Part A: lowest Dirichlet eigenvalue of -d^2/dt^2 + V_l on [-T,T]  (theory: > 1 for every T, -> 1)
 l   min V (exact 1-(l-1)^2/3)     T=10          T=20          T=40          T=80
 1   +1.000000 (+1.000000)   1.08892067  1.02343081  1.00601100  1.00152228
 2   +0.666667 (+0.666667)   1.08413855  1.02271291  1.00591450  1.00150983
 3   -0.333333 (-0.333333)   1.08302198  1.02254979  1.00589255  1.00150699
 4   -2.000000 (-2.000000)   1.08258784  1.02248685  1.00588408  1.00150589
 5   -4.333333 (-4.333333)   1.08237382  1.02245594  1.00587992  1.00150535
 6   -7.333333 (-7.333333)   1.08225241  1.02243845  1.00587757  1.00150505
reference: pure V=1 on [-T,T] gives 1 + (pi/2T)^2 = ['1.02467401', '1.00616850', '1.00154213', '1.00038553']

Sanity control: V_2 - 3 sech^2(t) (a genuine well) must produce an eigenvalue < 1:
   T=40: 0.130890

Part A cross-check by FEM on the fibre z=1, x in (1e-6, 1e3) (log mesh):
  l=1  lowest generalized eigenvalue = 1.047972
  l=2  lowest generalized eigenvalue = 1.045953
  l=3  lowest generalized eigenvalue = 1.045491
  l=4  lowest generalized eigenvalue = 1.045313

Part B: ridge example f = x((z0-x)^2 + x^4), fibre z = z0, x in (z0*1e-4, 4 z0):
   z0        FEM lowest eigenvalue    ratio to z0     explicit trapezoid test function quotient (<= 873 z0 by hand)
  0.2       5.255527e-01            2.6278          1.325523e+00
  0.1       3.183217e-01            3.1832          7.901559e-01
  0.05      1.751473e-01            3.5029          4.370050e-01
  0.02      7.401360e-02            3.7007          1.864260e-01
  0.01      3.766149e-02            3.7661          9.530145e-02
  0.005     1.899250e-02            3.7985          4.818853e-02
  0.002     7.635806e-03            3.8179          1.940660e-02
  0.001     3.827398e-03            3.8274          9.725342e-03

Note: the numerator estimate uses ramp slopes 4/z0 on [z0/4,z0/2] and 2/z0 on [3z0/2,2z0] (the hand bound in
RESULT.md uses the cruder slope 4/z0 on both ramps); both quotients are O(z0) -> 0.
