This bibliography supports the literate source and executable mathematical essays in tests/classical/ and tests/research/. Individual tests should still cite the specific entries they rely on and, when practical, include chapter/section/equation locators close to the argument.
The repository is public-domain software; scholarly attribution remains mandatory for mathematical and historical claims.
[Arnold-1989] V. I. Arnold, Mathematical Methods of Classical Mechanics, 2nd ed., Graduate Texts in Mathematics 60, Springer, 1989. DOI: 10.1007/978-1-4757-2063-1. See especially the chapters on Lagrangian/Hamiltonian mechanics and integrable systems.
[Marsden-Ratiu-1999] Jerrold E. Marsden and Tudor S. Ratiu, Introduction to Mechanics and Symmetry, 2nd ed., Texts in Applied Mathematics 17, Springer, 1999. DOI: 10.1007/978-0-387-21792-5.
[Carinena-Martinez-MunozLecanda-2022] J. F. Carinena, E. Martinez, and M. C. Munoz-Lecanda, “Infinitesimal Time Reparametrisation and Its Applications,” Journal of Nonlinear Mathematical Physics 29 (2022), 523–555. DOI: 10.1007/s44198-022-00037-w. Section 2 reviews the classical Sundman transformation dt=r dτ, collision regularization, and fixed-energy linearization of the Kepler radial equation.
[Curtis-Ingerman-Morrow-1998] Edward B. Curtis, David Ingerman, and James A. Morrow, “Circular planar graphs and resistor networks,” Linear Algebra and its Applications 283 (1998), 115–150. DOI: 10.1016/S0024-3795(98)10087-3. Develops circular-planar network response matrices, critical networks, recovery of conductances from boundary response, and Y–Delta equivalence.
[Curtis-Morrow-1991] Edward B. Curtis and James A. Morrow, “The Dirichlet to Neumann map for a resistor network,” SIAM Journal on Applied Mathematics 51 (1991), 1011–1029. DOI: 10.1137/0151051. Classical source for the discrete boundary voltage-to-current map and inverse-network questions.
[Dorfler-Bullo-2013] Florian Dörfler and Francesco Bullo, “Kron reduction of graphs with applications to electrical networks,” IEEE Transactions on Circuits and Systems I: Regular Papers 60 (2013), 150–163. DOI: 10.1109/TCSI.2012.2215780. Treats Schur-complement/Kron reduction of weighted graph Laplacians and its electrical-network interpretation.
[Birman-1974] Joan S. Birman, Braids, Links, and Mapping Class Groups, Annals of Mathematics Studies 82, Princeton University Press, 1974. See especially Chapter 2 for closed braids, Markov equivalence, and the relation between braid representations and link invariants. Classical source for the complete Markov theorem and Burau/Alexander machinery used by the braid calibration.
[Carretero-Frantzeskakis-Kevrekidis-2024] R. Carretero-Gonzalez, D. J. Frantzeskakis, and P. G. Kevrekidis, “Traveling Wave Reduction, Elliptic Functions, and Connections to KdV,” in Nonlinear Waves & Hamiltonian Systems: From One To Many Degrees of Freedom, From Discrete To Continuum, Oxford University Press, 2024, Chapter 6. DOI: 10.1093/oso/9780192843234.003.0006. The traveling-wave reduction gives a cubic effective potential whose elliptic solutions degenerate to solitary waves.
[Hirota-1971] Ryogo Hirota, “Exact Solution of the Korteweg–de Vries Equation for Multiple Collisions of Solitons,” Physical Review Letters 27 (1971), 1192–1194. DOI: 10.1103/PhysRevLett.27.1192. Classical source for the exact KdV multi-soliton construction and pair-factorized collision structure.
[Ablowitz-Segur-1981] Mark J. Ablowitz and Harvey Segur, Solitons and the Inverse Scattering Transform, SIAM, 1981. DOI: 10.1137/1.9781611970883. Standard reference for KdV inverse scattering, elastic soliton interactions, scattering data, and phase shifts.
[Bertola-Jenkins-Tovbis-2023] M. Bertola, R. Jenkins, and A. Tovbis, “Partial degeneration of finite gap solutions to the Korteweg–de Vries equation: soliton gas and scattering on elliptic background,” arXiv:2210.01350. Relevant here as a modern finite-gap/degeneration reference connecting algebraic-geometric KdV backgrounds to solitonic sectors.
[DLMF-5.12] NIST Digital Library of Mathematical Functions, §5.12, “Beta Function,” especially Euler’s beta integral (Eq. 5.12.1). https://dlmf.nist.gov/5.12
[DLMF-19] NIST Digital Library of Mathematical Functions, Chapter 19, “Elliptic Integrals.” https://dlmf.nist.gov/19
[DLMF-22] NIST Digital Library of Mathematical Functions, Chapter 22, “Jacobian Elliptic Functions.” https://dlmf.nist.gov/22
[Euler-1761] L. Euler, “Observationes de comparatione arcuum curvarum irrectificibilium,” Novi Commentarii Academiae Scientiarum Petropolitanae 6 (1761), 58–84. Historical source of the addition theorem for elliptic integrals.
[Siegel-1969] C. L. Siegel, Topics in Complex Function Theory, Vol. I: Elliptic Functions and Uniformization Theory, Wiley-Interscience, 1969. Chapter I treats Euler's addition theorem and Abel's theorem for elliptic integrals and their role in uniformization.
[DLMF-23.2] NIST Digital Library of Mathematical Functions, §23.2, “Definitions and Periodic Properties,” including lattices and double periodicity of the Weierstrass wp function. https://dlmf.nist.gov/23.2
[DLMF-23.3] NIST Digital Library of Mathematical Functions, §23.3, “Differential Equations,” including Weierstrass invariants, discriminant, roots, and the cubic differential equation. https://dlmf.nist.gov/23.3
[DLMF-23.5] NIST Digital Library of Mathematical Functions, §23.5, “Special Lattices,” including the lemniscatic case g3=0, tau=i, and the associated special complete elliptic integral. https://dlmf.nist.gov/23.5
[DLMF-23.19] NIST Digital Library of Mathematical Functions, §23.19, “Interrelations,” especially Eq. 23.19.3 for Klein’s invariant J=g2^3/(g2^3-27g3^2). https://dlmf.nist.gov/23.19
[DLMF-23] NIST Digital Library of Mathematical Functions, Chapter 23, “Weierstrass Elliptic and Modular Functions.” https://dlmf.nist.gov/23
[Whittaker-Watson-1927] E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed., Cambridge University Press, 1927. See Chapters XX–XXII for elliptic functions and their relation to elliptic integrals.
[Lawden-1989] Derek F. Lawden, Elliptic Functions and Applications, Applied Mathematical Sciences 80, Springer, 1989. DOI: 10.1007/978-1-4757-3988-0.
[Forster-1981] Otto Forster, Lectures on Riemann Surfaces, Graduate Texts in Mathematics 81, Springer, 1981. DOI: 10.1007/978-1-4612-5961-9.
[Farkas-Kra-1992] Hershel M. Farkas and Irwin Kra, Riemann Surfaces, 2nd ed., Graduate Texts in Mathematics 71, Springer, 1992. DOI: 10.1007/978-1-4612-2034-3.
[Frauendiener-Klein-2015] J. Frauendiener and C. Klein, “Computational approach to hyperelliptic Riemann surfaces,” Letters in Mathematical Physics 105 (2015), 379–400. DOI: 10.1007/s11005-015-0743-4; arXiv:1408.2201. The paper treats hyperelliptic surfaces from branch-point lists or cut systems, constructs a canonical homology basis algorithmically, and computes periods of the holomorphic differentials; see especially the Introduction and Section 2.
[McMullen-Riemann-Surfaces] Curtis T. McMullen, Riemann Surfaces, Harvard Math 213b course notes. In the hyperelliptic discussion the canonical holomorphic basis is written explicitly as x^i dx/y. https://abel.math.harvard.edu/~ctm/math213b/home/course/course.pdf
[Hartshorne-1977] Robin Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics 52, Springer, 1977. DOI: 10.1007/978-1-4757-3849-0.
[Silverman-2009] Joseph H. Silverman, The Arithmetic of Elliptic Curves, 2nd ed., Graduate Texts in Mathematics 106, Springer, 2009. DOI: 10.1007/978-0-387-09494-6.
[Mumford-1983] David Mumford, Tata Lectures on Theta I, Progress in Mathematics 28, Birkhäuser, 1983. DOI: 10.1007/978-1-4899-2843-6.
[Baker-1897] H. F. Baker, Abel's Theorem and the Allied Theory Including the Theory of the Theta Functions, Cambridge University Press, 1897. Historical source for Abelian integrals, inversion, and theta-function methods.
[Cox-Little-OShea-2015] David A. Cox, John Little, and Donal O’Shea, Ideals, Varieties, and Algorithms, 4th ed., Undergraduate Texts in Mathematics, Springer, 2015. DOI: 10.1007/978-3-319-16721-3. See the chapters on Gröbner bases and ideal membership.
[Kline-1972] Morris Kline, Mathematical Thought from Ancient to Modern Times, Oxford University Press, 1972. Useful secondary history for the nineteenth-century development from elliptic integrals to elliptic functions and complex analysis.
[Gray-2015] Jeremy Gray, The Real and the Complex: A History of Analysis in the 19th Century, Springer, 2015. See the treatment of elliptic functions, Riemann surfaces, and the algebraic/analytic interaction.
[Huffman-1952] David A. Huffman, “A Method for the Construction of Minimum-Redundancy Codes,” Proceedings of the I.R.E. 40(9) (1952), 1098–1101. DOI: 10.1109/JRPROC.1952.273898. Classical finite-source baseline for the exact binary prefix-code construction used in the projective-cylinder coding calibration.
[Series-1985] Caroline Series, “The modular surface and continued fractions,” Journal of the London Mathematical Society s2-31(1) (1985), 69–80. DOI: 10.1112/jlms/s2-31.1.69. Gives the classical symbolic coding relating regular continued fractions and geodesic flow on the modular surface.
[Reutenauer-2019] Christophe Reutenauer, “On the Stern--Brocot expansion of real numbers,” Journal de Théorie des Nombres de Bordeaux 31(3) (2019), 697–722. DOI: 10.5802/jtnb.1104. Develops finite and infinite left/right paths in the Stern--Brocot tree and their continued-fraction and (SL_2(\mathbb Z)) interpretations.
[Ruban-1970] A. A. Ruban, “Some metric properties of (p)-adic numbers,” Siberian Mathematical Journal 11 (1970), 176–180. DOI: 10.1007/BF00970247. Introduces the standard-residue (p)-adic continued-fraction algorithm used in the matched-selector calibration.
[Browkin-1978] Jerzy Browkin, “Continued fractions in local fields I,” Demonstratio Mathematica 11(1) (1978), 67–82. DOI: 10.1515/dema-1978-0108. Introduces the balanced-residue algorithm and proves finite expansion for rational inputs.
[Capuano-Murru-Terracini-2022] Laura Capuano, Nadir Murru, and Lea Terracini, “On the finiteness of (\mathfrak P)-adic continued fractions for number fields,” Bulletin de la Société Mathématique de France 150(4) (2022), 743–772. DOI: 10.24033/bsmf.2860. Treats a (p)-adic floor as a section/type, includes Ruban and Browkin as special types over (\mathbb Q), and records their distinct rational finiteness behavior.
[Bruhat-Tits-1972] François Bruhat and Jacques Tits, “Groupes réductifs sur un corps local,” Publications Mathématiques de l'IHÉS 41 (1972), 5–251. DOI: 10.1007/BF02715544. Foundational source for the buildings attached to reductive groups over non-Archimedean local fields.
[Serre-Trees-1980] Jean-Pierre Serre, Trees, translated by John Stillwell, Springer, 1980. See Chapter II for groups acting on trees and the tree associated with (PGL_2) over a discretely valued field.
[Ludwig-Merten-2026] Judith Ludwig and Christian Merten, “Formalising the Bruhat--Tits Tree,” arXiv:2505.12933, revised 2026. Gives a modern, machine-checked construction from homothety classes of lattices, proves the tree and regularity properties, and records the projective-line description of the neighbours of a lattice.
[Hirsh-Washington-2011] Jordan Hirsh and Lawrence C. Washington, “(p)-adic continued fractions,” Ramanujan Journal 25 (2011), 389–403. DOI: 10.1007/s11139-010-9266-x. Studies Schneider-type expansions, termination behavior, and a (p)-adic analogue of Khinchin's theorem.
[Wang-Deng-2023] Zhaonan Wang and Yingpu Deng, “Convergence, Finiteness and Periodicity of Several New Algorithms of (p)-adic Continued Fractions,” arXiv:2309.05601. Useful evidence that algorithm choice, termination, convergence, and periodicity must remain separate claims.
[Romeo-2024] Giuliano Romeo, “Real convergence and periodicity of (p)-adic continued fractions,” arXiv:2410.09215. Records the continuing difficulty of a (p)-adic analogue of Lagrange periodicity and analyzes Browkin-type expansions.
[Griewank-Walther-2000] Andreas Griewank and Andrea Walther, “Algorithm 799: Revolve: An Implementation of Checkpointing for the Reverse or Adjoint Mode of Computational Differentiation,” ACM Transactions on Mathematical Software 26(1) (2000), 19–45. DOI: 10.1145/347837.347846. Primary source for the provably optimal serial binomial checkpointing schedule and its runtime controller.\n\n**[Griewank-Walther-2008]** Andreas Griewank and Andrea Walther, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, 2nd ed., SIAM, 2008. DOI: 10.1137/1.9780898717761. Classical reference for reverse accumulation, checkpointing, and time-memory recomputation tradeoffs.
Claims labelled Shakespeare interpretation are not claims made by the references above. The references establish classical mathematics and historical context; the process-first reinterpretation is the research program implemented and tested in this repository.