AddMul Arithmetic Reconstruction

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1 {
2   "finite_observation": {
3     "cases": 108,
4     "sample_certificates": [
5       {
6         "p": 2,
7         "q": 3,
8         "M": 12,
9         "k": 2,
10         "L": 2,
11         "modular_state": 4,
12         "selected_powers": [
13           4,
14           16,
15           64
16         ],
17         "target_values": [
18           9,
19           81,
20           729
21         ],
22         "sharp_error": "36",
23         "witness_lambda": "12",
24         "witness_kappa": "-75"
25       },
26       {
27         "p": 2,
28         "q": 3,
29         "M": 360,
30         "k": 3,
31         "L": 12,
32         "modular_state": 8,
33         "selected_powers": [
34           8,
35           32768,
36           134217728
37         ],
38         "target_values": [
39           27,
40           14348907,
41           7625597484987
42         ],
43         "sharp_error": "3783405061800/4097",
44         "witness_lambda": "232771596/4097",
45         "witness_kappa": "-923911917"
46       },
47       {
48         "p": 3,
49         "q": 5,
50         "M": 27,
51         "k": 3,
52         "L": 1,
53         "modular_state": 0,
54         "selected_powers": [
55           27,
56           81,
57           243
58         ],
59         "target_values": [
60           125,
61           625,
62           3125
63         ],
64         "sharp_error": "125",
65         "witness_lambda": "125/9",
66         "witness_kappa": "-375"
67       }
68     ],
69     "max_period": 332,
70     "pass": true
71   },
72   "polyphase": {
73     "cases": 420,
74     "sample_certificates": [
75       {
76         "p": 2,
77         "q": 3,
78         "s": 1,
79         "d": 0,
80         "k": 1,
81         "sharp_error": "1",
82         "numerator": 6,
83         "filter_coefficients": [
84           2,
85           -3,
86           1
87         ],
88         "witness_coefficients": [
89           "4",
90           "-6"
91         ]
92       },
93       {
94         "p": 2,
95         "q": 3,
96         "s": 2,
97         "d": 1,
98         "k": 1,
99         "sharp_error": "48",
100         "numerator": 960,
101         "filter_coefficients": [
102           -4,
103           9,
104           -6,
105           1
106         ],
107         "witness_coefficients": [
108           "64/3",
109           "25/3",
110           "-200"
111         ]
112       },
113       {
114         "p": 3,
115         "q": 5,
116         "s": 2,
117         "d": 2,
118         "k": 2,
119         "sharp_error": "69120",
120         "numerator": 5529600,
121         "filter_coefficients": [
122           9,
123           -28,
124           30,
125           -12,
126           1
127         ],
128         "witness_coefficients": [
129           "195",
130           "-70850",
131           "312000",
132           "-187200"
133         ]
134       }
135     ],
136     "pass": true
137   },
138   "witt": {
139     "cases": 45,
140     "lift_pairs": 31398,
141     "cocycle_triples": 12093,
142     "nontrivial_cycle_each": true,
143     "pass": true,
144     "sample": [
145       {
146         "p": 2,
147         "N": 2,
148         "cycle": 1,
149         "pairs": 4,
150         "triples": 8
151       },
152       {
153         "p": 3,
154         "N": 2,
155         "cycle": 1,
156         "pairs": 9,
157         "triples": 27
158       },
159       {
160         "p": 5,
161         "N": 3,
162         "cycle": 1,
163         "pairs": 25,
164         "triples": 125
165       },
166       {
167         "p": 11,
168         "N": 4,
169         "cycle": 1,
170         "pairs": 121,
171         "triples": 1331
172       }
173     ]
174   },
175   "boundary_tests": {
176     "no_additive_split_mod_p_squared": 328,
177     "explicit_p3_carry_1_plus_1": 1,
178     "note": "classical nonsplit additive extension; no abc-height claim"
179   }
180 }

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