Realization Calculus

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1 @book{AndrewsAskeyRoy1999,
2   author    = {George E. Andrews and Richard Askey and Ranjan Roy},
3   title     = {Special Functions},
4   series    = {Encyclopedia of Mathematics and its Applications},
5   volume    = {71},
6   publisher = {Cambridge University Press},
7   address   = {Cambridge},
8   year      = {1999}
9 }
10 
11 @book{Apostol1976,
12   author    = {Tom M. Apostol},
13   title     = {Introduction to Analytic Number Theory},
14   series    = {Undergraduate Texts in Mathematics},
15   publisher = {Springer},
16   address   = {New York},
17   year      = {1976}
18 }
19 
20 @book{Boas1954,
21   author    = {Ralph P. Boas},
22   title     = {Entire Functions},
23   publisher = {Academic Press},
24   address   = {New York},
25   year      = {1954}
26 }
27 
28 @book{Comtet1974,
29   author    = {Louis Comtet},
30   title     = {Advanced Combinatorics: The Art of Finite and Infinite Expansions},
31   publisher = {D. Reidel Publishing Company},
32   address   = {Dordrecht},
33   year      = {1974}
34 }
35 
36 @book{FlajoletSedgewick2009,
37   author    = {Philippe Flajolet and Robert Sedgewick},
38   title     = {Analytic Combinatorics},
39   publisher = {Cambridge University Press},
40   address   = {Cambridge},
41   year      = {2009}
42 }
43 
44 @book{Levin1980,
45   author    = {Boris Ya. Levin},
46   title     = {Distribution of Zeros of Entire Functions},
47   edition   = {Revised},
48   series    = {Translations of Mathematical Monographs},
49   volume    = {5},
50   publisher = {American Mathematical Society},
51   address   = {Providence},
52   year      = {1980}
53 }
54 
55 @book{Rainville1960,
56   author    = {Earl D. Rainville},
57   title     = {Special Functions},
58   publisher = {The Macmillan Company},
59   address   = {New York},
60   year      = {1960}
61 }
62 
63 @book{Roman1984,
64   author    = {Steven Roman},
65   title     = {The Umbral Calculus},
66   series    = {Pure and Applied Mathematics},
67   volume    = {111},
68   publisher = {Academic Press},
69   address   = {New York},
70   year      = {1984}
71 }
72 
73 @book{Titchmarsh1939,
74   author    = {Edward C. Titchmarsh},
75   title     = {The Theory of Functions},
76   edition   = {Second},
77   publisher = {Oxford University Press},
78   address   = {Oxford},
79   year      = {1939}
80 }
81 
82 @article{Polya1920,
83   author  = {George P{\'o}lya},
84   title   = {Geometrisches {\"u}ber die Verteilung der Nullstellen gewisser ganzer transzendenter Funktionen},
85   journal = {Sitzungsberichte der Bayerischen Akademie der Wissenschaften, Mathematisch Physikalische Klasse},
86   volume  = {50},
87   year    = {1920},
88   pages   = {285{\textendash}290}
89 }
90 
91 @article{Langer1931,
92   author  = {Rudolph E. Langer},
93   title   = {On the Zeros of Exponential Sums and Integrals},
94   journal = {Bulletin of the American Mathematical Society},
95   volume  = {37},
96   number  = {4},
97   year    = {1931},
98   pages   = {213{\textendash}239}
99 }
100 
101 @article{Moreno1973,
102   author  = {Carlos J. Moreno},
103   title   = {The Zeros of Exponential Polynomials. {I}},
104   journal = {Compositio Mathematica},
105   volume  = {26},
106   number  = {1},
107   year    = {1973},
108   pages   = {69{\textendash}78}
109 }
110 
111 @article{BleherMallison2006,
112   author  = {Bleher, Pavel and Mallison, Jr., Robert},
113   title   = {Zeros of Sections of Exponential Sums},
114   journal = {International Mathematics Research Notices},
115   volume  = {2006},
116   year    = {2006},
117   pages   = {Article ID 38937, 49 pages},
118   doi     = {10.1155/IMRN/2006/38937},
119   url     = {https://doi.org/10.1155/IMRN/2006/38937},
120   note    = {\href{https://doi.org/10.1155/IMRN/2006/38937}{doi: 10.1155/IMRN/2006/38937}}
121 }
122 
123 @article{Schwaiger1992,
124   author  = {Jens Schwaiger},
125   title   = {On Generalized Hyperbolic Functions and Their Characterization by Functional Equations},
126   journal = {Aequationes Mathematicae},
127   volume  = {43},
128   year    = {1992},
129   pages   = {198--210},
130   doi     = {10.1007/BF01835702},
131   url     = {https://doi.org/10.1007/BF01835702},
132   note    = {\href{https://doi.org/10.1007/BF01835702}{doi: 10.1007/BF01835702}}
133 }
134 
135 @article{Muldoon2005,
136   author  = {Martin E. Muldoon},
137   title   = {Generalized Hyperbolic Functions, Circulant Matrices and Functional Equations},
138   journal = {Linear Algebra and its Applications},
139   volume  = {406},
140   year    = {2005},
141   pages   = {272--284},
142   doi     = {10.1016/j.laa.2005.04.011},
143   url     = {https://doi.org/10.1016/j.laa.2005.04.011},
144   note    = {\href{https://doi.org/10.1016/j.laa.2005.04.011}{doi: 10.1016/j.laa.2005.04.011}}
145 }
146 
147 @misc{PaperI2026,
148   author = {Komorebi P.},
149   title  = {Projector-Resolved Seed Calculus I: Typed Seeds, Operator Grammars, and Exact Reconstruction},
150   note   = {Version 1.2.1},
151   year   = {2026}
152 }
153 
154 @misc{PaperII2026,
155   author = {Komorebi P.},
156   title  = {Projector-Resolved Seed Calculus II: Polyphase Refinement, Weighted Transfer, and Dyadic--Odd Resolution},
157   note   = {Version 1.2.1},
158   year   = {2026}
159 }
160 
161 @misc{PaperIII2026,
162   author = {Komorebi P.},
163   title  = {Projector-Resolved Seed Calculus III: Typed Edge Operators, Connection Defects, and Obstruction Packets},
164   note   = {Version 1.0.1},
165   year   = {2026}
166 }
167 
168 @inproceedings{deMouraUllrich2021,
169   author    = {Leonardo de Moura and Sebastian Ullrich},
170   title     = {The {Lean} 4 Theorem Prover and Programming Language},
171   booktitle = {Automated Deduction -- CADE 28},
172   series    = {Lecture Notes in Computer Science},
173   volume    = {12699},
174   pages     = {625--635},
175   publisher = {Springer},
176   year      = {2021},
177   doi       = {10.1007/978-3-030-79876-5_37}
178 }
179 
180 @inproceedings{mathlib2020,
181   author    = {{The mathlib Community}},
182   title     = {The {Lean} Mathematical Library},
183   booktitle = {Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs},
184   pages     = {367--381},
185   publisher = {Association for Computing Machinery},
186   year      = {2020},
187   doi       = {10.1145/3372885.3373824}
188 }

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