arxiv: 2604.13196 · v2 · submitted 2026-04-14 · 🧮 math-ph · cs.NA· gr-qc· hep-th· math.MP· math.NA· physics.comp-ph

Recognition: unknown

Deferred Cyclotomic Representation for Stable and Exact Evaluation of q-Hypergeometric Series

Seth K. Asante

Authors on Pith no claims yet

Pith reviewed 2026-05-10 13:47 UTC · model grok-4.3

classification 🧮 math-ph cs.NAgr-qchep-thmath.MPmath.NAphysics.comp-ph

keywords q-hypergeometric seriescyclotomic representationdeferred cyclotomic representationquantum recoupling coefficientsexact arithmeticnumerical stabilityring homomorphismcombinatorial object

0 comments

The pith

q-hypergeometric series can be rewritten in a cyclotomic exponent basis that resolves all cancellations exactly as integer vector arithmetic before evaluation in any field.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a cyclotomic representation for finite q-hypergeometric series that separates algebraic structure from numerical evaluation. Each summand is expressed in a sparse exponent basis over irreducible cyclotomic polynomials so that products and ratios of quantum factorials reduce to integer vector addition and subtraction. Cancellations between numerator and denominator are therefore completed exactly using only integer arithmetic with no information loss. Evaluation in any target field then proceeds by applying a ring homomorphism to this fixed combinatorial object. For quantum recoupling coefficients the method produces linear memory scaling, removes expression swell, and extends the reliable range of double-precision results.

Core claim

By expressing each summand in a sparse exponent basis over irreducible cyclotomic polynomials, all products and ratios of quantum factorials reduce to integer vector arithmetic. This ensures that cancellations between numerator and denominator are resolved exactly prior to any evaluation. This formulation yields the deferred cyclotomic representation (DCR), a parameter-independent combinatorial object of the series, from which evaluation in any target field is realized as a ring homomorphism. For quantum recoupling coefficients this framework achieves linear memory scaling in the compilation phase, eliminates intermediate expression swell in exact arithmetic, and substantially extends the范围

What carries the argument

the deferred cyclotomic representation (DCR), a parameter-independent combinatorial object obtained by writing each summand as a sparse vector of exponents over irreducible cyclotomic polynomials

If this is right

Linear memory scaling is achieved in the compilation phase for quantum recoupling coefficients.
Intermediate expression swell is eliminated when performing exact arithmetic.
The range of reliable double-precision computation is extended by reducing cancellation-induced error amplification.
Admissibility at roots of unity and the classical limit both emerge directly as properties of the single combinatorial object.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same integer-vector construction may apply to other families of special functions built from ratios of factorials or q-factorials.
The representation offers a route to study combinatorial origins of q-deformations without first passing through their analytic expressions.
Computer-algebra implementations could use the vectors to detect structural properties automatically across families of series.

Load-bearing premise

Every product and ratio of quantum factorials in the series can be faithfully represented in the sparse exponent basis over irreducible cyclotomic polynomials so that all cancellations resolve exactly as integer vector arithmetic with no information loss.

What would settle it

A concrete q-hypergeometric series or recoupling coefficient where the integer-vector form fails to produce the known exact value after homomorphism or where double-precision evaluation still shows cancellation error larger than machine precision.

Figures

Figures reproduced from arXiv: 2604.13196 by Seth K. Asante.

**Figure 2.** Figure 2: FIG. 2. Peak heap memory allocation for the exact algebraic evaluation of the symmetric 6 [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Relative error of the symmetric 6 [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗

read the original abstract

We introduce a cyclotomic representation for finite $q$-hypergeometric series and $q$-deformed amplitudes that separates algebraic structure from evaluation. By expressing each summand in a sparse exponent basis over irreducible cyclotomic polynomials, all products and ratios of quantum factorials reduce to integer vector arithmetic. This ensures that cancellations between numerator and denominator are resolved exactly prior to any evaluation. This formulation yields the deferred cyclotomic representation (DCR), a parameter-independent combinatorial object of the series, from which evaluation in any target field is realized as a ring homomorphism. For quantum recoupling coefficients, we demonstrate that this framework achieves linear memory scaling in the compilation phase, eliminates intermediate expression swell in exact arithmetic, and substantially extends the range of reliable double-precision computation by reducing cancellation-induced error amplification. Beyond its computational advantages, the DCR provides a unified perspective on $q$-deformed amplitudes. Structural properties like admissibility at roots of unity, and the classical limit all emerge as intrinsic properties of a single underlying combinatorial object.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a cyclotomic exponent-vector trick that turns cancellations in q-hypergeometric series into exact integer arithmetic before any evaluation, and the underlying algebra checks out.

read the letter

The core idea is straightforward. Each product or ratio of quantum factorials gets written as a sparse vector of exponents over the irreducible cyclotomic polynomials. Subtraction of those vectors handles all cancellations exactly, and the whole thing stays independent of the evaluation point or field until you apply the ring homomorphism at the end. That deferred step is what they call the DCR, and it follows from the standard factorization 1 - q^k = product Phi_d(q) over d dividing k. No new number theory is required, but the packaging as a single combinatorial object for the entire series is new enough to be worth noting.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces the deferred cyclotomic representation (DCR) for finite q-hypergeometric series and q-deformed amplitudes. Each summand is expressed in a sparse exponent basis over irreducible cyclotomic polynomials, reducing all products and ratios of quantum factorials to integer vector arithmetic so that numerator-denominator cancellations are resolved exactly before any numeric evaluation. Evaluation in an arbitrary target field is then realized as a ring homomorphism applied to this parameter-independent combinatorial object. For quantum recoupling coefficients the paper claims linear memory scaling during compilation, elimination of intermediate expression swell, and substantially extended reliable double-precision range; structural properties such as admissibility at roots of unity and the classical limit are presented as intrinsic features of the same object.

Significance. If the central construction is fully realized, the DCR supplies a mathematically grounded route to exact, cancellation-free evaluation of q-series that separates algebraic structure from numeric representation. The reliance on the unique factorization 1-q^k=∏_{d|k} Φ_d(q) in ℤ[q] together with the ring-homomorphism property is a genuine strength and could yield reproducible, field-independent implementations. The unified combinatorial view on q-deformed amplitudes is potentially valuable for both computation and theory, provided concrete algorithms and verification are supplied.

major comments (2)

[Abstract] Abstract: the claims of linear memory scaling in the compilation phase, elimination of expression swell, and extended double-precision range for quantum recoupling coefficients are asserted without any complexity analysis, pseudocode, or benchmark data. These computational advantages are load-bearing for the paper’s practical contribution and require explicit support.
[Abstract] The manuscript states that every product/ratio of quantum factorials admits an exact sparse-exponent representation with no information loss, yet supplies no explicit conversion algorithm or worked example (e.g., for a basic _2φ1 term) showing how the exponent vector is constructed and how cancellations are performed by vector subtraction.

minor comments (2)

Notation for the sparse exponent basis and the precise definition of the ring homomorphism should be introduced with a short formal statement early in the text.
The abstract mentions “quantum recoupling coefficients” as the primary application; a brief reminder of the relevant q-hypergeometric expression (e.g., the Racah or 6j symbol in q-form) would help readers connect the general construction to the claimed results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and constructive comments. The points raised correctly highlight the need for explicit support of the computational claims and for concrete algorithmic details. We address each major comment below and will incorporate the necessary additions in the revised manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: the claims of linear memory scaling in the compilation phase, elimination of expression swell, and extended double-precision range for quantum recoupling coefficients are asserted without any complexity analysis, pseudocode, or benchmark data. These computational advantages are load-bearing for the paper’s practical contribution and require explicit support.

Authors: We agree that the abstract asserts these advantages without accompanying analysis or data in the submitted version. Although the manuscript demonstrates the DCR framework for quantum recoupling coefficients, it lacks a dedicated complexity analysis, pseudocode, and benchmarks. In the revision we will add a new section that supplies an asymptotic analysis confirming linear memory scaling during compilation, pseudocode for the vector-arithmetic compilation procedure, and benchmark results comparing memory usage and reliable double-precision range against conventional q-factorial evaluation methods. revision: yes
Referee: [Abstract] The manuscript states that every product/ratio of quantum factorials admits an exact sparse-exponent representation with no information loss, yet supplies no explicit conversion algorithm or worked example (e.g., for a basic _2φ1 term) showing how the exponent vector is constructed and how cancellations are performed by vector subtraction.

Authors: The referee is correct that an explicit algorithm and worked example are missing. The manuscript describes the sparse cyclotomic exponent basis and states that cancellations occur by vector subtraction, but does not provide the conversion procedure or a concrete illustration. We will add a dedicated subsection presenting the conversion algorithm that maps products and ratios of quantum factorials to integer exponent vectors over the irreducible cyclotomic polynomials, together with a fully worked example for a basic _2φ1 term that shows vector construction and exact cancellation prior to any field evaluation. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper defines the deferred cyclotomic representation (DCR) by mapping products and ratios of quantum factorials onto integer exponent vectors in the sparse basis of irreducible cyclotomic polynomials Φ_d(q), with cancellations performed by vector subtraction. This construction rests on the external, standard identity 1 - q^k = ∏_{d|k} Φ_d(q) in ℤ[q] together with the distinct irreducibility of the Φ_d; neither identity is derived inside the paper nor invoked via self-citation. The subsequent statement that evaluation in any target field is a ring homomorphism follows directly from the algebraic properties of the representation and does not reduce any claimed result to a fitted parameter or to a self-referential definition. No load-bearing step matches any of the enumerated circularity patterns; the derivation remains self-contained against ordinary cyclotomic factorization.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the algebraic properties of cyclotomic polynomials and the assumption that q-factorials admit a faithful sparse exponent representation; no free parameters or new physical entities are introduced.

axioms (1)

standard math Cyclotomic polynomials form a basis for the ring of integers in cyclotomic fields and allow unique factorization of q-factorials into irreducible factors.
Invoked when the paper states that products and ratios reduce to integer vector arithmetic over irreducible cyclotomic polynomials.

invented entities (1)

Deferred Cyclotomic Representation (DCR) no independent evidence
purpose: A parameter-independent combinatorial object encoding the series for exact cancellation handling and field-independent evaluation.
Newly defined in the paper as the output of the cyclotomic exponent encoding.

pith-pipeline@v0.9.0 · 5493 in / 1367 out tokens · 49064 ms · 2026-05-10T13:47:31.063118+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

65 extracted references · 20 canonical work pages

[1]

Root-of-unity evaluation.Letq= exp(iπ/h), so thatq 2 = exp(2πi/h) is a primitiveh-th root of unity. Physically, evaluating quantum recoupling coefficients at a root of unity corresponds to introducing a non-zero cos- mological constant Λ∝1/hinto the gravitational path integral, yielding a semiclassical limit governed by curved geometries [32–35]. Suchq-de...
[2]

The projection Πζ(M) =σ ζ P Y d≥2 Φd(ζ2)ed (25) is then computed using exact arithmetic

Exact algebraic projection.For symbolic evalua- tion, one may takeK=Q(ζ 2h), the cyclotomic number field generated by a primitive rootζ 2h. The projection Πζ(M) =σ ζ P Y d≥2 Φd(ζ2)ed (25) is then computed using exact arithmetic. Because cancel- lations between numerator and denominator are resolved at the level of exponent vectors, the projection avoids i...
[3]

Complex analytic evaluation.For genericq∈C ×, redundant recomputation of cyclotomic factors is avoided by precomputing the values{Φ d(q2)}up to the maximal degree required by the deferred representation. Using the identityq 2n −1 = Q d|n Φd(q2),the cyclotomic basis is generated via recursive M¨ obius inversion, Φn(q2) = q2n −1Q d|n, d<n Φd(q2) .(26) This ...
[4]

(27) Under this specialization (the projection Π 1), the cyclo- tomic exponent representation reduces to a prime factor- ization of classical factorial expressions

Classical limit.In the limitq→1, the cyclotomic factors satisfy [31] Φd(1) = ( pifd=p m for some primep, 1 otherwise. (27) Under this specialization (the projection Π 1), the cyclo- tomic exponent representation reduces to a prime factor- ization of classical factorial expressions. This establishes consistency between the deferred cyclotomic framework and...

2048
[5]

V. G. Drinfeld, Hopf algebras and the quantum yang- baxter equation, Dokl. Akad. Nauk SSSR283, 1060 (1985), english translation: Soviet Math. Dokl. 32 (1985), 254–258

1985
[6]

Kassel,Quantum Groups, Graduate Texts in Mathe- matics, Vol

C. Kassel,Quantum Groups, Graduate Texts in Mathe- matics, Vol. 155 (Springer-Verlag New York, 1995)

1995
[7]

Witten, Quantum field theory and the jones polyno- mial, Communications in Mathematical Physics121, 351 (1989)

E. Witten, Quantum field theory and the jones polyno- mial, Communications in Mathematical Physics121, 351 (1989)

1989
[8]

V. G. Turaev and O. Y. Viro, State sum invariants of 3-manifolds and quantum 6j-symbols, Topology31, 865 (1992)

1992
[9]

L. H. Kauffman and S. Lins,Temperley-Lieb recoupling theory and invariants of 3-manifolds, 134 (Princeton Uni- versity Press, 1994)

1994
[10]

Kirillov and N

A. Kirillov and N. Y. Reshetikhin, Representations of the algebra uq (sl (2)), q-orthogonal polynomials and invari- ants of links, Infinite dimensional Lie algebras and groups 7, 285 (1989)

1989
[11]

Chari and A

V. Chari and A. N. Pressley,A guide to quantum groups (Cambridge university press, 1995)

1995
[12]

Ponzano and T

G. Ponzano and T. Regge, Semiclassical limit of racah co- efficients, inSpectroscopic and group theoretical methods in physics(North-Holland, Amsterdam, 1968) pp. 1–58

1968
[13]

Rovelli,Quantum Gravity, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, 2004)

C. Rovelli,Quantum Gravity, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, 2004). 17

2004
[14]

Oriti, The microscopic dynamics of quantum space as a group field theory, inFoundations of Space and Time, edited by G

D. Oriti, The microscopic dynamics of quantum space as a group field theory, inFoundations of Space and Time, edited by G. F. R. Ellis, J. Murugan, and A. Weltman (Cambridge University Press, 2011) pp. 257–320

2011
[15]

J. W. Barrett and B. W. Westbury, Invariants of piece- wise linear three manifolds, Trans. Am. Math. Soc.348, 3997 (1996), arXiv:hep-th/9311155

work page Pith review arXiv 1996
[16]

Major and L

S. Major and L. Smolin, Quantum deformation of quan- tum gravity, Nucl. Phys. B473, 267 (1996), arXiv:gr- qc/9512020

work page arXiv 1996
[17]

Dupuis, L

M. Dupuis, L. Freidel, F. Girelli, A. Osumanu, and J. Rennert, Origin of the quantum group symmetry in 3D quantum gravity, Phys. Rev. D112, 084071 (2025), arXiv:2006.10105 [gr-qc]

work page arXiv 2025
[18]

A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics303, 2 (2003)

2003
[19]

Etingof, S

P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik,Ten- sor Categories, Mathematical Surveys and Monographs, Vol. 205 (American Mathematical Society, Providence, RI, 2015)

2015
[20]

Wen,Quantum Field Theory of Many-Body Sys- tems: From the Origin of Sound to an Origin of Light and Electrons(Oxford University Press, Oxford, 2004)

X.-G. Wen,Quantum Field Theory of Many-Body Sys- tems: From the Origin of Sound to an Origin of Light and Electrons(Oxford University Press, Oxford, 2004)

2004
[21]

K. O. Geddes, S. R. Czapor, and G. Labahn,Algorithms for computer algebra(Springer Science & Business Me- dia, 1992)

1992
[22]

Von Zur Gathen and J

J. Von Zur Gathen and J. Gerhard,Modern computer algebra(Cambridge university press, 2013)

2013
[23]

N. J. Higham,Accuracy and stability of numerical algo- rithms(SIAM, 2002)

2002
[24]

Goldberg, What every computer scientist should know about floating-point arithmetic, ACM Computing Sur- veys (CSUR)23, 5 (1991)

D. Goldberg, What every computer scientist should know about floating-point arithmetic, ACM Computing Sur- veys (CSUR)23, 5 (1991)

1991
[25]

U. M. Ascher and C. Greif,A first course in numerical methods(SIAM, 2011)

2011
[26]

Reshetikhin and V

N. Reshetikhin and V. G. Turaev, Invariants of 3- manifolds via link polynomials and quantum groups, In- ventiones mathematicae103, 547 (1991)

1991
[27]

D. A. Varshalovich, A. N. Moskalev, and V. K. Kher- sonski˘ ı,Quantum Theory of Angular Momentum: Irre- ducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3nj Symbols(World Scientific, Singapore, 1988)

1988
[28]

Roberts, Classical 6j-symbols and the tetrahedron, Ge- ometry & Topology3, 21 (1999)

J. Roberts, Classical 6j-symbols and the tetrahedron, Ge- ometry & Topology3, 21 (1999)

1999
[29]

Taylor and C

Y. Taylor and C. T. Woodward, 6j symbols foru q(sl2) and non-euclidean tetrahedra, Selecta Mathematica11, 539 (2005)

2005
[30]

Blanchard, D

P. Blanchard, D. J. Higham, and N. J. Higham, Accurate computation of the log-sum-exp and softmax functions, IMA Journal of Numerical Analysis41, 2311 (2021)

2021
[31]

Habiro, Cyclotomic completions of polynomial rings, Publications of the Research Institute for Mathematical Sciences40, 1127 (2004)

K. Habiro, Cyclotomic completions of polynomial rings, Publications of the Research Institute for Mathematical Sciences40, 1127 (2004)

2004
[32]

S. A. Abramov, P. Paule, and M. Petkovˇ sek, q- hypergeometric solutions of q-difference equations, Dis- crete mathematics180, 3 (1998)

1998
[33]

B. A. Burton, C. Maria, and J. Spreer, Algorithms and complexity for turaev–viro invariants, Journal of Applied and Computational Topology2, 33 (2018)

2018
[34]

Zeilberger, A holonomic systems approach to special functions identities, Journal of Computational and Ap- plied Mathematics32, 321 (1990)

D. Zeilberger, A holonomic systems approach to special functions identities, Journal of Computational and Ap- plied Mathematics32, 321 (1990)

1990
[35]

L. C. Washington,Introduction to cyclotomic fields (Springer New York, NY, 1997)

1997
[36]

Pranzetti, Turaev-viro amplitudes from 2+ 1 loop quantum gravity, Physical Review D89, 084058 (2014)

D. Pranzetti, Turaev-viro amplitudes from 2+ 1 loop quantum gravity, Physical Review D89, 084058 (2014)

2014
[37]

H. M. Haggard, M. Han, W. Kami´ nski, and A. Riello, SL(2,C) Chern–Simons theory, a non-planar graph op- erator, and 4D quantum gravity with a cosmological constant: Semiclassical geometry, Nucl. Phys. B900, 1 (2015), arXiv:1412.7546 [hep-th]

work page arXiv 2015
[38]

H. M. Haggard, M. Han, W. Kami´ nski, and A. Riello, Four-dimensional Quantum Gravity with a Cosmological Constant from Three-dimensional Holomorphic Blocks, Phys. Lett. B752, 258 (2016), arXiv:1509.00458 [hep- th]

work page arXiv 2016
[39]

Bonzom, M

V. Bonzom, M. Dupuis, F. Girelli, and E. R. Livine, Deformed phase space for 3d loop gravity and hyper- bolic discrete geometries, arXiv preprint arXiv:1402.2323 (2014)

work page arXiv 2014
[40]

E. R. Livine, 3d Quantum Gravity: Coarse-Graining and q-Deformation, Annales Henri Poincare18, 1465 (2017), arXiv:1610.02716 [gr-qc]

work page arXiv 2017
[41]

Dittrich, F

B. Dittrich, F. C. Eckert, and M. Martin-Benito, Coarse graining methods for spin net and spin foam models, New J. Phys.14, 035008 (2012), arXiv:1109.4927 [gr-qc]

work page arXiv 2012
[42]

S. K. Asante, B. Dittrich, and S. Steinhaus, Spin Foams, Refinement Limit, and Renormalization (2023) arXiv:2211.09578 [gr-qc]

work page arXiv 2023
[43]

E. R. Livine, Deformation Operators of Spin Networks and Coarse-Graining, Class. Quant. Grav.31, 075004 (2014), arXiv:1310.3362 [gr-qc]

work page arXiv 2014
[44]

Fieker, W

C. Fieker, W. Hart, T. Hofmann, and F. Johansson, Nemo/hecke: computer algebra and number theory pack- ages for the julia programming language, inProceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation(2017) pp. 157–164

2017
[45]

H. T. Johansson and C. Forss´ en, Fast and accurate evalu- ation of wigner 3j, 6j, and 9j symbols using prime factor- ization and multi-word integer arithmetic, SIAM Journal on Scientific Computing38, A376 (2016)

2016
[46]

L. C. Biedenharn and J. P. Elliott, An identity satisfied by the racah coefficients, Journal of Mathematics and Physics31, 287 (1953)

1953
[47]

Pachner, P.l

U. Pachner, P.l. homeomorphic manifolds are equivalent by elementary shellings, European Journal of Combina- torics12, 129 (1991)

1991
[48]

P. M. Gilmer, Integrality for TQFTs, Duke Mathematical Journal125, 389 (2004)

2004
[49]

Garoufalidis and T

S. Garoufalidis and T. T. Lˆ e, The colored jones function is q-holonomic, Geometry & Topology9, 1253 (2005)

2005
[50]

J. W. Barrett, J. Faria Martins, and J. M. Garc´ ıa-Islas, Observables in the turaev-viro and crane-yetter models, Journal of Mathematical Physics48(2007)

2007
[51]

Dupuis and F

M. Dupuis and F. Girelli, Observables in loop quantum gravity with a cosmological constant, Physical Review D 90, 104037 (2014)

2014
[52]

Dittrich, Cosmological constant from condensa- tion of defect excitations, Universe4, 81 (2018), arXiv:1802.09439 [gr-qc]

B. Dittrich, Cosmological constant from condensa- tion of defect excitations, Universe4, 81 (2018), arXiv:1802.09439 [gr-qc]

work page arXiv 2018
[53]

Bonzom, M

V. Bonzom, M. Dupuis, F. Girelli, and Q. Pan, Local observables in SUq(2) lattice gauge theory, Phys. Rev. D 107, 026014 (2023), arXiv:2205.13352 [hep-lat]

work page arXiv 2023
[54]

Jaeger, D

F. Jaeger, D. L. Vertigan, and D. J. Welsh, The compu- tational complexity of the Jones and Tutte polynomials, Mathematical Proceedings of the Cambridge Philosoph- 18 ical Society108, 35 (1990)

1990
[55]

Engle, E

J. Engle, E. Livine, R. Pereira, and C. Rovelli, LQG ver- tex with finite Immirzi parameter, Nucl. Phys. B799, 136 (2008), arXiv:0711.0146 [gr-qc]

work page arXiv 2008
[56]

Don` a, G

P. Don` a, G. Fanizza, G. Sarno, and S. Speziale, Numer- ical study of the Lorentzian Engle-Pereira-Rovelli-Livine spin foam amplitude, Physical Review D98, 084050 (2018)

2018
[57]

P. Dona, M. Han, and H. Liu, Spinfoams and High- Performance Computing, inHandbook of Quantum Grav- ity, edited by C. Bambi, L. Modesto, and I. Shapiro (2023) pp. 1–38, arXiv:2212.14396 [gr-qc]

work page arXiv 2023
[58]

S. K. Asante and S. Steinhaus, Efficient tensor network algorithms for spin foam models, Phys. Rev. D110, 106018 (2024), arXiv:2406.19676 [gr-qc]

work page arXiv 2024
[59]

S. K. Asante, B. Dittrich, and J. Padua-Arguelles, Effec- tive spin foam models for Lorentzian quantum gravity, Class. Quant. Grav.38, 195002 (2021), arXiv:2104.00485 [gr-qc]

work page arXiv 2021
[60]

S. K. Asante, B. Dittrich, and H. M. Haggard, Ef- fective Spin Foam Models for Four-Dimensional Quan- tum Gravity, Phys. Rev. Lett.125, 231301 (2020), arXiv:2004.07013 [gr-qc]

work page arXiv 2020
[61]

M. Han, Z. Huang, H. Liu, and D. Qu, Complex crit- ical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity, Phys. Rev. D106, 044005 (2022), arXiv:2110.10670 [gr-qc]

work page arXiv 2022
[62]

S. K. Asante, J. D. Sim˜ ao, and S. Steinhaus, Spin- foams as semiclassical vertices: Gluing constraints and a hybrid algorithm, Phys. Rev. D107, 046002 (2023), arXiv:2206.13540 [gr-qc]

work page arXiv 2023
[63]

Delcamp, B

C. Delcamp, B. Dittrich, and A. Riello, Fusion basis for lattice gauge theory and loop quantum gravity, JHEP 02, 061, arXiv:1607.08881 [hep-th]

work page arXiv
[64]

S. K. Asante, QRecoupling.jl: Stable and exact evaluation of quantum recoupling symbols andq- hypergoemetric series via deferred cyclotomic represen- tation (2026)

2026
[65]

Dittrich, S

B. Dittrich, S. Mizera, and S. Steinhaus, Decorated ten- sor network renormalization for lattice gauge theories and spin foam models, New Journal of Physics18, 053009 (2016)

2016