Initialize interpolation index in interp_profile (fixes nondeterministic solve)

[krystophny]

Problem

interp_profile (in both QL-Balance/src/base/wave_code_data_64bit.f90 and KiLCA/interface/wave_code_data_64bit.f90) declares a local integer ind and passes it to eval_neville_polynom without initializing it:

integer :: deg = 9, Dmin = 0, Dmax = 0, l, ind;   ! ind never set
do l = 1, dim_new
    call eval_neville_polynom(dim_old, r_old, q_old, deg, r_new(l), Dmin, Dmax, ind, q_new(l));
end do

ind is the in/out warm-start window index for the interpolation. On the first call it is read uninitialized. In eval_neville_polynom (KiLCA/interp/interp.h) the guard if (*ind < 0 || *ind > dim-1) *ind = dim/2; only catches out-of-range garbage; in-range garbage flows through find_index_for_interp, and out-of-range garbage triggers an out-of-bounds read of the grid array xg[*ind].

Because interp_profile interpolates the initial background profiles (q, n, Ti, Te, ...) onto the balance grid, this seeds a stack-garbage-dependent perturbation that propagates through the entire linear solve. The result is a solve that is not reproducible run to run for identical inputs, even single-threaded.

This is a pre-existing bug on main, independent of the fortnum migration. It is a major contributor to the ql-balance / KiLCA golden-record instability seen in the fortnum PR stack (#144).

Fix

Initialize ind = 0 before the loop in both copies of interp_profile. 0 is a valid warm-start window index; the interpolation is otherwise unchanged.

Verification

Case: ql-balance golden f_6_2 (m=6, n=2). Comparison quantity: flre/linear-data/m_6_n_2_flab_[1,0]/EB.dat.

Fails on main

valgrind --tool=memcheck --track-origins=yes on the unfixed binary:

ERROR SUMMARY: 40 errors from 23 contexts
  12 Conditional jump or move depends on uninitialised value(s)   at eval_neville_polynom_
  10 Use of uninitialised value of size 8                         at eval_neville_polynom_
   ... Uninitialised value was created by a stack allocation
       at interp_background_profiles_ (wave_code_data_64bit.f90:712)   [interp_profile ind]

Run-to-run (same binary, same inputs, OMP_NUM_THREADS=1): EB.dat differs at the first data value; max ~7e-4 relative.

Passes after fix

valgrind on the fixed binary: the 22 uninitialised-value reads in eval_neville_polynom are gone (remaining 1 error is an unrelated strcpy over-read, fixed separately).

5 fresh single-thread runs, EB.dat md5:

      5 8b5d3ba0f8a32aee

All byte-identical.

Notes

• A smaller, separate run-to-run nondeterminism (~1e-9, valgrind-clean) remains and is tracked separately.