Hilbert 12: analytic Fourier branch

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1 Exact rational-polynomial audits:
2   PASS SL2 determinant 1
3   PASS matrix trace 1
4   PASS matrix cubic order
5   PASS matrix component
6   PASS matrix component
7   PASS matrix component
8   PASS projective Phi squared
9   PASS projective Phi cubed
10   PASS Delta invariant under Phi
11   PASS cubic orbit trace
12   PASS cubic orbit pair sum
13   PASS cubic orbit product
14   PASS perfect-square discriminant
15   PASS generic Fourier norm
16   PASS generic primitive Fourier cube
17   PASS generic complementary Fourier cube
18   PASS Möbius inverse: cubic polynomial residual
19   PASS Möbius determinant / derivative
20   PASS polynomial Y(x) inverse modulo f (identity)
21   PASS explicit rational gamma obstruction
22   PASS transport determinant
23   PASS transported C3 action determinant
24   PASS transported C3 action trace
25   PASS transported C3 action cubic relation
26   PASS transported C3 action cubic relation
27   PASS transported C3 action cubic relation
28   PASS transported C3 action cubic relation
29   PASS trace normalizer numerator
30   PASS trace normalizer denominator
31   PASS spurious quadratic orbit control
32 Exact audit complete. None of these checks establishes Delta_gamma(1/3)=0.
33 
34 Numerical diagnostic at z= 0.33333333333333333333 with 64 digits
35  chart 1 N 4000 time 0.36 s
36    U = (-4.024029545371045206657 - 41.8559517671101857119j)
37    delta_gamma = (-2.56747504505612e-64 - 1.51655332081808e-64j) abs 2.9819225e-64
38    rigorous truncation tail for log(U) <= 1.4983425e-105
39  chart 10 N 19000 time 1.34 s
40    U = (-0.8326432366807291506723 + 3.550247070468073036805j)
41    delta_gamma = (8.97663858822928e-56 + 1.27314867031338e-55j) abs 1.5577894e-55
42    rigorous truncation tail for log(U) <= 2.9945114e-48
43  chart 23 N 34000 time 3.41 s
44    U = (0.03081041650699615493098 + 0.2519662235081715374107j)
45    delta_gamma = (-1.83899146724893e-43 - 1.45202312196119e-43j) abs 2.3431305e-43
46    rigorous truncation tail for log(U) <= 2.3271661e-36
47  analytic orbit check |v_23 - Phi(v_1)| = 7.5817966579e-44
48  analytic orbit check |v_10 - Phi²(v_1)| = 3.7535503223e-56
49  analytic trace |Y_1+Y_10+Y_23-target| = 1.4106092855e-42
50  No small residual is an equality certificate.
51 
52 Numerical diagnostic at z= 0.25 with 64 digits
53  chart 1 N 4000 time 0.36 s
54    U = (0.2237999593860142675135 - 0.3042840387610698503069j)
55    delta_gamma = (0.119587479580191 + 0.0458002924452422j) abs 0.12805792
56    rigorous truncation tail for log(U) <= 1.4983425e-105
57  chart 10 N 19000 time 1.63 s
58    U = (5.98568089192252589105 - 0.9949129102075743010349j)
59    delta_gamma = (0.132635327475 + 0.0529982157507676j) abs 0.14283186
60    rigorous truncation tail for log(U) <= 2.9945114e-48
61  chart 23 N 34000 time 3.0 s
62    U = (6.064805307724134115853 + 1.528434773107991075381j)
63    delta_gamma = (0.132798726070377 + 0.0531419953502676j) abs 0.14303696
64    rigorous truncation tail for log(U) <= 2.3271661e-36
65  analytic orbit check |v_23 - Phi(v_1)| = 0.34293461022
66  analytic orbit check |v_10 - Phi²(v_1)| = 0.20985202693
67  analytic trace |Y_1+Y_10+Y_23-target| = 48.273278389
68  No small residual is an equality certificate.

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