Paper X: Universal Residual Seeds and Conditional Occupied-System Completion

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1 [
2   {
3     "name": "01_three_questions",
4     "title": "A root, a branch, and an occupied carrier",
5     "kind": "editable TikZ vector drawing",
6     "numerical_geometry_only": true
7   },
8   {
9     "name": "03_residual_grid",
10     "title": "Residual fibers in a finite coefficient ring",
11     "kind": "editable TikZ vector drawing",
12     "numerical_geometry_only": true
13   },
14   {
15     "name": "04_digits",
16     "title": "A compatible stream for one quarter in Z5",
17     "kind": "editable TikZ vector drawing",
18     "numerical_geometry_only": true
19   },
20   {
21     "name": "05_smooth_grid",
22     "title": "All points of a two-parameter smooth chart at depth three",
23     "kind": "editable TikZ vector drawing",
24     "numerical_geometry_only": true
25   },
26   {
27     "name": "06_weights",
28     "title": "Delayed activation of weighted coordinates",
29     "kind": "editable TikZ vector drawing",
30     "numerical_geometry_only": true
31   },
32   {
33     "name": "07_singular_forest",
34     "title": "Actual reductions of square-zero residues",
35     "kind": "editable TikZ vector drawing",
36     "numerical_geometry_only": true
37   },
38   {
39     "name": "08_prime_forests",
40     "title": "One scalar equation gives different local forests",
41     "kind": "editable TikZ vector drawing",
42     "numerical_geometry_only": true
43   },
44   {
45     "name": "09_infinite_tail",
46     "title": "Nonempty infinite levels can have no compatible branch",
47     "kind": "editable TikZ vector drawing",
48     "numerical_geometry_only": true
49   },
50   {
51     "name": "10_cohomology",
52     "title": "Cycles and boundaries in an exact packet complex",
53     "kind": "editable TikZ vector drawing",
54     "numerical_geometry_only": true
55   },
56   {
57     "name": "11_chain_defect",
58     "title": "Degreewise projectors need not define a subcomplex",
59     "kind": "editable TikZ vector drawing",
60     "numerical_geometry_only": true
61   },
62   {
63     "name": "12_source_scc",
64     "title": "Minimum seeds in the actual seven-vertex transport graph",
65     "kind": "editable TikZ vector drawing",
66     "numerical_geometry_only": true
67   },
68   {
69     "name": "13_transport",
70     "title": "An actual horizontal map must preserve the equations",
71     "kind": "editable TikZ vector drawing",
72     "numerical_geometry_only": true
73   },
74   {
75     "name": "14_spine",
76     "title": "A common polynomial does not mean identical residue coefficients",
77     "kind": "editable TikZ vector drawing",
78     "numerical_geometry_only": true
79   },
80   {
81     "name": "15_separator",
82     "title": "Finite character evaluations recover a multiplicity vector",
83     "kind": "editable TikZ vector drawing",
84     "numerical_geometry_only": true
85   },
86   {
87     "name": "16_multiplicities",
88     "title": "A unique rational solution can fail the carrier test",
89     "kind": "editable TikZ vector drawing",
90     "numerical_geometry_only": true
91   },
92   {
93     "name": "17_precision",
94     "title": "One digit is lost by the separating lattice",
95     "kind": "editable TikZ vector drawing",
96     "numerical_geometry_only": true
97   },
98   {
99     "name": "18_occupancy",
100     "title": "Pairwise occupancy can conceal an empty joint packet",
101     "kind": "editable TikZ vector drawing",
102     "numerical_geometry_only": true
103   },
104   {
105     "name": "19_hypotheses",
106     "title": "Trace and ordinary eigenspaces have different boundaries",
107     "kind": "editable TikZ vector drawing",
108     "numerical_geometry_only": true
109   },
110   {
111     "name": "20_closedness",
112     "title": "Nonzero values can converge to zero p-adically",
113     "kind": "editable TikZ vector drawing",
114     "numerical_geometry_only": true
115   },
116   {
117     "name": "21_signed_norm",
118     "title": "Congruent generators can have different absolute norms",
119     "kind": "editable TikZ vector drawing",
120     "numerical_geometry_only": true
121   },
122   {
123     "name": "22_norm_table",
124     "title": "The determinant norm on a 25-element quotient algebra",
125     "kind": "editable TikZ vector drawing",
126     "numerical_geometry_only": true
127   },
128   {
129     "name": "23_mean_cancellation",
130     "title": "A nonscalar unit pairs positive and negative character weights",
131     "kind": "editable TikZ vector drawing",
132     "numerical_geometry_only": true
133   },
134   {
135     "name": "24_scalar_exception",
136     "title": "Exactly when does a scalar witness exist?",
137     "kind": "editable TikZ vector drawing",
138     "numerical_geometry_only": true
139   },
140   {
141     "name": "25_avoidance",
142     "title": "Avoiding several primes is a simultaneous residue problem",
143     "kind": "editable TikZ vector drawing",
144     "numerical_geometry_only": true
145   },
146   {
147     "name": "26_boundary_count",
148     "title": "Complete residue cells cancel; the boundary remains",
149     "kind": "editable TikZ vector drawing",
150     "numerical_geometry_only": true
151   },
152   {
153     "name": "27_mellin",
154     "title": "Power saving leaves a regular endpoint at s = 1",
155     "kind": "editable TikZ vector drawing",
156     "numerical_geometry_only": true
157   },
158   {
159     "name": "28_frobenius_boundary",
160     "title": "Having samples is not the same as sampling every class",
161     "kind": "editable TikZ vector drawing",
162     "numerical_geometry_only": true
163   },
164   {
165     "name": "29_coefficients",
166     "title": "No scalar root is not the absence of every representation",
167     "kind": "editable TikZ vector drawing",
168     "numerical_geometry_only": true
169   }
170 ]

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