==========================================================================
TEST 1 — does tracking error collapse onto R = tau/T across systems?
==========================================================================

system                       E(R=0.1)     E(R=1)    E(R=10)
1st order                      0.1001     0.7030     0.9950
2nd order zeta=0.3             0.0617     1.9259     1.0102
2nd order zeta=0.7             0.1412     1.2240     1.0100
2nd order zeta=1.0             0.1994     1.1154     1.0098
2nd order zeta=2.0             0.3766     1.0301     1.0088
3rd order spread=(1.0, 0.5, 0.25)     0.1749     1.1278     1.0047
3rd order spread=(1.0, 1.0, 1.0)     0.2977     1.2764     1.0003
3rd order spread=(1.0, 0.1, 0.01)     0.1111     0.7796     1.0509

At R = 1: min 0.7030, max 1.9259, ratio 2.74x across systems

system                       max |E - E_1st|  relative to E_1st
2nd order zeta=0.3                    1.2654             175.4%
2nd order zeta=0.7                    0.5229              75.9%
2nd order zeta=1.0                    0.4261             100.0%
2nd order zeta=2.0                    0.5206             299.7%
3rd order spread=(1.0, 0.5, 0.25)            0.4268              75.0%
3rd order spread=(1.0, 1.0, 1.0)            0.6947             200.0%
3rd order spread=(1.0, 0.1, 0.01)            0.0964              11.0%

Worst relative departure from the first-order collapse: 299.7%
Verdict: a shared single curve is NOT supported across orders and damping.

==========================================================================
TEST 2 — does a membrane selectivity reversal survive constrained isotherms?
==========================================================================

(a) free scan over surface parameters (the unconstrained case)
    crossings found in 48/600 parameter draws (1.2%)
    example crossing pressures (bar): [99.141, 24.638, 74.588, 0.174, 2.448]

(b) constrained: one shared surface coefficient, isotherm values fixed
       k_surf  crossing P* (bar)  alpha(0.1)  alpha(100)
         0.05                nan       2.732       2.751
         0.10                nan       2.741       2.778
         0.20                nan       2.758       2.825
         0.40                nan       2.793       2.905
         0.80                nan       2.863       3.021
         1.60                nan       3.001       3.162
         3.20                nan       3.275       3.298

    crossings present for 0/7 values of the one free
    coefficient.
    NO crossing survives once the surface coefficient is shared and the
    isotherm values are fixed. The reversal was an artefact of the free
    scan, in which two independent surface coefficients could be tuned
    against each other.

wrote /home/toby/Desktop/incoprea_nov3/code/../results/nov3_results.json
