C5 = 0.8551004555; Dirac arc [x_lo, x_hi] = [1.338868, 1.496900]
(1) closed-form first variations vs one-sided differences (eps = 1e-7, exact enumeration): 240 pairs (12 x on the arc, 19 atoms y and the Gaussian part), max |difference| = 2.9e-07
(2) on a 400 x 800 grid: every D(x, y) with |y - x| > 1e-3 is negative (largest -2.02e-07, at x = 1.4700); the largest off-band slope is -0.105427 at x = 1.4969, y = 0.8498; D(x_hi, 0.85-) = -0.105198
(3) residual mass r: the two-atom law at the kink, and a Nelder-Mead search (3 atoms + Gaussian part, V+ = 1 - r)
  r = 0.001: two-atom at the kink (x* = 1.49615, y = 0.85-): Phi = -0.00010598 = -0.10598 r; Nelder-Mead best Phi = -0.00010598 = -0.10598 r at x = 1.49615, (0.85000, 0.00100), (-1.03559, 0.00000), s2 = 0.00000
  r = 0.005: two-atom at the kink (x* = 1.49315, y = 0.85-): Phi = -0.00054540 = -0.10908 r; Nelder-Mead best Phi = -0.00054540 = -0.10908 r at x = 1.49315, (0.85000, 0.00500), (-0.89555, 0.00000), s2 = 0.00000
  r = 0.01 : two-atom at the kink (x* = 1.48940, y = 0.85-): Phi = -0.00112927 = -0.11293 r; Nelder-Mead best Phi = -0.00112927 = -0.11293 r at x = 1.48940, (0.85000, 0.01000), (-1.36151, 0.00000), s2 = 0.00000
  r = 0.02 : two-atom at the kink (x* = 1.48186, y = 0.85-): Phi = -0.00241016 = -0.12051 r; Nelder-Mead best Phi = -0.00241016 = -0.12051 r at x = 1.48186, (0.85000, 0.02000), (-0.30623, 0.00000), s2 = 0.00000
  r = 0.05 : two-atom at the kink (x* = 1.45900, y = 0.85-): Phi = -0.00711955 = -0.14239 r; Nelder-Mead best Phi = -0.00711955 = -0.14239 r at x = 1.45900, (0.85000, 0.05000), (-0.99744, 0.00000), s2 = 0.00000
  r = 0.1  : two-atom at the kink (x* = 1.42008, y = 0.85-): Phi = -0.01761300 = -0.17613 r; Nelder-Mead best Phi = -0.01543942 = -0.15439 r at x = 1.42024, (0.85000, 0.07048), (-1.26271, 0.02952), s2 = 0.00000
(4) two-atom laws on the lattices of a40i and a40j against the band values their searches reported
  r = 0.02, step 1/100: best two-atom law (1.48, 0.98), (0.84, 0.02): Phi = -0.0026642436; the search reported -0.0032562496 (below the two-atom law)
  r = 0.02, step 1/200: best two-atom law (1.48, 0.98), (0.845, 0.02): Phi = -0.0025542179; the search reported -0.0030130924 (below the two-atom law)
  r = 0.1, step 1/100: best two-atom law (1.47, 0.9), (0.84, 0.1): Phi = -0.0181672739; the search reported -0.0165675956 (not below the two-atom law)
  r = 0.1, step 1/200: best two-atom law (1.465, 0.9), (0.845, 0.1): Phi = -0.0175671879; the search reported -0.0159943868 (not below the two-atom law)
(5) r = 0.1: three-atom laws (x, 0.9), (0.85-, w), (z, 0.1 - w) on the lattices, the shape Nelder-Mead finds
  step 1/100: best on the grid Phi = -0.0161486806 at (1.42, 0.9), (0.84, 0.0675), (-1.27, 0.0325); the search reported -0.0165675956 (below this law)
  step 1/200: best on the grid Phi = -0.0157962750 at (1.42, 0.9), (0.845, 0.0700), (-1.255, 0.0300); the search reported -0.0159943868 (below this law)
A40L_DONE

real	0m4.589s
user	0m4.548s
sys	0m0.040s
