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References and Citations

How to Cite This Software

If CDT++ contributes to research or a project, cite it using the structured metadata in CITATION.cff. GitHub and other citation tools can generate BibTeX, APA, and additional formats from that file.

Quick citation for the current declared release:

Adam Getchell. 2026. CDT-plusplus: Causal Dynamical Triangulations in C++.
Version 1.0.0. GitHub. https://github.com/acgetchell/CDT-plusplus
Zenodo concept DOI: https://doi.org/10.5281/zenodo.21487043

The sections below are grouped by scientific domain. Cite the entries relevant to the algorithms or results used in a given work. Source documentation links directly to the applicable entry so that provenance stays close to the implementation while complete metadata remains centralized here.

Foundational Causal Dynamical Triangulations Theory

Original CDT framework

CDT framework (2001)

J. Ambjørn, J. Jurkiewicz, and R. Loll, “Dynamically triangulating Lorentzian quantum gravity,” Nuclear Physics B 610, no. 1–2 (2001), 347–382. DOI: 10.1016/S0550-3213(01)00297-8

Three-dimensional CDT (2001)

J. Ambjørn, J. Jurkiewicz, and R. Loll, “Nonperturbative 3D Lorentzian quantum gravity,” Physical Review D 64, no. 4 (2001), 044011. DOI: 10.1103/PhysRevD.64.044011

Monte Carlo Methods

Metropolis algorithm

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” The Journal of Chemical Physics 21, no. 6 (1953), 1087–1092. DOI: 10.1063/1.1699114

Metropolis-Hastings algorithm

W. K. Hastings, “Monte Carlo sampling methods using Markov chains and their applications,” Biometrika 57, no. 1 (1970), 97–109. DOI: 10.1093/biomet/57.1.97

Regge Calculus and Discrete Action

Regge calculus

T. Regge, “General relativity without coordinates,” Il Nuovo Cimento 19, no. 3 (1961), 558–571. DOI: 10.1007/BF02733251

Simplicial Topology and Local Moves

Pachner moves

U. Pachner, “P.L. homeomorphic manifolds are equivalent by elementary shellings,” European Journal of Combinatorics 12, no. 2 (1991), 129–145. DOI: 10.1016/S0195-6698(13)80080-7

Computational Geometry and Random-Number Generation

Delaunay empty-sphere construction

B. Delaunay, “Sur la sphère vide. À la mémoire de Georges Voronoï,” Bulletin de l’Académie des Sciences de l’URSS. Classe des sciences mathématiques et naturelles, no. 6 (1934), 793–800. Primary-source scan and bibliographic record.

CGAL design

E. Fogel and M. Teillaud, “The computational geometry algorithms library CGAL,” ACM Communications in Computer Algebra 47, no. 3/4 (2014), 85–87. DOI: 10.1145/2576802.2576806

CGAL triangulations

The CGAL Project, CGAL User and Reference Manual. CGAL Editorial Board, 6.2 edition (2026). https://doc.cgal.org/6.2/Manual/packages.html

Robust geometric predicates

J. R. Shewchuk, “Adaptive precision floating-point arithmetic and fast robust geometric predicates,” Discrete & Computational Geometry 18, no. 3 (1997), 305–363. DOI: 10.1007/PL00009321

This paper provides primary background for adaptive robust-predicate methodology. CDT++ delegates its production predicates to CGAL's EPICK kernel; it does not claim to reimplement Shewchuk's predicate code.

Random Voronoi and Delaunay expected complexity

R. A. Dwyer, “Higher-dimensional Voronoi diagrams in linear expected time,” Discrete & Computational Geometry 6 (1991), 343–367. DOI: 10.1007/BF02574694

Three-dimensional Delaunay complexity

S.-W. Cheng, T. K. Dey, and J. R. Shewchuk, Delaunay Mesh Generation, Chapter 4, “Three-dimensional Delaunay triangulation.” CRC Press (2013), ISBN 978-1-58488-730-0. DOI metadata issued 2016: 10.1201/b12987; see the publisher record. The authors’ Chapter 4 preprint states the finite three-dimensional tetrahedron bound used by CDT++.

PCG random-number generators

M. E. O’Neill, “PCG: A family of simple fast space-efficient statistically good algorithms for random number generation,” Harvey Mudd College Computer Science Department technical report HMC-CS-2014-0905 (2014). https://www.pcg-random.org/paper.html