=== [A] parametrisation checks ===
  a=1 b=0.5 N=5 tau=1: k=0.9385773 lam=0.148624              dev =    1.227e-40  PASS
  a=1 b=0.8 N=6 tau=1: k=0.66978757 lam=0.197531             dev =   6.6936e-41  PASS
  a=1 b=0.3 N=7 tau=1: k=0.97467501 lam=0.0420966            dev =    1.808e-40  PASS
  a=2 b=1.2 N=4 tau=1: k=0.9329523 lam=1.05882               dev =   4.1326e-40  PASS
  a=1 b=0.6 N=7 tau=2: k=0.96236575 lam=0.308966             dev =   1.6685e-40  PASS
  a=1 b=0.7 N=8 tau=3: k=0.99404377 lam=0.48387              dev =   2.5255e-40  PASS
=== [B] derived polygons: P'' on C and on the side; P^x = midpoints of P''; P'^- = midpoints of P ===
  a=1 b=0.5 N=5 tau=1                                        dev =   1.2627e-40  PASS
  a=1 b=0.8 N=6 tau=1                                        dev =   1.1479e-40  PASS
  a=2 b=1.2 N=4 tau=1                                        dev =   9.0688e-40  PASS
  a=1 b=0.6 N=7 tau=2                                        dev =   2.5255e-40  PASS
=== [C] the five rows on the real family (and controls) ===
-- a=1 b=0.5 N=3  (k=0.9971311, a''=0.86851709, b''=0.065741454)
  k808  A/A^x      (odd)  value=35.0277563773                dev =   4.1949e-41  PASS
  k810  A'/A'^-    (odd)  value=35.0277563773                dev =   1.8877e-40  PASS
  k103  A'/A       (odd, known)  value=8.75693909433         dev =   1.2585e-40  PASS
  k109  A/A''      (odd, known)  value=8.75693909433         dev =   6.2923e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=0.00732671870327  dev =    0.0016527  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=0.561841967372    dev =      0.12674  PASS
  ctrl  A*A''      (odd: must vary)  value=0.0293068748131   dev =     0.006611  PASS
-- a=1 b=0.5 N=4  (k=0.96824584, a''=0.89442719, b''=0.2236068)
  k110  A*A''      (even)  value=0.32                        dev =   5.7397e-42  PASS
  k807  A*A^x      (even)  value=0.16                        dev =   2.8699e-42  PASS
  k809  A'*A'^-    (even)  value=1.0                         dev =   2.2959e-41  PASS
  k106  A*A'       (even, known)  value=2.0                  dev =   4.5918e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=4.90442871142    dev =      0.27436  PASS
  ctrl  A'/A'^-    (even: must vary)  value=5.23138070465    dev =      0.23538  PASS
  ctrl  A/A''      (even: must vary)  value=2.45221435571    dev =      0.27436  PASS
-- a=1 b=0.5 N=5  (k=0.9385773, a''=0.92270014, b''=0.31839528)
  k808  A/A^x      (odd)  value=2.57748264084                dev =    3.563e-41  PASS
  k810  A'/A'^-    (odd)  value=2.57748264084                dev =    3.563e-41  PASS
  k103  A'/A       (odd, known)  value=1.70193433373         dev =    2.698e-41  PASS
  k109  A/A''      (odd, known)  value=1.70193433373         dev =    4.047e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=0.48596202433     dev =   0.00016053  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=1.40762811191     dev =   0.00033033  PASS
  ctrl  A*A''      (odd: must vary)  value=0.735961815327    dev =   0.00024311  PASS
-- a=1 b=0.5 N=6  (k=0.91855865, a''=0.94280904, b''=0.372678)
  k110  A*A''      (even)  value=1.09739368999               dev =   4.1843e-41  PASS
  k807  A*A^x      (even)  value=0.82304526749               dev =   3.4438e-41  PASS
  k809  A'*A'^-    (even)  value=1.66666666667               dev =   4.1326e-41  PASS
  k106  A*A'       (even, known)  value=2.22222222222        dev =   4.1326e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.89400405654    dev =     0.013725  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.90084077358    dev =     0.013594  PASS
  ctrl  A/A''      (even: must vary)  value=1.42050304241    dev =     0.013725  PASS
-- a=1 b=0.5 N=7  (k=0.90542947, a''=0.95648025, b''=0.40602274)
  k808  A/A^x      (odd)  value=1.59504821199                dev =   2.8788e-41  PASS
  k810  A'/A'^-    (odd)  value=1.59504821199                dev =   1.4394e-41  PASS
  k103  A'/A       (odd, known)  value=1.28748932147         dev =   1.7832e-41  PASS
  k109  A/A''      (odd, known)  value=1.28748932147         dev =   3.5665e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=1.11156661747     dev =    1.4828e-6  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=1.84256478589     dev =    1.4828e-6  PASS
  ctrl  A*A''      (odd: must vary)  value=1.37710062222     dev =    1.4828e-6  PASS
-- a=1 b=0.5 N=8  (k=0.89655183, a''=0.9659513, b''=0.42785735)
  k110  A*A''      (even)  value=1.58778317122               dev =   2.8919e-41  PASS
  k807  A*A^x      (even)  value=1.34427000612               dev =   1.7079e-41  PASS
  k809  A'*A'^-    (even)  value=1.96751505875               dev =   3.5007e-41  PASS
  k106  A*A'       (even, known)  value=2.32392844086        dev =   3.9517e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.42945299428    dev =    0.0011571  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.42847015242    dev =    0.0011582  PASS
  ctrl  A/A''      (even: must vary)  value=1.21022241588    dev =    0.0011571  PASS
-- a=1 b=0.5 N=9  (k=0.89032336, a''=0.97270884, b''=0.44290235)
  k808  A/A^x      (odd)  value=1.32609608697                dev =   1.7313e-41  PASS
  k810  A'/A'^-    (odd)  value=1.32609608697                dev =   3.4626e-41  PASS
  k103  A'/A       (odd, known)  value=1.16059087367         dev =   1.9782e-41  PASS
  k109  A/A''      (odd, known)  value=1.16059087367         dev =   3.9564e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=1.52884473499     dev =    7.2683e-9  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=2.05930979067     dev =    7.2683e-9  PASS
  ctrl  A*A''      (odd: must vary)  value=1.74686452103     dev =    7.2683e-9  PASS
-- a=1 b=0.5 N=10  (k=0.88580393, a''=0.97767167, b''=0.45369802)
  k110  A*A''      (even)  value=1.86845676751               dev =   2.4575e-41  PASS
  k807  A*A^x      (even)  value=1.67519145994               dev =    2.741e-41  PASS
  k809  A'*A'^-    (even)  value=2.12855383981               dev =   2.1572e-41  PASS
  k106  A*A'       (even, known)  value=2.37412315076        dev =   1.9341e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.25726472618    dev =    6.5855e-5  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.25727611603    dev =    6.5852e-5  PASS
  ctrl  A/A''      (even: must vary)  value=1.12721855213    dev =    6.5855e-5  PASS
-- a=1 b=0.5 N=11  (k=0.88242804, a''=0.98141193, b''=0.46170269)
  k808  A/A^x      (odd)  value=1.20865428855                dev =   3.7991e-41  PASS
  k810  A'/A'^-    (odd)  value=1.20865428855                dev =   3.7991e-41  PASS
  k103  A'/A       (odd, known)  value=1.10345917649         dev =   2.0806e-41  PASS
  k109  A/A''      (odd, known)  value=1.10345917649         dev =   4.1613e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=1.7919750196      dev =   4.4038e-11  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=2.1819484836      dev =   4.4038e-11  PASS
  ctrl  A*A''      (odd: must vary)  value=1.96280781253     dev =   4.4038e-11  PASS
-- a=1 b=0.5 N=12  (k=0.87984318, a''=0.98429518, b''=0.46780018)
  k110  A*A''      (even)  value=2.03715298076               dev =    4.508e-41  PASS
  k807  A*A^x      (even)  value=1.88602520506               dev =   3.6519e-41  PASS
  k809  A'*A'^-    (even)  value=2.22390384407               dev =   2.0647e-41  PASS
  k106  A*A'       (even, known)  value=2.40210593831        dev =   3.8231e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.17289816635    dev =    5.0639e-6  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.17289870954    dev =    5.0639e-6  PASS
  ctrl  A/A''      (even: must vary)  value=1.08588580514    dev =    5.0639e-6  PASS
-- a=1 b=0.8 N=3  (k=0.91036109, a''=0.65907913, b''=0.27273669)
  k808  A/A^x      (odd)  value=17.8020020018                dev =    4.127e-41  PASS
  k810  A'/A'^-    (odd)  value=17.8020020018                dev =   6.1905e-41  PASS
  k103  A'/A       (odd, known)  value=4.45050050044         dev =   6.1905e-41  PASS
  k109  A/A''      (odd, known)  value=4.45050050044         dev =    4.127e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=0.0565559359498   dev =   0.00058456  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=1.12020086163     dev =     0.010336  PASS
  ctrl  A*A''      (odd: must vary)  value=0.226223743799    dev =    0.0023382  PASS
-- a=1 b=0.8 N=4  (k=0.76837491, a''=0.78086881, b''=0.49975604)
  k110  A*A''      (even)  value=1.21832242713               dev =   1.8845e-41  PASS
  k807  A*A^x      (even)  value=0.609161213563              dev =   1.1479e-41  PASS
  k809  A'*A'^-    (even)  value=2.56                        dev =   3.5873e-41  PASS
  k106  A*A'       (even, known)  value=5.12                 dev =   1.7937e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=4.08147747339    dev =     0.029652  PASS
  ctrl  A'/A'^-    (even: must vary)  value=4.11957559121    dev =     0.029026  PASS
  ctrl  A/A''      (even: must vary)  value=2.04073873669    dev =     0.029652  PASS
-- a=1 b=0.8 N=5  (k=0.70321021, a''=0.85322993, b''=0.60663112)
  k808  A/A^x      (odd)  value=2.35922654006                dev =   1.9463e-41  PASS
  k810  A'/A'^-    (odd)  value=2.35922654006                dev =   3.8926e-41  PASS
  k103  A'/A       (odd, known)  value=1.54560752771         dev =   2.9709e-41  PASS
  k109  A/A''      (odd, known)  value=1.54560752771         dev =   2.9709e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=1.51365028318     dev =    1.3257e-6  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=3.61596314195     dev =    1.3257e-6  PASS
  ctrl  A*A''      (odd: must vary)  value=2.31044677023     dev =    1.3257e-6  PASS
-- a=1 b=0.8 N=6  (k=0.66978757, a''=0.89580642, b''=0.66518354)
  k110  A*A''      (even)  value=3.19122687184               dev =   1.4389e-41  PASS
  k807  A*A^x      (even)  value=2.39342015388               dev =   1.9185e-41  PASS
  k809  A'*A'^-    (even)  value=4.31407407407               dev =   6.3862e-41  PASS
  k106  A*A'       (even, known)  value=5.75209876543        dev =   3.1931e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.79011958304    dev =    0.0004304  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.79004566336    dev =   0.00043053  PASS
  ctrl  A/A''      (even: must vary)  value=1.34258968728    dev =    0.0004304  PASS
-- a=1 b=0.8 N=7  (k=0.65041861, a''=0.92248283, b''=0.70069578)
  k808  A/A^x      (odd)  value=1.52562713208                dev =   3.0098e-41  PASS
  k810  A'/A'^-    (odd)  value=1.52562713208                dev =   6.0195e-41  PASS
  k103  A'/A       (odd, known)  value=1.2376623992          dev =     3.71e-41  PASS
  k109  A/A''      (odd, known)  value=1.2376623992          dev =     3.71e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=3.12315177834     dev =   4.7816e-10  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=4.78406954887     dev =   4.7816e-10  PASS
  ctrl  A*A''      (odd: must vary)  value=3.84981000772     dev =   4.7816e-10  PASS
-- a=1 b=0.8 N=8  (k=0.63817492, a''=0.9401811, b''=0.72383734)
  k110  A*A''      (even)  value=4.33692116947               dev =   2.1175e-41  PASS
  k807  A*A^x      (even)  value=3.69853669575               dev =   3.7245e-41  PASS
  k809  A'*A'^-    (even)  value=5.110988554                 dev =   1.7968e-41  PASS
  k106  A*A'       (even, known)  value=5.99316872595        dev =   3.0647e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.37844916243    dev =    1.2926e-5  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.37843856493    dev =    1.2926e-5  PASS
  ctrl  A/A''      (even: must vary)  value=1.17554472661    dev =    1.2926e-5  PASS
-- a=1 b=0.8 N=9  (k=0.62993137, a''=0.95248471, b''=0.73974801)
  k808  A/A^x      (odd)  value=1.28704333904                dev =   1.7838e-41  PASS
  k810  A'/A'^-    (odd)  value=1.28704333904                dev =   1.7838e-41  PASS
  k103  A'/A       (odd, known)  value=1.13539811165         dev =   2.0221e-41  PASS
  k109  A/A''      (odd, known)  value=1.13539811165         dev =   4.0442e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=4.14684043997     dev =   2.6848e-13  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=5.34581173848     dev =   2.6848e-13  PASS
  ctrl  A*A''      (odd: must vary)  value=4.70069776543     dev =   2.6848e-13  PASS
-- a=1 b=0.8 N=10  (k=0.62411028, a''=0.96136856, b''=0.75115212)
  k110  A*A''      (even)  value=4.97674956208               dev =   3.6906e-41  PASS
  k807  A*A^x      (even)  value=4.49725124296               dev =   4.0841e-41  PASS
  k809  A'*A'^-    (even)  value=5.51939526259               dev =   4.9916e-41  PASS
  k106  A*A'       (even, known)  value=6.10787489336        dev =   3.0071e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.22594442858    dev =    2.7974e-7  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.22594457038    dev =    2.7974e-7  PASS
  ctrl  A/A''      (even: must vary)  value=1.10782751603    dev =    2.7974e-7  PASS
-- a=1 b=0.8 N=11  (k=0.61984388, a''=0.96798569, b''=0.75960272)
  k808  A/A^x      (odd)  value=1.18287639024                dev =   1.9409e-41  PASS
  k810  A'/A'^-    (odd)  value=1.18287639024                dev =   3.8819e-41  PASS
  k103  A'/A       (odd, known)  value=1.08801414456         dev =   2.1102e-41  PASS
  k109  A/A''      (odd, known)  value=1.08801414456         dev =   4.2203e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=4.77367730713     dev =   1.6221e-16  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=5.65095879817     dev =   1.6221e-16  PASS
  ctrl  A*A''      (odd: must vary)  value=5.18988673946     dev =   1.6221e-16  PASS
-- a=1 b=0.8 N=12  (k=0.61662201, a''=0.97304343, b''=0.76603754)
  k110  A*A''      (even)  value=5.35722347271               dev =   5.1427e-41  PASS
  k807  A*A^x      (even)  value=4.99422710613               dev =   1.8388e-41  PASS
  k809  A'*A'^-    (even)  value=5.75285863146               dev =   3.1927e-41  PASS
  k106  A*A'       (even, known)  value=6.17099475869        dev =   2.9764e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.15127528669    dev =    7.1794e-9  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.15127529015    dev =    7.1794e-9  PASS
  ctrl  A/A''      (even: must vary)  value=1.07326682799    dev =    7.1794e-9  PASS
-- a=1 b=0.3 N=3  (k=0.99989556, a''=0.95403885, b''=0.013788346)
  k808  A/A^x      (odd)  value=91.2227169215                dev =   1.1275e-40  PASS
  k810  A'/A'^-    (odd)  value=91.2227169215                dev =   2.4483e-39  PASS
  k103  A'/A       (odd, known)  value=22.8056792304         dev =   2.3034e-39  PASS
  k109  A/A''      (odd, known)  value=22.8056792304         dev =   9.6645e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=0.000703494303707 dev =    0.0003736  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=0.365886687493    dev =      0.19431  PASS
  ctrl  A*A''      (odd: must vary)  value=0.00281397721483  dev =    0.0014944  PASS
-- a=1 b=0.3 N=4  (k=0.99594177, a''=0.95782629, b''=0.086204366)
  k110  A*A''      (even)  value=0.0545408635637             dev =   1.4349e-42  PASS
  k807  A*A^x      (even)  value=0.0272704317818             dev =   7.1746e-43  PASS
  k809  A'*A'^-    (even)  value=0.36                        dev =   1.1479e-41  PASS
  k106  A*A'       (even, known)  value=0.72                 dev =   3.4438e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=6.85707368155    dev =      0.92518  PASS
  ctrl  A'/A'^-    (even: must vary)  value=9.27062531735    dev =      0.56853  PASS
  ctrl  A/A''      (even: must vary)  value=3.42853684078    dev =      0.92518  PASS
-- a=1 b=0.3 N=5  (k=0.98787776, a''=0.96564498, b''=0.1499007)
  k808  A/A^x      (odd)  value=3.09050066719                dev =   4.4573e-41  PASS
  k810  A'/A'^-    (odd)  value=3.09050066719                dev =   4.4573e-41  PASS
  k103  A'/A       (odd, known)  value=2.07252651563         dev =   4.4311e-41  PASS
  k109  A/A''      (odd, known)  value=2.07252651563         dev =   4.4311e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=0.118036345679    dev =   0.00048953  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=0.507009324645    dev =    0.0021027  PASS
  ctrl  A*A''      (odd: must vary)  value=0.176012901318    dev =   0.00072998  PASS
-- a=1 b=0.3 N=6  (k=0.9804017, a''=0.97300851, b''=0.19169132)
  k110  A*A''      (even)  value=0.303011616992              dev =   5.7397e-42  PASS
  k807  A*A^x      (even)  value=0.227258712744              dev =   5.7397e-42  PASS
  k809  A'*A'^-    (even)  value=0.587928994083              dev =   1.1479e-41  PASS
  k106  A*A'       (even, known)  value=0.783905325444       dev =   2.2959e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=2.13285933324    dev =     0.065139  PASS
  ctrl  A'/A'^-    (even: must vary)  value=2.15990216625    dev =     0.062699  PASS
  ctrl  A/A''      (even: must vary)  value=1.59964449993    dev =     0.065139  PASS
-- a=1 b=0.3 N=7  (k=0.97467501, a''=0.97872542, b''=0.21886855)
  k808  A/A^x      (odd)  value=1.75211563947                dev =   3.9311e-41  PASS
  k810  A'/A'^-    (odd)  value=1.75211563947                dev =   3.9311e-41  PASS
  k103  A'/A       (odd, known)  value=1.40048039433         dev =   3.2787e-41  PASS
  k109  A/A''      (odd, known)  value=1.40048039433         dev =   4.9181e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=0.32898537051     dev =     1.577e-5  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=0.645253921697    dev =     3.093e-5  PASS
  ctrl  A*A''      (odd: must vary)  value=0.411587634616    dev =    1.9729e-5  PASS
-- a=1 b=0.3 N=8  (k=0.97045328, a''=0.98298313, b''=0.23718312)
  k110  A*A''      (even)  value=0.497799014844              dev =   2.2959e-41  PASS
  k807  A*A^x      (even)  value=0.415469559916              dev =   1.1479e-41  PASS
  k809  A'*A'^-    (even)  value=0.687894828817              dev =   1.1479e-41  PASS
  k106  A*A'       (even, known)  value=0.824208079578       dev =   2.2959e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.54128198559    dev =    0.0071333  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.54219186237    dev =    0.0071011  PASS
  ctrl  A/A''      (even: must vary)  value=1.28637407701    dev =    0.0071333  PASS
-- a=1 b=0.3 N=9  (k=0.96732959, a''=0.98615737, b''=0.2500127)
  k808  A/A^x      (odd)  value=1.41249389014                dev =   3.2508e-41  PASS
  k810  A'/A'^-    (odd)  value=1.41249389014                dev =   3.2508e-41  PASS
  k103  A'/A       (odd, known)  value=1.21678251447         dev =   1.8869e-41  PASS
  k109  A/A''      (odd, known)  value=1.21678251447         dev =   3.7737e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=0.486780054235    dev =    4.2428e-7  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=0.720706924995    dev =    6.2818e-7  PASS
  ctrl  A*A''      (odd: must vary)  value=0.565075388798    dev =    4.9253e-7  PASS
-- a=1 b=0.3 N=10  (k=0.96498183, a''=0.98855664, b''=0.25931494)
  k110  A*A''      (even)  value=0.617618126718              dev =   2.2959e-41  PASS
  k807  A*A^x      (even)  value=0.545015789848              dev =   1.1479e-41  PASS
  k809  A'*A'^-    (even)  value=0.746437403593              dev =   1.1479e-41  PASS
  k106  A*A'       (even, known)  value=0.845871403189       dev =   2.2959e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.32574292025    dev =    0.0012113  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.32662145041    dev =    0.0012101  PASS
  ctrl  A/A''      (even: must vary)  value=1.1698989935     dev =    0.0012113  PASS
-- a=1 b=0.3 N=11  (k=0.96318448, a''=0.99040134, b''=0.26626079)
  k808  A/A^x      (odd)  value=1.2651569639                 dev =   3.6294e-41  PASS
  k810  A'/A'^-    (odd)  value=1.2651569639                 dev =   1.8147e-41  PASS
  k103  A'/A       (odd, known)  value=1.13763465536         dev =   2.0181e-41  PASS
  k109  A/A''      (odd, known)  value=1.13763465536         dev =   2.0181e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=0.59258122597     dev =    9.6966e-9  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=0.766926094551    dev =    1.2549e-8  PASS
  ctrl  A*A''      (odd: must vary)  value=0.659006176705    dev =    1.0783e-8  PASS
-- a=1 b=0.3 N=12  (k=0.96178345, a''=0.99184406, b''=0.27157807)
  k110  A*A''      (even)  value=0.691975224331              dev =   3.4438e-41  PASS
  k807  A*A^x      (even)  value=0.631608723568              dev =   1.1479e-41  PASS
  k809  A'*A'^-    (even)  value=0.783455687746              dev =   2.2959e-41  PASS
  k106  A*A'       (even, known)  value=0.858335081598       dev =   2.2959e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.2202067104     dev =   0.00013632  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.22016275015    dev =   0.00013633  PASS
  ctrl  A/A''      (even: must vary)  value=1.1137583771     dev =   0.00013632  PASS
-- a=2 b=1.2 N=3  (k=0.98981479, a''=1.616464, b''=0.23012159)
  k808  A/A^x      (odd)  value=25.8076127072                dev =   5.6935e-41  PASS
  k810  A'/A'^-    (odd)  value=25.8076127072                dev =   1.7081e-40  PASS
  k103  A'/A       (odd, known)  value=6.45190317681         dev =   1.4234e-40  PASS
  k109  A/A''      (odd, known)  value=6.45190317681         dev =   5.6935e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=0.280957993708    dev =     0.027904  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=11.6954537452     dev =     0.099317  PASS
  ctrl  A*A''      (odd: must vary)  value=1.12383197483     dev =     0.099317  PASS
-- a=2 b=1.2 N=4  (k=0.9329523, a''=1.7149859, b''=0.61739491)
  k110  A*A''      (even)  value=8.96885813149               dev =   4.0957e-41  PASS
  k807  A*A^x      (even)  value=4.48442906574               dev =   4.0957e-41  PASS
  k809  A'*A'^-    (even)  value=23.04                       dev =   4.7831e-41  PASS
  k106  A*A'       (even, known)  value=46.08                dev =   4.7831e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=4.37580280608    dev =      0.17413  PASS
  ctrl  A'/A'^-    (even: must vary)  value=4.7257293484     dev =      0.15357  PASS
  ctrl  A/A''      (even: must vary)  value=2.18790140304    dev =      0.17413  PASS
-- a=2 b=1.2 N=5  (k=0.88933664, a''=1.7990938, b''=0.82264109)
  k808  A/A^x      (odd)  value=2.46550323461                dev =   1.8624e-41  PASS
  k810  A'/A'^-    (odd)  value=2.46550323461                dev =   3.7248e-41  PASS
  k103  A'/A       (odd, known)  value=1.62161235021         dev =   2.8316e-41  PASS
  k109  A/A''      (odd, known)  value=1.62161235021         dev =   4.2474e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=12.3508057922     dev =    8.1215e-5  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=32.4780076199     dev =    8.1215e-5  PASS
  ctrl  A*A''      (odd: must vary)  value=18.7781942007     dev =    8.1215e-5  PASS
-- a=2 b=1.2 N=6  (k=0.86297582, a''=1.8540496, b''=0.9367497)
  k110  A*A''      (even)  value=26.9591308594               dev =   2.7252e-41  PASS
  k807  A*A^x      (even)  value=20.2193481445               dev =   1.8168e-41  PASS
  k809  A'*A'^-    (even)  value=38.61                       dev =   1.9028e-41  PASS
  k106  A*A'       (even, known)  value=51.48                dev =   2.8543e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.84337645435    dev =    0.0052988  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.8416262387     dev =    0.0053145  PASS
  ctrl  A/A''      (even: must vary)  value=1.38253234076    dev =    0.0052988  PASS
-- a=2 b=1.2 N=7  (k=0.84653698, a''=1.8900533, b''=1.0061319)
  k808  A/A^x      (odd)  value=1.55963987739                dev =   2.9441e-41  PASS
  k810  A'/A'^-    (odd)  value=1.55963987739                dev =   4.4162e-41  PASS
  k103  A'/A       (odd, known)  value=1.26206659916         dev =   1.8191e-41  PASS
  k109  A/A''      (odd, known)  value=1.26206659916         dev =   3.6383e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=26.8410874888     dev =    1.8023e-7  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=42.7528089487     dev =    1.8023e-7  PASS
  ctrl  A*A''      (odd: must vary)  value=33.1697474822     dev =    1.8023e-7  PASS
-- a=2 b=1.2 N=8  (k=0.83572292, a''=1.9145101, b''=1.0513558)
  k110  A*A''      (even)  value=37.800687864                dev =   1.9436e-41  PASS
  k807  A*A^x      (even)  value=32.1194899051               dev =   2.2873e-41  PASS
  k809  A'*A'^-    (even)  value=45.6642519479               dev =   4.8266e-41  PASS
  k106  A*A'       (even, known)  value=53.7412063369        dev =   2.7342e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.40321616478    dev =   0.00026859  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.4032830172     dev =   0.00026855  PASS
  ctrl  A/A''      (even: must vary)  value=1.19232188582    dev =   0.00026859  PASS
-- a=2 b=1.2 N=9  (k=0.82826231, a''=1.9317552, b''=1.0824408)
  k808  A/A^x      (odd)  value=1.30624720953                dev =   3.5152e-41  PASS
  k810  A'/A'^-    (odd)  value=1.30624720953                dev =   3.5152e-41  PASS
  k103  A'/A       (odd, known)  value=1.14777040293         dev =   4.0006e-41  PASS
  k109  A/A''      (odd, known)  value=1.14777040293         dev =   4.0006e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=36.2683986777     dev =   5.5135e-10  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=47.7791505399     dev =   5.5135e-10  PASS
  ctrl  A*A''      (odd: must vary)  value=41.2761075264     dev =   5.5135e-10  PASS
-- a=2 b=1.2 N=10  (k=0.82290856, a''=1.9443229, b''=1.1047134)
  k110  A*A''      (even)  value=43.9219392996               dev =   3.3454e-41  PASS
  k807  A*A^x      (even)  value=39.5344761115               dev =   1.8583e-41  PASS
  k809  A'*A'^-    (even)  value=49.3585525349               dev =   2.9769e-41  PASS
  k106  A*A'       (even, known)  value=54.8362735918        dev =   2.6796e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.24136187067    dev =    1.4404e-5  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.24136376447    dev =    1.4404e-5  PASS
  ctrl  A/A''      (even: must vary)  value=1.11735938814    dev =    1.4404e-5  PASS
-- a=2 b=1.2 N=11  (k=0.8189403, a''=1.9537444, b''=1.1212123)
  k808  A/A^x      (odd)  value=1.1955713416                 dev =   3.8407e-41  PASS
  k810  A'/A'^-    (odd)  value=1.1955713416                 dev =   3.8407e-41  PASS
  k103  A'/A       (odd, known)  value=1.09560910667         dev =   2.0955e-41  PASS
  k109  A/A''      (odd, known)  value=1.09560910667         dev =   4.1911e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=42.1258275782     dev =   1.3477e-12  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=50.5661295197     dev =   1.3477e-12  PASS
  ctrl  A*A''      (odd: must vary)  value=45.9693442552     dev =   1.3477e-12  PASS
-- a=2 b=1.2 N=12  (k=0.81591893, a''=1.9609791, b''=1.1337721)
  k110  A*A''      (even)  value=47.579404104                dev =   4.6324e-41  PASS
  k807  A*A^x      (even)  value=44.2030514304               dev =   1.6621e-41  PASS
  k809  A'*A'^-    (even)  value=51.5083023225               dev =   2.8527e-41  PASS
  k106  A*A'       (even, known)  value=55.4426504868        dev =   2.6502e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.16192824391    dev =      9.52e-7  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.1619278801     dev =    9.5201e-7  PASS
  ctrl  A/A''      (even: must vary)  value=1.07947493019    dev =      9.52e-7  PASS
-- a=1 b=0.95 N=3  (k=0.58000112, a''=0.53836085, b''=0.43855719)
  k808  A/A^x      (odd)  value=16.094737168                 dev =   2.2824e-41  PASS
  k810  A'/A'^-    (odd)  value=16.094737168                 dev =   9.1295e-41  PASS
  k103  A'/A       (odd, known)  value=4.023684292           dev =   4.5647e-41  PASS
  k109  A/A''      (odd, known)  value=4.023684292           dev =   2.2824e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=0.0942532879247   dev =    1.3193e-5  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=1.52596405692     dev =   0.00013997  PASS
  ctrl  A*A''      (odd: must vary)  value=0.377013151699    dev =     5.277e-5  PASS
-- a=1 b=0.95 N=4  (k=0.43068985, a''=0.72499943, b''=0.65431199)
  k110  A*A''      (even)  value=1.80025935858               dev =   3.8259e-41  PASS
  k807  A*A^x      (even)  value=0.90012967929               dev =   1.1479e-41  PASS
  k809  A'*A'^-    (even)  value=3.61                        dev =   2.5439e-41  PASS
  k106  A*A'       (even, known)  value=7.22                 dev =   3.8159e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=4.00578797392    dev =    0.0014449  PASS
  ctrl  A'/A'^-    (even: must vary)  value=4.00474189858    dev =    0.0014461  PASS
  ctrl  A/A''      (even: must vary)  value=2.00289398696    dev =    0.0014449  PASS
-- a=1 b=0.95 N=5  (k=0.38088837, a''=0.81979374, b''=0.75799854)
  k808  A/A^x      (odd)  value=2.33568006384                dev =   1.9659e-41  PASS
  k810  A'/A'^-    (odd)  value=2.33568006384                dev =   3.9319e-41  PASS
  k103  A'/A       (odd, known)  value=1.52879986936         dev =   1.5018e-41  PASS
  k109  A/A''      (odd, known)  value=1.52879986936         dev =   3.0035e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=2.18285572778     dev =   7.3925e-10  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=5.10183379833     dev =   7.3925e-10  PASS
  ctrl  A*A''      (odd: must vary)  value=3.33493788677     dev =   7.3925e-10  PASS
-- a=1 b=0.95 N=6  (k=0.35755094, a''=0.87330186, b''=0.81557106)
  k110  A*A''      (even)  value=4.56523530052               dev =   2.0116e-41  PASS
  k807  A*A^x      (even)  value=3.42392647539               dev =   2.6822e-41  PASS
  k809  A'*A'^-    (even)  value=6.09142998028               dev =   3.0152e-41  PASS
  k106  A*A'       (even, known)  value=8.12190664037        dev =   2.2614e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.77842765129    dev =     5.118e-6  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.77842722153    dev =     5.118e-6  PASS
  ctrl  A/A''      (even: must vary)  value=1.33382073847    dev =     5.118e-6  PASS
-- a=1 b=0.95 N=7  (k=0.34455826, a''=0.90623251, b''=0.8507393)
  k808  A/A^x      (odd)  value=1.51803581743                dev =   3.0248e-41  PASS
  k810  A'/A'^-    (odd)  value=1.51803581743                dev =   3.0248e-41  PASS
  k103  A'/A       (odd, known)  value=1.23221778457         dev =   3.7264e-41  PASS
  k109  A/A''      (odd, known)  value=1.23221778457         dev =   3.7264e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=4.45035967938     dev =   1.6603e-14  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=6.75725109839     dev =   1.6603e-14  PASS
  ctrl  A*A''      (odd: must vary)  value=5.48263909054     dev =   1.6603e-14  PASS
-- a=1 b=0.95 N=8  (k=0.33652288, a''=0.92787122, b''=0.8737534)
  k110  A*A''      (even)  value=6.16016245602               dev =   2.9816e-41  PASS
  k807  A*A^x      (even)  value=5.25778183593               dev =   3.4933e-41  PASS
  k809  A'*A'^-    (even)  value=7.219325192                 dev =   3.8162e-41  PASS
  k106  A*A'       (even, known)  value=8.45836084366        dev =   2.1715e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.37289279141    dev =    2.7108e-8  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.37289279592    dev =    2.7108e-8  PASS
  ctrl  A/A''      (even: must vary)  value=1.17178253543    dev =    2.7108e-8  PASS
-- a=1 b=0.95 N=9  (k=0.33118483, a''=0.94282669, b''=0.88961911)
  k808  A/A^x      (odd)  value=1.28273843792                dev =   1.7898e-41  PASS
  k810  A'/A'^-    (odd)  value=1.28273843792                dev =   3.5797e-41  PASS
  k103  A'/A       (odd, known)  value=1.13262888149         dev =    2.027e-41  PASS
  k109  A/A''      (odd, known)  value=1.13262888149         dev =   4.0541e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=5.88563663541     dev =   5.8678e-19  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=7.55037826458     dev =   5.8678e-19  PASS
  ctrl  A*A''      (odd: must vary)  value=6.66567175471     dev =   5.8678e-19  PASS
-- a=1 b=0.95 N=10  (k=0.32744878, a''=0.95358395, b''=0.90101185)
  k110  A*A''      (even)  value=7.04904214446               dev =   3.9084e-41  PASS
  k807  A*A^x      (even)  value=6.37559822008               dev =   2.8808e-41  PASS
  k809  A'*A'^-    (even)  value=7.79451841321               dev =   2.3564e-41  PASS
  k106  A*A'       (even, known)  value=8.61784053729        dev =   4.2626e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.22248443901    dev =   1.6167e-10  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.22248443906    dev =   1.6167e-10  PASS
  ctrl  A/A''      (even: must vary)  value=1.10569201513    dev =   1.6167e-10  PASS
-- a=1 b=0.95 N=11  (k=0.32472753, a''=0.96157508, b''=0.90946503)
  k808  A/A^x      (odd)  value=1.18002553024                dev =   3.8913e-41  PASS
  k810  A'/A'^-    (odd)  value=1.18002553024                dev =   3.8913e-41  PASS
  k103  A'/A       (odd, known)  value=1.08631156643         dev =   6.3404e-41  PASS
  k109  A/A''      (odd, known)  value=1.08631156643         dev =   2.1135e-41  PASS
  ctrl  A*A^x      (odd: must vary)  value=6.76160187787     dev =    1.611e-23  PASS
  ctrl  A'*A'^-    (odd: must vary)  value=7.9791825914      dev =    1.611e-23  PASS
  ctrl  A*A''      (odd: must vary)  value=7.34491198268     dev =    1.611e-23  PASS
-- a=1 b=0.95 N=12  (k=0.32268183, a''=0.96767117, b''=0.91590802)
  k110  A*A''      (even)  value=7.57713043854               dev =    3.636e-41  PASS
  k807  A*A^x      (even)  value=7.06924912114               dev =   2.5982e-41  PASS
  k809  A'*A'^-    (even)  value=8.12196604333               dev =   2.2614e-41  PASS
  k106  A*A'       (even, known)  value=8.7054784848         dev =   4.2197e-41  PASS
  ctrl  A/A^x      (even: must vary)  value=1.14888198231    dev =   9.9927e-13  PASS
  ctrl  A'/A'^-    (even: must vary)  value=1.14888198231    dev =   9.9927e-13  PASS
  ctrl  A/A''      (even: must vary)  value=1.07187450574    dev =   9.9927e-13  PASS
=== [D] structural theorem: even N products/ratios; odd N proportionality ===
-- a=1 b=0.5 N=3
  ratio Ap/A constant  value=8.75693909433                   dev =   2.5169e-40  PASS
  ratio App/A constant  value=0.114195153036                 dev =   4.3048e-42  PASS
  ratio Aox/A constant  value=0.0285487882589                dev =   1.4349e-42  PASS
  ratio Aom/A constant  value=0.25                           dev =   1.4349e-41  PASS
  ratio A2/A constant  value=-1.0                            dev =          0.0  PASS
  ratio App2/A constant  value=-0.114195153036               dev =   4.3048e-42  PASS
  ctrl product A*Ap (odd: must vary)                         dev =      0.20995  PASS
-- a=1 b=0.5 N=4
  product A*Ap constant                                      dev =   4.5918e-41  PASS
  product A*App constant                                     dev =   5.7397e-42  PASS
  product A*App2 constant                                    dev =          0.0  PASS
  product A*Aox constant                                     dev =   5.7397e-42  PASS
  product Aom*Ap constant                                    dev =   2.2959e-41  PASS
  product Aom*App constant                                   dev =   5.7397e-42  PASS
  product Aom*App2 constant                                  dev =          0.0  PASS
  product Aom*Aox constant                                   dev =   1.4349e-42  PASS
  ratio A/Aom constant  value=2.0                            dev =   4.5918e-41  PASS
  ratio Ap/App constant  value=6.25                          dev =   2.9387e-41  PASS
  ratio Ap/Aox constant  value=12.5                          dev =   4.4081e-41  PASS
  ratio App/Aox constant  value=2.0                          dev =   4.5918e-41  PASS
  ctrl product A*Aom (same group: must vary)                 dev =      0.10277  PASS
  ctrl ratio A/App (across groups: must vary)                dev =      0.24309  PASS
-- a=1 b=0.5 N=5
  ratio Ap/A constant  value=1.70193433373                   dev =    4.047e-41  PASS
  ratio App/A constant  value=0.587566735204                 dev =   3.4438e-41  PASS
  ratio Aox/A constant  value=0.38797545487                  dev =   1.7219e-41  PASS
  ratio Aom/A constant  value=0.660308747287                 dev =   2.2959e-41  PASS
  ratio A2/A constant  value=0.641234989147                  dev =   1.1479e-41  PASS
  ratio App2/A constant  value=0.376768349072                dev =   1.1479e-41  PASS
  ctrl product A*Ap (odd: must vary)                         dev =   0.00030635  PASS
-- a=1 b=0.5 N=6
  product A*Ap constant                                      dev =   2.0663e-41  PASS
  product A*App constant                                     dev =   2.0921e-41  PASS
  product A*App2 constant                                    dev =   2.0921e-41  PASS
  product A*Aox constant                                     dev =   2.2959e-41  PASS
  product A2*Ap constant                                     dev =   4.1326e-41  PASS
  product A2*App constant                                    dev =   4.1843e-41  PASS
  product A2*App2 constant                                   dev =   2.0921e-41  PASS
  product A2*Aox constant                                    dev =   3.4438e-41  PASS
  product Aom*Ap constant                                    dev =   5.5101e-41  PASS
  product Aom*App constant                                   dev =   3.4438e-41  PASS
  product Aom*App2 constant                                  dev =   2.2959e-41  PASS
  product Aom*Aox constant                                   dev =   2.2959e-41  PASS
  ratio A/A2 constant  value=1.0                             dev =   2.2959e-41  PASS
  ratio A/Aom constant  value=1.33333333333                  dev =   3.4438e-41  PASS
  ratio A2/Aom constant  value=1.33333333333                 dev =   3.4438e-41  PASS
  ratio Ap/App constant  value=2.025                         dev =   4.5351e-41  PASS
  ratio Ap/App2 constant  value=2.025                        dev =   2.2675e-41  PASS
  ratio Ap/Aox constant  value=2.7                           dev =   1.7007e-41  PASS
  ratio App/App2 constant  value=1.0                         dev =   2.2959e-41  PASS
  ratio App/Aox constant  value=1.33333333333                dev =   3.4438e-41  PASS
  ratio App2/Aox constant  value=1.33333333333               dev =   3.4438e-41  PASS
  ctrl product A*Aom (same group: must vary)                 dev =     0.013687  PASS
  ctrl ratio A/App (across groups: must vary)                dev =     0.013687  PASS
-- a=1 b=0.5 N=7
  ratio Ap/A constant  value=1.28748932147                   dev =   1.7832e-41  PASS
  ratio App/A constant  value=0.776705471123                 dev =   2.2959e-41  PASS
  ratio Aox/A constant  value=0.626940297154                 dev =   2.2959e-41  PASS
  ratio Aom/A constant  value=0.807178937786                 dev =   3.4438e-41  PASS
  ratio A2/A constant  value=1.22871575115                   dev =   1.8685e-41  PASS
  ratio App2/A constant  value=0.95435024637                 dev =   3.4438e-41  PASS
  ctrl product A*Ap (odd: must vary)                         dev =    1.3431e-6  PASS
-- a=1 b=0.5 N=8
  product A*Ap constant                                      dev =   3.9517e-41  PASS
  product A*App constant                                     dev =   4.3379e-41  PASS
  product A*App2 constant                                    dev =   2.0857e-41  PASS
  product A*Aox constant                                     dev =   3.4158e-41  PASS
  product A2*Ap constant                                     dev =   2.8501e-41  PASS
  product A2*App constant                                    dev =   2.0857e-41  PASS
  product A2*App2 constant                                   dev =   4.5128e-41  PASS
  product A2*Aox constant                                    dev =   2.4636e-41  PASS
  product Aom*Ap constant                                    dev =   3.5007e-41  PASS
  product Aom*App constant                                   dev =   3.4158e-41  PASS
  product Aom*App2 constant                                  dev =   2.4636e-41  PASS
  product Aom*Aox constant                                   dev =   2.0173e-41  PASS
  ratio A/A2 constant  value=0.721223394695                  dev =   1.1479e-41  PASS
  ratio A/Aom constant  value=1.18114899834                  dev =   3.8875e-41  PASS
  ratio A2/Aom constant  value=1.63770200333                 dev =   4.2057e-41  PASS
  ratio Ap/App constant  value=1.46363085526                 dev =   3.1372e-41  PASS
  ratio Ap/App2 constant  value=1.05560481401                dev =   2.1749e-41  PASS
  ratio Ap/Aox constant  value=1.72876611862                 dev =   2.6561e-41  PASS
  ratio App/App2 constant  value=0.721223394695              dev =   1.1479e-41  PASS
  ratio App/Aox constant  value=1.18114899834                dev =   3.8875e-41  PASS
  ratio App2/Aox constant  value=1.63770200333               dev =   4.2057e-41  PASS
  ctrl product A*Aom (same group: must vary)                 dev =   0.00093388  PASS
  ctrl ratio A/App (across groups: must vary)                dev =   0.00093388  PASS
-- a=1 b=0.5 N=9
  ratio Ap/A constant  value=1.16059087367                   dev =   3.9564e-41  PASS
  ratio App/A constant  value=0.861630073687                 dev =   3.4438e-41  PASS
  ratio Aox/A constant  value=0.754093168533                 dev =   1.1479e-41  PASS
  ratio Aom/A constant  value=0.875193649296                 dev =   2.2959e-41  PASS
  ratio A2/A constant  value=1.50077459718                   dev =   1.5298e-41  PASS
  ratio App2/A constant  value=1.29311252676                 dev =   3.5509e-41  PASS
  ctrl product A*Ap (odd: must vary)                         dev =    6.3007e-9  PASS
-- a=1 b=0.5 N=10
  product A*Ap constant                                      dev =   1.9341e-41  PASS
  product A*App constant                                     dev =   2.4575e-41  PASS
  product A*App2 constant                                    dev =   3.0985e-41  PASS
  product A*Aox constant                                     dev =    2.741e-41  PASS
  product A2*Ap constant                                     dev =   1.2193e-41  PASS
  product A2*App constant                                    dev =   1.5493e-41  PASS
  product A2*App2 constant                                   dev =   1.9534e-41  PASS
  product A2*Aox constant                                    dev =    1.728e-41  PASS
  product Aom*Ap constant                                    dev =   2.1572e-41  PASS
  product Aom*App constant                                   dev =    2.741e-41  PASS
  product Aom*App2 constant                                  dev =    3.456e-41  PASS
  product Aom*Aox constant                                   dev =   3.0573e-41  PASS
  ratio A/A2 constant  value=0.630414938192                  dev =   2.2959e-41  PASS
  ratio A/Aom constant  value=1.11536908598                  dev =   4.1168e-41  PASS
  ratio A2/Aom constant  value=1.76926182805                 dev =   2.5953e-41  PASS
  ratio Ap/App constant  value=1.27063317281                 dev =   1.8069e-41  PASS
  ratio Ap/App2 constant  value=0.801026133102               dev =   2.2959e-41  PASS
  ratio Ap/Aox constant  value=1.41722496057                 dev =     3.24e-41  PASS
  ratio App/App2 constant  value=0.630414938192              dev =   1.1479e-41  PASS
  ratio App/Aox constant  value=1.11536908598                dev =   2.0584e-41  PASS
  ratio App2/Aox constant  value=1.76926182805               dev =   2.5953e-41  PASS
  ctrl product A*Aom (same group: must vary)                 dev =    6.7575e-5  PASS
  ctrl ratio A/App (across groups: must vary)                dev =    6.7575e-5  PASS
-- a=1 b=0.8 N=3
  ratio Ap/A constant  value=4.45050050044                   dev =    4.127e-41  PASS
  ratio App/A constant  value=0.224693829357                 dev =   2.8699e-42  PASS
  ratio Aox/A constant  value=0.0561734573392                dev =   1.4349e-42  PASS
  ratio Aom/A constant  value=0.25                           dev =   5.7397e-42  PASS
  ratio A2/A constant  value=-1.0                            dev =   2.2959e-41  PASS
  ratio App2/A constant  value=-0.224693829357               dev =   2.8699e-42  PASS
  ctrl product A*Ap (odd: must vary)                         dev =     0.013212  PASS
-- a=1 b=0.8 N=4
  product A*Ap constant                                      dev =   1.7937e-41  PASS
  product A*App constant                                     dev =   1.8845e-41  PASS
  product A*App2 constant                                    dev =          0.0  PASS
  product A*Aox constant                                     dev =   1.1479e-41  PASS
  product Aom*Ap constant                                    dev =   1.7937e-41  PASS
  product Aom*App constant                                   dev =   2.2959e-41  PASS
  product Aom*App2 constant                                  dev =          0.0  PASS
  product Aom*Aox constant                                   dev =   1.1479e-41  PASS
  ratio A/Aom constant  value=2.0                            dev =   3.4438e-41  PASS
  ratio Ap/App constant  value=4.2025                        dev =   4.3705e-41  PASS
  ratio Ap/Aox constant  value=8.405                         dev =   2.1853e-41  PASS
  ratio App/Aox constant  value=2.0                          dev =   3.4438e-41  PASS
  ctrl product A*Aom (same group: must vary)                 dev =     0.029653  PASS
  ctrl ratio A/App (across groups: must vary)                dev =     0.029653  PASS
-- a=1 b=0.8 N=5
  ratio Ap/A constant  value=1.54560752771                   dev =   1.4854e-41  PASS
  ratio App/A constant  value=0.646994778476                 dev =   1.1479e-41  PASS
  ratio Aox/A constant  value=0.42386773081                  dev =   5.7397e-42  PASS
  ratio Aom/A constant  value=0.655133155492                 dev =   1.1479e-41  PASS
  ratio A2/A constant  value=0.62053262197                   dev =   1.1479e-41  PASS
  ratio App2/A constant  value=0.401481366288                dev =   1.1479e-41  PASS
  ctrl product A*Ap (odd: must vary)                         dev =    1.1365e-6  PASS
-- a=1 b=0.8 N=6
  product A*Ap constant                                      dev =   1.5966e-41  PASS
  product A*App constant                                     dev =   2.8777e-41  PASS
  product A*App2 constant                                    dev =   1.4389e-41  PASS
  product A*Aox constant                                     dev =    3.837e-41  PASS
  product A2*Ap constant                                     dev =   3.1931e-41  PASS
  product A2*App constant                                    dev =   4.3166e-41  PASS
  product A2*App2 constant                                   dev =   1.4389e-41  PASS
  product A2*Aox constant                                    dev =   5.7555e-41  PASS
  product Aom*Ap constant                                    dev =   2.1287e-41  PASS
  product Aom*App constant                                   dev =    3.837e-41  PASS
  product Aom*App2 constant                                  dev =    3.837e-41  PASS
  product Aom*Aox constant                                   dev =    3.837e-41  PASS
  ratio A/A2 constant  value=1.0                             dev =   2.2959e-41  PASS
  ratio A/Aom constant  value=1.33333333333                  dev =   3.4438e-41  PASS
  ratio A2/Aom constant  value=1.33333333333                 dev =   3.4438e-41  PASS
  ratio Ap/App constant  value=1.80247252747                 dev =   2.5475e-41  PASS
  ratio Ap/App2 constant  value=1.80247252747                dev =   2.5475e-41  PASS
  ratio Ap/Aox constant  value=2.4032967033                  dev =   3.8212e-41  PASS
  ratio App/App2 constant  value=1.0                         dev =   2.2959e-41  PASS
  ratio App/Aox constant  value=1.33333333333                dev =   3.4438e-41  PASS
  ratio App2/Aox constant  value=1.33333333333               dev =   5.1657e-41  PASS
  ctrl product A*Aom (same group: must vary)                 dev =    0.0004638  PASS
  ctrl ratio A/App (across groups: must vary)                dev =    0.0004638  PASS
-- a=1 b=0.8 N=7
  ratio Ap/A constant  value=1.2376623992                    dev =    1.855e-41  PASS
  ratio App/A constant  value=0.807974776195                 dev =   2.2959e-41  PASS
  ratio Aox/A constant  value=0.655468154029                 dev =   2.2959e-41  PASS
  ratio Aom/A constant  value=0.811248288116                 dev =   2.2959e-41  PASS
  ratio A2/A constant  value=1.24499315246                   dev =   1.8441e-41  PASS
  ratio App2/A constant  value=1.00592306373                 dev =   4.5647e-41  PASS
  ctrl product A*Ap (odd: must vary)                         dev =   5.5559e-10  PASS
-- a=1 b=0.8 N=8
  product A*Ap constant                                      dev =   3.0647e-41  PASS
  product A*App constant                                     dev =   2.1175e-41  PASS
  product A*App2 constant                                    dev =    3.001e-41  PASS
  product A*Aox constant                                     dev =   3.7245e-41  PASS
  product A2*Ap constant                                     dev =   4.3433e-41  PASS
  product A2*App constant                                    dev =   4.5015e-41  PASS
  product A2*App2 constant                                   dev =   4.2531e-41  PASS
  product A2*Aox constant                                    dev =    3.519e-41  PASS
  product Aom*Ap constant                                    dev =   3.5936e-41  PASS
  product Aom*App constant                                   dev =    2.483e-41  PASS
  product Aom*App2 constant                                  dev =   1.7595e-41  PASS
  product Aom*Aox constant                                   dev =   4.3674e-41  PASS
  ratio A/A2 constant  value=0.70861199947                   dev =   3.4438e-41  PASS
  ratio A/Aom constant  value=1.17260460724                  dev =   3.9159e-41  PASS
  ratio A2/Aom constant  value=1.65479078553                 dev =   4.1623e-41  PASS
  ratio Ap/App constant  value=1.38189478014                 dev =   1.6614e-41  PASS
  ratio Ap/App2 constant  value=0.979227223209               dev =   2.2959e-41  PASS
  ratio Ap/Aox constant  value=1.6204161859                  dev =   4.2506e-41  PASS
  ratio App/App2 constant  value=0.70861199947               dev =   1.1479e-41  PASS
  ratio App/Aox constant  value=1.17260460724                dev =   5.8738e-41  PASS
  ratio App2/Aox constant  value=1.65479078553               dev =   4.1623e-41  PASS
  ctrl product A*Aom (same group: must vary)                 dev =    9.3893e-6  PASS
  ctrl ratio A/App (across groups: must vary)                dev =    9.3893e-6  PASS
-- a=1 b=0.8 N=9
  ratio Ap/A constant  value=1.13539811165                   dev =   2.0221e-41  PASS
  ratio App/A constant  value=0.880748338173                 dev =   2.2959e-41  PASS
  ratio Aox/A constant  value=0.776974612797                 dev =   2.2959e-41  PASS
  ratio Aom/A constant  value=0.882175508169                 dev =   4.5918e-41  PASS
  ratio A2/A constant  value=1.52870203268                   dev =   3.0037e-41  PASS
  ratio App2/A constant  value=1.34640177484                 dev =   3.4104e-41  PASS
  ctrl product A*Ap (odd: must vary)                         dev =   2.7975e-13  PASS
-- a=1 b=0.8 N=10
  product A*Ap constant                                      dev =   6.0142e-41  PASS
  product A*App constant                                     dev =   5.5359e-41  PASS
  product A*App2 constant                                    dev =   2.2857e-41  PASS
  product A*Aox constant                                     dev =    2.042e-41  PASS
  product A2*Ap constant                                     dev =   3.7249e-41  PASS
  product A2*App constant                                    dev =   2.2857e-41  PASS
  product A2*App2 constant                                   dev =    4.247e-41  PASS
  product A2*Aox constant                                    dev =   2.5294e-41  PASS
  product Aom*Ap constant                                    dev =   3.3277e-41  PASS
  product Aom*App constant                                   dev =   4.0841e-41  PASS
  product Aom*App2 constant                                  dev =   2.5294e-41  PASS
  product Aom*Aox constant                                   dev =   2.2598e-41  PASS
  ratio A/A2 constant  value=0.61934489955                   dev =   1.1479e-41  PASS
  ratio A/Aom constant  value=1.10662030943                  dev =   4.1494e-41  PASS
  ratio A2/Aom constant  value=1.78675938114                 dev =   3.8548e-41  PASS
  ratio Ap/App constant  value=1.22728194722                 dev =   3.7414e-41  PASS
  ratio Ap/App2 constant  value=0.760110814319               dev =   2.2959e-41  PASS
  ratio Ap/Aox constant  value=1.35813512819                 dev =   3.3809e-41  PASS
  ratio App/App2 constant  value=0.61934489955               dev =   2.2959e-41  PASS
  ratio App/Aox constant  value=1.10662030943                dev =   2.0747e-41  PASS
  ratio App2/Aox constant  value=1.78675938114               dev =   2.5699e-41  PASS
  ctrl product A*Aom (same group: must vary)                 dev =    2.3982e-7  PASS
  ctrl ratio A/App (across groups: must vary)                dev =    2.3982e-7  PASS
=== [E] complex phases: symmetries, oddness at the singular phases, simple poles, constancy ===
-- a=1 b=0.5 N=6 tau=1
  periods h, 2K; anti-period 2iK'; evenness in u             dev =   2.3623e-41  PASS
  oddness X(p+e) = -X(p-e) at S0: p=iK'                      dev =   1.2532e-39  PASS
  oddness X(p+e) = -X(p-e) at S1: p=iK'-Delta                dev =   2.9786e-38  PASS
  pole-order estimates at S0 (+1 = simple pole, 0 = regular or identically 0, -1 = simple zero): A:1.0 Ap:-1.0 App:-1.0 Aox:-1.0 Aom:1.0 A2:1.0 App2:-1.0
  pole-order estimates at S1 (+1 = simple pole, 0 = regular or identically 0, -1 = simple zero): A:-1.0 Ap:1.0 App:1.0 Aox:1.0 Aom:-1.0 A2:-1.0 App2:1.0
  complex: product A*App constant                            dev =   2.5909e-41  PASS
  complex: product A*Aox constant                            dev =    2.574e-41  PASS
  complex: product Ap*Aom constant                           dev =    2.775e-41  PASS
  complex: product A*Ap constant                             dev =   3.2778e-41  PASS
  complex: ratio Ap/App constant                             dev =   4.6475e-41  PASS
  complex: ratio Ap/Aox constant                             dev =   3.8029e-41  PASS
  complex: ratio A/Aom constant                              dev =   3.8672e-41  PASS
-- a=1 b=0.8 N=8 tau=1
  periods h, 2K; anti-period 2iK'; evenness in u             dev =   1.1145e-40  PASS
  oddness X(p+e) = -X(p-e) at S0: p=iK'                      dev =   4.3719e-39  PASS
  oddness X(p+e) = -X(p-e) at S1: p=iK'-Delta                dev =   9.2768e-38  PASS
  pole-order estimates at S0 (+1 = simple pole, 0 = regular or identically 0, -1 = simple zero): A:1.0 Ap:-1.0 App:-1.0 Aox:-1.0 Aom:1.0 A2:1.0 App2:-1.0
  pole-order estimates at S1 (+1 = simple pole, 0 = regular or identically 0, -1 = simple zero): A:-1.0 Ap:1.0 App:1.0 Aox:1.0 Aom:-1.0 A2:-1.0 App2:1.0
  complex: product A*App constant                            dev =    2.369e-41  PASS
  complex: product A*Aox constant                            dev =   3.8644e-41  PASS
  complex: product Ap*Aom constant                           dev =   3.6346e-41  PASS
  complex: product A*Ap constant                             dev =   3.0652e-41  PASS
  complex: ratio Ap/App constant                             dev =   3.7519e-41  PASS
  complex: ratio Ap/Aox constant                             dev =   5.7901e-41  PASS
  complex: ratio A/Aom constant                              dev =   2.1273e-41  PASS
-- a=1 b=0.5 N=5 tau=1
  periods h, 2K; anti-period 2iK'; evenness in u             dev =   2.0695e-40  PASS
  oddness X(p+e) = -X(p-e) at S0: p=iK'                      dev =   7.1307e-38  PASS
  oddness X(p+e) = -X(p-e) at S1: p=iK'-Delta                dev =    7.907e-38  PASS
  pole-order estimates at S0 (+1 = simple pole, 0 = regular or identically 0, -1 = simple zero): A:1.0 Ap:1.0 App:1.0 Aox:1.0 Aom:1.0 A2:1.0 App2:1.0
  pole-order estimates at S1 (+1 = simple pole, 0 = regular or identically 0, -1 = simple zero): A:1.0 Ap:1.0 App:1.0 Aox:1.0 Aom:1.0 A2:1.0 App2:1.0
  complex: ratio Ap/A constant                               dev =   9.5289e-41  PASS
  complex: ratio App/A constant                              dev =   2.5992e-41  PASS
  complex: ratio Aox/A constant                              dev =   1.8456e-41  PASS
  complex: ratio Aom/A constant                              dev =   4.5962e-41  PASS
-- a=1 b=0.7 N=7 tau=1
  periods h, 2K; anti-period 2iK'; evenness in u             dev =   2.0535e-40  PASS
  oddness X(p+e) = -X(p-e) at S0: p=iK'                      dev =   7.6681e-38  PASS
  oddness X(p+e) = -X(p-e) at S1: p=iK'-Delta                dev =   7.4674e-38  PASS
  pole-order estimates at S0 (+1 = simple pole, 0 = regular or identically 0, -1 = simple zero): A:1.001 Ap:1.001 App:1.001 Aox:1.001 Aom:1.001 A2:1.001 App2:1.001
  pole-order estimates at S1 (+1 = simple pole, 0 = regular or identically 0, -1 = simple zero): A:1.001 Ap:1.001 App:1.001 Aox:1.001 Aom:1.001 A2:1.001 App2:1.001
  complex: ratio Ap/A constant                               dev =   1.1589e-40  PASS
  complex: ratio App/A constant                              dev =   6.0606e-41  PASS
  complex: ratio Aox/A constant                              dev =   3.0152e-41  PASS
  complex: ratio Aom/A constant                              dev =   5.7751e-41  PASS
-- a=1 b=0.6 N=7 tau=2
  periods h, 2K; anti-period 2iK'; evenness in u             dev =   9.6782e-40  PASS
  oddness X(p+e) = -X(p-e) at S0: p=iK'                      dev =   3.1449e-37  PASS
  oddness X(p+e) = -X(p-e) at S1: p=iK'-Delta                dev =   5.6761e-39  PASS
  pole-order estimates at S0 (+1 = simple pole, 0 = regular or identically 0, -1 = simple zero): A:1.0 Ap:1.0 App:1.0 Aox:1.0 Aom:1.0 A2:1.0 App2:1.0
  pole-order estimates at S1 (+1 = simple pole, 0 = regular or identically 0, -1 = simple zero): A:1.0 Ap:1.0 App:1.0 Aox:1.0 Aom:1.0 A2:1.0 App2:1.0
  complex: ratio Ap/A constant                               dev =   1.3579e-39  PASS
  complex: ratio App/A constant                              dev =   2.1535e-40  PASS
  complex: ratio Aox/A constant                              dev =   8.8556e-41  PASS
  complex: ratio Aom/A constant                              dev =   7.7675e-41  PASS
-- a=1 b=0.7 N=8 tau=3
  periods h, 2K; anti-period 2iK'; evenness in u             dev =   1.6934e-38  PASS
  oddness X(p+e) = -X(p-e) at S0: p=iK'                      dev =   1.0333e-38  PASS
  oddness X(p+e) = -X(p-e) at S1: p=iK'-Delta                dev =   2.0689e-36  PASS
  pole-order estimates at S0 (+1 = simple pole, 0 = regular or identically 0, -1 = simple zero): A:1.0 Ap:-1.0 App:-1.0 Aox:-1.0 Aom:1.0 A2:1.0 App2:-1.0
  pole-order estimates at S1 (+1 = simple pole, 0 = regular or identically 0, -1 = simple zero): A:-1.0 Ap:1.0 App:1.0 Aox:1.0 Aom:-1.0 A2:-1.0 App2:1.0
  complex: product A*App constant                            dev =   1.1014e-40  PASS
  complex: product A*Aox constant                            dev =   1.9884e-41  PASS
  complex: product Ap*Aom constant                           dev =   2.7416e-39  PASS
  complex: product A*Ap constant                             dev =   2.6246e-39  PASS
  complex: ratio Ap/App constant                             dev =   2.5902e-39  PASS
  complex: ratio Ap/Aox constant                             dev =   2.6011e-39  PASS
  complex: ratio A/Aom constant                              dev =   2.1505e-40  PASS
-- a=2 b=1.2 N=4 tau=1
  periods h, 2K; anti-period 2iK'; evenness in u             dev =   3.6806e-40  PASS
  oddness X(p+e) = -X(p-e) at S0: p=iK'                      dev =   3.2562e-39  PASS
  oddness X(p+e) = -X(p-e) at S1: p=iK'-Delta                dev =   2.7699e-38  PASS
  pole-order estimates at S0 (+1 = simple pole, 0 = regular or identically 0, -1 = simple zero): A:1.0 Ap:-1.0 App:-1.0 Aox:-1.0 Aom:1.0 A2:0.0 App2:0.0
  pole-order estimates at S1 (+1 = simple pole, 0 = regular or identically 0, -1 = simple zero): A:-1.0 Ap:1.0 App:1.0 Aox:1.0 Aom:-1.0 A2:0.0 App2:0.0
  complex: product A*App constant                            dev =   4.3572e-41  PASS
  complex: product A*Aox constant                            dev =   2.0558e-41  PASS
  complex: product Ap*Aom constant                           dev =   1.7332e-41  PASS
  complex: product A*Ap constant                             dev =   4.8689e-41  PASS
  complex: ratio Ap/App constant                             dev =   7.1661e-41  PASS
  complex: ratio Ap/Aox constant                             dev =   7.2319e-41  PASS
  complex: ratio A/Aom constant                              dev =   4.6666e-41  PASS
=== [F] N = 4 closed forms ===
  a=1 b=0.5: AA''=8a^4b^4/(a^2+b^2)^2, AA^x=4a^4b^4/(a^2+b^2)^2, A'A'^-=4a^2b^2, AA'=8a^2b^2, A'/A''=(a^2+b^2)^2/(a^2b^2), lam dev =   3.8571e-39  PASS
  a=2 b=1.2: AA''=8a^4b^4/(a^2+b^2)^2, AA^x=4a^4b^4/(a^2+b^2)^2, A'A'^-=4a^2b^2, AA'=8a^2b^2, A'/A''=(a^2+b^2)^2/(a^2b^2), lam dev =   6.4285e-39  PASS
  a=3 b=1: AA''=8a^4b^4/(a^2+b^2)^2, AA^x=4a^4b^4/(a^2+b^2)^2, A'A'^-=4a^2b^2, AA'=8a^2b^2, A'/A''=(a^2+b^2)^2/(a^2b^2), lam dev =   3.9673e-38  PASS
=== [G] half-shift reductions (Lemma 2.1/2.5 of RESULT.md), equivalences of rows, residue and gamma formulas ===
  a=1 b=0.5 N=3 tau=1: half-shift identities and row equivalences dev =   3.4203e-46  PASS
    residue check |eps F(iK'+eps) - rho|/|rho| = 5.95e-13 (eps ~ 1e-6: expect ~1e-12);  gamma = -1.0;  |G/F - gamma| = 0.0;  |k808 - 4 kappa/(2+gamma)| = 1.71e-46
      gamma formula and k808 = k810 = 4 kappa/(2+gamma)      dev =   1.7071e-46  PASS
  a=1 b=0.5 N=4 tau=1: half-shift identities and row equivalences dev =   2.3064e-48  PASS
    c1 = F(u)F(u+Delta) = 0.8, c2 = F(u)G(u+Delta) = 0.0, kappa = 2.5
      k110 = c1/kappa, k106 = kappa c1, k807 = (c1/2+c2/4)/kappa, k809 = kappa (c1/2+c2/4) dev =   3.7419e-49  PASS
  a=1 b=0.8 N=5 tau=1: half-shift identities and row equivalences dev =   1.8175e-49  PASS
    residue check |eps F(iK'+eps) - rho|/|rho| = 7.51e-12 (eps ~ 1e-6: expect ~1e-12);  gamma = 0.620532621969501;  |G/F - gamma| = 1.34e-51;  |k808 - 4 kappa/(2+gamma)| = 8.55e-50
      gamma formula and k808 = k810 = 4 kappa/(2+gamma)      dev =   8.5528e-50  PASS
  a=1 b=0.5 N=6 tau=1: half-shift identities and row equivalences dev =   5.0783e-49  PASS
    c1 = F(u)F(u+Delta) = 1.56161859761401, c2 = F(u)G(u+Delta) = 1.56161859761401, kappa = 1.42302494707577
      k110 = c1/kappa, k106 = kappa c1, k807 = (c1/2+c2/4)/kappa, k809 = kappa (c1/2+c2/4) dev =   2.6193e-49  PASS
  a=1 b=0.7 N=7 tau=1: half-shift identities and row equivalences dev =   9.5685e-49  PASS
    residue check |eps F(iK'+eps) - rho|/|rho| = 1.35e-11 (eps ~ 1e-6: expect ~1e-12);  gamma = 1.24194894936993;  |G/F - gamma| = 2.67e-51;  |k808 - 4 kappa/(2+gamma)| = 4.92e-49
      gamma formula and k808 = k810 = 4 kappa/(2+gamma)      dev =   4.9179e-49  PASS
  a=1 b=0.8 N=8 tau=1: half-shift identities and row equivalences dev =   1.2215e-48  PASS
    c1 = F(u)F(u+Delta) = 5.09822521273348, c2 = F(u)G(u+Delta) = 7.19466395791987, kappa = 1.17554020779209
      k110 = c1/kappa, k106 = kappa c1, k807 = (c1/2+c2/4)/kappa, k809 = kappa (c1/2+c2/4) dev =   2.5659e-48  PASS
  a=1 b=0.6 N=9 tau=1: half-shift identities and row equivalences dev =   3.8755e-49  PASS
    residue check |eps F(iK'+eps) - rho|/|rho| = 1.97e-11 (eps ~ 1e-6: expect ~1e-12);  gamma = 1.51471113447616;  |G/F - gamma| = 0.0;  |k808 - 4 kappa/(2+gamma)| = 2.0e-49
      gamma formula and k808 = k810 = 4 kappa/(2+gamma)      dev =   2.0046e-49  PASS
  a=1 b=0.9 N=10 tau=1: half-shift identities and row equivalences dev =   5.8801e-49  PASS
    c1 = F(u)F(u+Delta) = 6.99210623313275, c2 = F(u)G(u+Delta) = 11.308107784488, kappa = 1.10607571787524
      k110 = c1/kappa, k106 = kappa c1, k807 = (c1/2+c2/4)/kappa, k809 = kappa (c1/2+c2/4) dev =   1.1653e-48  PASS
  a=1 b=0.6 N=7 tau=2: half-shift identities and row equivalences dev =   7.5693e-48  PASS
    residue check |eps F(iK'+eps) - rho|/|rho| = 6.8e-12 (eps ~ 1e-6: expect ~1e-12);  gamma = -0.478887026288916;  |G/F - gamma| = 2.67e-51;  |k808 - 4 kappa/(2+gamma)| = 3.51e-48
      gamma formula and k808 = k810 = 4 kappa/(2+gamma)      dev =   3.5067e-48  PASS
  a=1 b=0.7 N=8 tau=3: half-shift identities and row equivalences dev =   2.7459e-46  PASS
    c1 = F(u)F(u+Delta) = 3.02466410795679, c2 = F(u)G(u+Delta) = -3.82038360185599, kappa = 12.4447416279342
      k110 = c1/kappa, k106 = kappa c1, k807 = (c1/2+c2/4)/kappa, k809 = kappa (c1/2+c2/4) dev =    6.637e-47  PASS
  a=1 b=0.5 N=9 tau=4: half-shift identities and row equivalences dev =   2.2108e-36  PASS
    residue check |eps F(iK'+eps) - rho|/|rho| = 6.01e-13 (eps ~ 1e-6: expect ~1e-12);  gamma = -1.14285712180215;  |G/F - gamma| = 2.67e-51;  |k808 - 4 kappa/(2+gamma)| = 1.17e-36
      gamma formula and k808 = k810 = 4 kappa/(2+gamma)      dev =   1.1743e-36  PASS
=== ALL CHECKS PASSED ===
