Paper IX: Arithmetic Packets, Dyadic Towers, and Local Polynomial Deformation

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1 {
2   "status": "PASS",
3   "scope": "Exact finite worked examples, not new universal theorems or a Lean run.",
4   "counts": {
5     "independent_coefficient_equalities": 312,
6     "displayed_definitions": 2,
7     "normalization_counterexample": 2,
8     "odd_prime_sign_control": 3,
9     "newton_valuations": 32,
10     "newton_exact_reconstruction": 33,
11     "newton_precision_256": 33,
12     "smooth_tower": 21,
13     "singular_no_lift": 3,
14     "singular_positive_control": 3,
15     "shared_obstruction": 7,
16     "weighted_motion": 12
17   },
18   "total_checks": 463,
19   "first_rows": [
20     [
21       "1",
22       "-1",
23       "69"
24     ],
25     [
26       "1",
27       "-1/5",
28       "121/45"
29     ],
30     [
31       "1",
32       "-1/15",
33       "13/45"
34     ],
35     [
36       "1",
37       "-1/35",
38       "59/1155"
39     ]
40   ],
41   "normalization": {
42     "C1": "-1/84",
43     "C2": "703/5460",
44     "difference": "64/455",
45     "original_difference": "384/455"
46   },
47   "sign": {
48     "C": [
49       "1",
50       "-1",
51       "19"
52     ],
53     "twisted": [
54       "1",
55       "1",
56       "19"
57     ]
58   },
59   "newton": {
60     "first_five": [
61       "1",
62       "-2",
63       "72",
64       "-33872",
65       "60511872"
66     ],
67     "mod256": [
68       1,
69       254,
70       72,
71       176,
72       128
73     ],
74     "valuations": [
75       0,
76       1,
77       3,
78       4,
79       7,
80       8,
81       10,
82       11,
83       15,
84       16,
85       18,
86       19,
87       22,
88       23,
89       25,
90       26,
91       31,
92       32,
93       34,
94       35,
95       38,
96       39,
97       41,
98       42,
99       46,
100       47,
101       49,
102       50,
103       53,
104       54,
105       56,
106       57,
107       63
108     ]
109   },
110   "tower": [
111     {
112       "L": 1,
113       "modulus": 3,
114       "x": 1,
115       "residual": -2,
116       "digit": 1,
117       "next": 4
118     },
119     {
120       "L": 2,
121       "modulus": 9,
122       "x": 4,
123       "residual": 1,
124       "digit": 1,
125       "next": 13
126     },
127     {
128       "L": 3,
129       "modulus": 27,
130       "x": 13,
131       "residual": 6,
132       "digit": 0,
133       "next": 13
134     },
135     {
136       "L": 4,
137       "modulus": 81,
138       "x": 13,
139       "residual": 2,
140       "digit": 2,
141       "next": 175
142     },
143     {
144       "L": 5,
145       "modulus": 243,
146       "x": 175,
147       "residual": 126,
148       "digit": 0,
149       "next": 175
150     },
151     {
152       "L": 6,
153       "modulus": 729,
154       "x": 175,
155       "residual": 42,
156       "digit": 0,
157       "next": 175
158     },
159     {
160       "L": 7,
161       "modulus": 2187,
162       "x": 175,
163       "residual": 14,
164       "digit": 2,
165       "next": 4549
166     }
167   ],
168   "blocked_residues": [
169     6,
170     6,
171     6
172   ],
173   "shared_residuals": [
174     [
175       0,
176       2
177     ],
178     [
179       1,
180       0
181     ],
182     [
183       2,
184       1
185     ]
186   ],
187   "motion": [
188     {
189       "A": 2,
190       "root": -3,
191       "coefficient_valuation": 2,
192       "motion_valuation": 1
193     },
194     {
195       "A": 3,
196       "root": -9,
197       "coefficient_valuation": 3,
198       "motion_valuation": 2
199     },
200     {
201       "A": 4,
202       "root": -27,
203       "coefficient_valuation": 4,
204       "motion_valuation": 3
205     },
206     {
207       "A": 5,
208       "root": -81,
209       "coefficient_valuation": 5,
210       "motion_valuation": 4
211     },
212     {
213       "A": 6,
214       "root": -243,
215       "coefficient_valuation": 6,
216       "motion_valuation": 5
217     },
218     {
219       "A": 7,
220       "root": -729,
221       "coefficient_valuation": 7,
222       "motion_valuation": 6
223     }
224   ]
225 }

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