
    extreme value member, is now an interior point of the free search.
    
    It fails silently if you do not act. Code that passed hfix = -1 to
    mean "fit h freely" now gets h HELD at -1, which fits the
    log-logistic and returns a plausible number. Replace any negative
    hfix meant as a free-fit request with NA_real_ in R, or hfix=None in
    Python. Passing hfix = 0 for the generalised extreme value submodel
    is unaffected, as is NA.
    
    Both fronts move together: the shared C back end, the R wrapper and
    the Python wrapper all take the new sentinel, and the Python front
    had been sending -1.0 internally for a free fit.

  - The quantile-family routines arck4_q(), arck4_tau34(),
    arck4_fit_lmom(), arceq2_bc_q() and arceq2_bc_pdf() are now
    registered as C callables and declared in inst/include/arcstatAPI.h,
    so a dependent package can call them from its own C rather than
    through R. The registration is additive: nothing already exported
    changes, no numerics are affected, and dynamic symbol lookup stays
    disabled, which is why each entry point is registered explicitly.

  - arck4_readings() now requires the density's grid maximum to be
    INTERIOR before reporting a mode. For k >= 1 with h < 1 both terms
    of (log q)'(u) = (h-1)/u - (k-1) h u^(h-1)/(1-u^h) are negative, so
    the quantile density is strictly decreasing, the density is strictly
    increasing, and the argmax lands on the support endpoint. The
    routine previously returned that endpoint as a mode together with
    two readings computed from it -- finite, plausible-looking, and
    meaningless. Both readings are now NaN there, which is correct:
    neither is defined when the curve has no interior steepest point.
    Found while re-deriving the equivalence locus of the four-parameter
    kappa family, where the artefact had been read as a second branch of
    the locus.

                        Changes in version 0.1.0                        

  - First release. The computation runs on a shared pure-C back-end that
    is also bound from Python, and the two fronts are checked against
    each other value by value.