Realization Calculus

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1 @article{ConstantineSavits1996,
2   author = {Constantine, Gregory M. and Savits, Thomas H.},
3   title = {A multivariate {Fa\`a di Bruno} formula with applications},
4   journal = {Transactions of the American Mathematical Society},
5   volume = {348},
6   number = {2},
7   year = {1996},
8   pages = {503--520}
9 }
10 
11 @book{Deimling1985,
12   author = {Deimling, Klaus},
13   title = {Nonlinear Functional Analysis},
14   publisher = {Springer},
15   address = {Berlin},
16   year = {1985}
17 }
18 
19 @book{LodayVallette2012,
20   author = {Loday, Jean Louis and Vallette, Bruno},
21   title = {Algebraic Operads},
22   publisher = {Springer},
23   address = {Berlin},
24   year = {2012}
25 }
26 
27 
28 @book{McCleary2001,
29   author = {McCleary, John},
30   title = {A User's Guide to Spectral Sequences},
31   edition = {Second},
32   publisher = {Cambridge University Press},
33   address = {Cambridge},
34   year = {2001}
35 }
36 
37 @book{Weibel1994,
38   author = {Weibel, Charles A.},
39   title = {An Introduction to Homological Algebra},
40   publisher = {Cambridge University Press},
41   address = {Cambridge},
42   year = {1994}
43 }
44 
45 @article{Kato1950,
46   author = {Kato, Tosio},
47   title = {On the adiabatic theorem of quantum mechanics},
48   journal = {Journal of the Physical Society of Japan},
49   volume = {5},
50   year = {1950},
51   pages = {435--439}
52 }
53 
54 @book{Kato1995,
55   author = {Kato, Tosio},
56   title = {Perturbation Theory for Linear Operators},
57   publisher = {Springer},
58   address = {Berlin},
59   year = {1995}
60 }
61 
62 @book{KobayashiNomizu1963,
63   author = {Kobayashi, Shoshichi and Nomizu, Katsumi},
64   title = {Foundations of Differential Geometry. Volume I},
65   publisher = {John Wiley and Sons},
66   address = {New York},
67   year = {1963}
68 }
69 
70 @book{GrossTucker1987,
71   author = {Gross, Jonathan L. and Tucker, Thomas W.},
72   title = {Topological Graph Theory},
73   publisher = {John Wiley and Sons},
74   address = {New York},
75   year = {1987}
76 }
77 
78 @book{AbrahamMarsdenRatiu1988,
79   author = {Abraham, Ralph and Marsden, Jerrold E. and Ratiu, Tudor},
80   title = {Manifolds, Tensor Analysis, and Applications},
81   edition = {Second},
82   series = {Applied Mathematical Sciences},
83   volume = {75},
84   publisher = {Springer},
85   address = {New York},
86   year = {1988}
87 }
88 
89 
90 @book{Stanley2012,
91   author = {Stanley, Richard P.},
92   title = {Enumerative Combinatorics. Volume 1},
93   edition = {Second},
94   series = {Cambridge Studies in Advanced Mathematics},
95   volume = {49},
96   publisher = {Cambridge University Press},
97   address = {Cambridge},
98   year = {2012}
99 }
100 
101 
102 @book{HairerLubichWanner2006,
103   author = {Hairer, Ernst and Lubich, Christian and Wanner, Gerhard},
104   title = {Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations},
105   edition = {Second},
106   publisher = {Springer},
107   address = {Berlin},
108   year = {2006}
109 }
110 
111 @book{Kielhoefer2012,
112   author = {Kielh{\"o}fer, Hansj{\"o}rg},
113   title = {Bifurcation Theory: An Introduction with Applications to Partial Differential Equations},
114   edition = {Second},
115   publisher = {Springer},
116   address = {New York},
117   year = {2012}
118 }
119 
120 @book{Zeidler1986,
121   author = {Zeidler, Eberhard},
122   title = {Nonlinear Functional Analysis and Its Applications. I: Fixed Point Theorems},
123   publisher = {Springer},
124   address = {New York},
125   year = {1986}
126 }
127 
128 @article{Penrose1955,
129   author = {Penrose, Roger},
130   title = {A generalized inverse for matrices},
131   journal = {Proceedings of the Cambridge Philosophical Society},
132   volume = {51},
133   year = {1955},
134   pages = {406--413}
135 }
136 
137 @misc{paperI,author={Komorebi P.},title={Projector-Resolved Seed Calculus I: Typed Seeds, Operator Grammars, and Exact Reconstruction},year={2026},note={Version 1.2.1}}
138 @misc{paperII,author={Komorebi P.},title={Projector-Resolved Seed Calculus II: Polyphase Refinement, Weighted Transfer, and Dyadic--Odd Resolution},year={2026},note={Version 1.2.1}}
139 @incollection{lean,author={de Moura, Leonardo and Ullrich, Sebastian},title={The {Lean 4} Theorem Prover and Programming Language},booktitle={Automated Deduction -- CADE 28},series={Lecture Notes in Computer Science},volume={12699},pages={625--635},publisher={Springer},year={2021},doi={10.1007/978-3-030-79876-5_37}}
140 @inproceedings{mathlib,author={{The mathlib Community}},title={The {Lean} mathematical library},booktitle={Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs},pages={367--381},publisher={Association for Computing Machinery},year={2020},doi={10.1145/3372885.3373824}}

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