Pith. sign in

REVIEW 4 major objections 5 minor 50 references

The paper constructs an explicit, discretized path-integral definition of quantum gravity coupled to the full Standard Model, using the Standard Model 3-group and the constrained 3BF action on a piecewise-flat spacetime.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-02 20:13 UTC pith:FL2CBKPL

load-bearing objection The paper really does produce an explicit lattice path integral for the SM 3BF action — that much is new — but the “rigorous definition” claim is not supported, because convergence of the noncompact integrals is explicitly left open. the 4 major comments →

arxiv 2602.23661 v3 pith:FL2CBKPL submitted 2026-02-27 hep-th gr-qc

A 3BF model of quantum gravity coupled to Standard Model matter

Pavle Stipsic , Marko Vojinovic This is my paper
classification hep-th gr-qc
keywords quantum gravityhigher gauge theory3-group3BF actionpath integral quantizationpiecewise-flat manifoldStandard Modelsimplicial discretization
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper aims to provide a concrete, nonperturbative definition of the path integral for quantum gravity coupled to all matter fields of the Standard Model. It replaces smooth spacetime with a piecewise-flat triangulation, assumes every field is constant within each simplex, and discretizes both the 3BF action and the integration measure accordingly. The central result is an explicit formula, equation (121), for the expectation value of any observable in the resulting theory, built from the Standard Model 3-group and the constrained 3BF action. If the definition is sound, it gives a quantum theory whose semiclassical limit is the Regge gravitational action together with the Standard Model matter action and a spin-spin contact interaction, and it opens the model to numerical evaluation. The authors note that the full convergence analysis of the discretized path integral remains open, particularly for integrals over noncompact groups.

Core claim

Starting from the topological 3BF action built on the 3-group (G = SO(3,1)×SU(3)×SU(2)×U(1), H = R^4, L = C^4×G64×G64×G64), the theory is deformed by simplicity constraints into the Standard Model 3BF action, which classically describes Einstein-Cartan gravity, gauge fields, fermions, the Higgs field, Yukawa interactions, and a cosmological constant. The paper's first two main results are general discretization identities: integrals of products of forms become weighted sums of contractions on 4-simplices (equation 50), and exterior derivatives are transported to the triangulation through the Stokes theorem (equation 71). Applied to the action and to the path-integral measure, these produce e

What carries the argument

The Standard Model 3-group—the triple of Lie groups (G = SO(3,1)×SU(3)×SU(2)×U(1), H = R^4, L = C^4×G64×G64×G64)—supplies the field content and the integration domains. The constrained 3BF action is the classical starting point. The two load-bearing discretization formulas are equation (50), which rewrites integrals of form products on a 4-simplex as combinatorially normalized sums of contractions with W sign factors, and equation (71), which defines exterior derivatives on a triangulation through oriented-boundary sums with z sign factors. Together they convert the path integral into a countable product of ordinary Lie-group integrals, with explicit Haar measures and window functions for ea

Load-bearing premise

The load-bearing premise is that the discretized path integral is actually well defined: the ordinary integrals over the noncompact groups SL(2,C), R, C and Grassmann variables must converge or be regulatable, and the paper states that this has not been established.

What would settle it

Evaluate the discretized path integral (121) on a fixed small triangulation, for example a single 4-simplex or a few glued simplices, and check numerically whether the integrals over the noncompact groups SL(2,C), R, and C converge for generic field configurations; divergent results would falsify the claim that the path integral is defined.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Equation (121) provides a concrete, algorithmically implementable definition of the path integral, so expectation values of observables can in principle be evaluated numerically on a chosen triangulation.
  • The semiclassical limit of the reduced model is the Regge action for gravity together with the discretized Standard Model matter action, including the spin-spin contact interaction, giving evidence that the model reproduces general relativity and known particle physics at low energy.
  • The discretization procedure yields a natural definition of the Hodge dual operator on a triangulation (equation 145), removing the obstruction that made direct quantization of the ECC action difficult.
  • The relation between 3BF and ECC expectation values derived earlier in the literature (equation 38) is recovered in the semiclassical approximation, with the same constant M = 150.
  • The framework extends to other 3-groups, such as GUT-like choices or modified matter groups, so future models of dark matter or fermion families could in principle be incorporated by changing the algebraic structure.

Where Pith is reading between the lines

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

  • Editorial inference: If the convergence question can be settled—say, by adding a dampening term to the measure—the same discretization scheme could serve as a lattice regulator for the full Standard Model coupled to gravity, not just a model of it.
  • Editorial inference: The explicit discretized Hodge dual (145) may be reusable in other lattice field theories where geometric, metric-dependent operators are difficult to define on a triangulation.
  • Editorial inference: The paper's assumption that the triangulation is a real physical structure near the Planck scale implies testable departures from exact Lorentz invariance; dispersion relations for photons or fermions could in principle probe the cutoff scale.
  • Editorial inference: Because the model is not a state sum and analytic evaluation seems out of reach, its practical payoff likely depends on numerical simulations of small triangulations; the first useful target would be checking whether the path integral is finite on a single 4-simplex.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper claims to provide a rigorous lattice definition of the path integral for the Standard-Model 3BF action, which describes Einstein-Cartan gravity coupled to all Standard Model matter in a higher gauge theory. The proposed definition is a discretized path integral over a piecewise-flat triangulation, obtained by (i) discretizing the action via contraction formulas (50) and (71), (ii) replacing the formal functional measure by a product of ordinary group/algebra integrals (85), and (iii) assembling the result into the explicit expression (121). The authors derive a simplified 'small model' by integrating out many Lagrange multipliers, using identity (127), and then claim that the semiclassical limit is the Regge action plus the ECC matter action, including a spin-spin contact interaction. The paper is largely constructive, and the main results are Eqs. (50), (71), (85), and (121).

Significance. If the construction were fully rigorous, this would be a significant step in higher-gauge-theory approaches to quantum gravity: it gives an explicit finite-dimensional lattice path integral for gravity coupled to the full Standard Model spectrum, together with concrete discretized expressions for the Yang-Mills kinetic term, the Hodge dual, the Regge deficit angle, and the spin-spin interaction. The explicit formulas, while unwieldy, are a useful concrete starting point for numerical work and for comparison with other spinfoam-like models. The derivation of a discretized Hodge dual from the 3BF point of view (145), (171) is a notable byproduct. However, the central claim of a rigorous definition is not yet established, because the convergence of the noncompact integrals is explicitly deferred, and the simplification and semiclassical analysis rest on assumptions about triangulations and averaging that are not justified in the stated generality.

major comments (4)
  1. [Section IV and Section VII.B, Eqs. (85), (116), (118), (121)] The paper does not establish that the path integral (121) is well-defined. The measure (85) consists of ordinary integrals over Lie algebras/groups, but for the noncompact groups R, C, and SL(2,C) the integration domains are noncompact and the phase exp(iS) has modulus one; the window functions (116) and (118) do not make these domains compact. Thus the integrals are at best conditionally convergent improper integrals, and no convergence factor or iε prescription is part of the definition. The authors explicitly concede in Section VII.B that 'some fields are integrated over noncompact groups and can therefore have arbitrarily large magnitude, leading to possible divergences even at finite distances' and that 'the full analysis of the finiteness of the model is out of the scope of this paper.' This gap is load-bearing: every expectation value computed from (121) presupposes the existence
  2. [Section V.A, Eq. (127)] Identity (127) is not valid for a 'rather large class' of triangulations, as claimed. The stated sufficient condition |σ|≤|k| is not generic for fine triangulations. For example, barycentrically subdividing any triangulation with at least one 4-simplex produces a triangulation with 120 times as many 4-simplices as the original, while the number of vertices is the total number of nonempty simplices of the original complex; hence |σ|>|v| for that subdivided triangulation. Such subdivisions are precisely the fine triangulations relevant for a Planck-scale cutoff. Since identity (127) is used to factor the constraints and integrate out the Q, Ξ, and Θ fields, the simplified model in Eqs. (123)–(139) and all subsequent semiclassical manipulations inherit this unproven restriction. The paper needs either a proof that the class of admissible triangulations includes all triangulations of interes
  3. [Section V.C and Section VI, Eqs. (149)–(150), (176)–(177)] The identification of the discretized gravitational term with the Regge action is asserted rather than proven. Equation (150) defines δ_Δ as a sum of quantities θ_{Δ,σ} and then 'interpret[s]' δ_Δ as the deficit angle; the paper states that a 'detailed proof... is quite involved and therefore out of the scope of this paper.' The three listed properties — locality, scale invariance, and proportionality to curvature — are necessary features of a deficit angle but not sufficient to single it out. The same applies to the identification of θ_{Δ,σ} as a dihedral angle in Eqs. (176)–(177). Since the semiclassical limit (183) is presented as the Regge action plus the ECC matter action, this unproven identification is load-bearing for the central physical claim. A controlling argument or a reference to a proof is needed before the semiclassical claim can be regarded as established.
  4. [Section VI, Eqs. (160)–(162)] The semiclassical averaging operations (160) and (161) are introduced without a controlled error estimate. Replacing δ(Σ_k F(k)) by ∏_k δ(F(k)) is not justified merely by assuming that F varies slowly; the linear algebra of the constraints changes, and the two expressions can differ even for slowly varying arguments. Similarly, substituting the spin connection by the linear form (161) is a strong truncation of the configuration space, not a systematic saddle-point or coarse-graining procedure unless accompanied by an estimate of the neglected fluctuations. Because these operations are used to integrate the remaining delta functions and obtain the final path integral (183), the semiclassical result is conditional on an approximation scheme whose validity is not demonstrated.
minor comments (5)
  1. [Abstract and Section I] Typographical errors: 'framwork' in the abstract, 'abreviated' in Section II.C, 'triangluations' in Section VII, 'Kronener' in Section III.C, and 'omiting' in Section VI.C. A careful proofread is needed.
  2. [Section IV, Eq. (100)] The relation between algebra integrals and group integrals via the periodicity factor N is written for general Lie groups, but for noncompact groups the integer N need not be finite. The statement should be restricted to compact or explicitly regulated cases, or the divergence of N should be discussed.
  3. [Section V.B, Eq. (131)] The change of variables (130)–(131) is described as one-to-one 'within a single simplex,' but the global consistency of this change of variables across neighboring 4-simplices is asserted rather than demonstrated. The argument based on |σ|≤|v| is itself tied to the questionable identity (127).
  4. [Section V.D, Eq. (153)] The text says '¯Q_A has the structure which encodes the operator →∇' but from Eq. (154) it is ¯Q_A that encodes the left-acting derivative; the sentence appears to have the two operators swapped. Please clarify the notation.
  5. [Section VI.D, Eq. (183)] The final path integral (183) integrates over dε, which is the edge-vector variable, but the measure and Jacobian relation to the original tetrad variables are not fully specified. This should be made explicit if (183) is to be used as a concrete starting point.

Circularity Check

0 steps flagged

No significant circularity: the discretization of the action and measure is derived in-paper, and the semiclassical term identifications are explicit lattice dictionaries rather than inputs disguised as predictions.

full rationale

The central derivation is self-contained in the sense required by the circularity rubric. Given the Standard-Model 3BF action written out in Eqs. (22)-(31), the paper derives its discretization rules (50) and (71) from explicit combinatorial and Stokes-theorem arguments, defines the measure (85) from ordinary group integrals, and transcribes the action into the explicit path integral (121). The main self-citations ([28] for the classical action, [35,36] for the topological invariant, [40] for the abstract 3BF/ECC relation) are prior constructions whose content is either restated fully in the present paper or used only as a consistency target; the present derivation does not reduce to those citations. Where semiclassical quantities are introduced — the discretized Hodge dual (145), the scalar-field Hodge dual (171), and the spin variables (179) — the paper explicitly 'reads off' or defines them by matching 3BF-derived expressions to ECC forms. This is a lattice dictionary, not a fitted parameter renamed as a prediction. The Regge/deficit-angle identification (150) is admittedly not proven ('a detailed proof that (150) is indeed the deficit angle is quite involved and therefore out of the scope of this paper'), and the convergence of noncompact integrals is explicitly deferred (Section VII.B); both are genuine limitations or correctness risks, but they do not exhibit an equation reducing to its own input by construction. No circular step satisfying the quoted-evidence requirement was found.

Axiom & Free-Parameter Ledger

1 free parameters · 6 axioms · 0 invented entities

No new physical particles, forces, or spacetime dimensions are postulated. The paper introduces a discretized Hodge dual definition and auxiliary Q/Ξ-type variables, but these are mathematical definitions and changes of variables rather than physical entities. The main extra 'free' input is the physical triangulation scale, which is a postulate rather than a fitted constant.

free parameters (1)
  • triangulation scale l_epsilon = unspecified (near Planck scale)
    Introduced in Section I as the physical piecewise-flatness cutoff; its value is not derived or fitted, and it enters all simplex-volume-dependent measure factors.
axioms (6)
  • domain assumption Spacetime is fundamentally a piecewise-flat simplicial complex and all fields are constant on each simplex.
    Section I item 3 and Section III A. This is the basis of the entire discretization and is postulated as physical structure, not derived.
  • domain assumption The Standard Model 3BF action (22) is the correct classical starting point for quantization.
    Inherited from [28]; the paper does not re-derive it but uses it as the action to quantize.
  • standard math Exterior derivatives appear at most once per term and can be discretized via Stokes' theorem with the sign functions z.
    Section III D uses the Poincare lemma and Stokes theorem to define dω on a simplex; the claim that this gives a unique natural derivative relies on the special form structure.
  • ad hoc to paper The path integral over noncompact groups is convergent, or can be made convergent by Wick rotation or damping.
    Section IV and VII. No proof is given; the paper explicitly acknowledges possible divergences from noncompact integration domains.
  • domain assumption Identity (127) holds for the triangulations considered, requiring |σ|≤|k|.
    Section V. The simplified model depends on rewriting summed delta functions as products; the paper restricts to this class but its genericity is not established.
  • ad hoc to paper The semiclassical averaging operations (160) and (161) are valid in the limit λ_φk ≫ l_ε ≳ l_p.
    Section VI uses slow variation of fields to replace delta functions of sums by products and connection fields by averages; this is an approximation, not a controlled expansion.

pith-pipeline@v1.3.0-alltime-deepseek · 47033 in / 16689 out tokens · 163624 ms · 2026-08-02T20:13:41.555573+00:00 · methodology

0 comments
read the original abstract

We develop an explicit model of quantum gravity coupled to the matter fields of the Standard Model, based on the 3-group structure and the 3BF action, within the framework of higher gauge theory. The model is constructed by providing a rigorous definition for the path integral of the theory, achieved by defining the whole theory on a piecewise-flat spacetime manifold. To that end, we develop a method to systematically discretize both the action and the path integral measure by passing from a smooth manifold to a piecewise-flat manifold. Finally, we discuss in some detail the structure of the resulting quantum gravity model, and provide a preliminary analysis of its semiclassical limit.

Figures

Figures reproduced from arXiv: 2602.23661 by Marko Vojinovic, Pavle Stipsic.

Figure 1
Figure 1. Figure 1: FIG. 1: Tetrahedra discussed in cases (2a), (2b), (3), respectively. [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: 4-simplices discussed in cases (4a), (4b), (4c), respectively. [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: 4-simplices discussed in cases (5a), (5b), (5c), respectively. [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: 4-simplices discussed in cases (6) and (7), respectively. [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

50 extracted references · 30 linked inside Pith

  1. [1]

    Polchinski,String Theory Vol

    J. Polchinski,String Theory Vol. I: An Introduction to the Bosonic String, Cambridge University Press, Cambridge (1998)

    1998

  2. [2]

    Polchinski,String Theory Vol

    J. Polchinski,String Theory Vol. II: Superstring Theory and Beyond, Cambridge University Press, Cambridge (1998)

    1998

  3. [3]

    Rovelli,Quantum Gravity, Cambridge University Press, Cambridge (2004)

    C. Rovelli,Quantum Gravity, Cambridge University Press, Cambridge (2004)

    2004

  4. [4]

    Thiemann,Modern Canonical Quantum General Relativity, Cambridge University Press, Cambridge (2007)

    T. Thiemann,Modern Canonical Quantum General Relativity, Cambridge University Press, Cambridge (2007)

    2007

  5. [5]

    Surya,Living Rev

    S. Surya,Living Rev. Relativ.22, 5 (2019),arXiv:1903.11544

    Pith/arXiv arXiv 2019

  6. [6]

    Rovelli and F

    C. Rovelli and F. Vidotto,Covariant Loop Quantum Gravity, Cambridge University Press, Cambridge (2014)

    2014

  7. [7]

    Bianchi, M

    E. Bianchi, M. Han, E. Magliaro, C. Perini, C. Rovelli and W. Wieland,Class. Quant. Grav.30, 235023 (2013), arXiv:1012.4719

    Pith/arXiv arXiv 2013

  8. [8]

    J. C. Baez and J. Huerta,Gen. Relativ. Gravit.43, 2335 (2011),arXiv:1003.4485

    Pith/arXiv arXiv 2011

  9. [9]

    Baez and J

    J. Baez and J. Dolan,Jour. Math. Phys.36, 6073 (1995),arxiv:q-alg/9503002

    Pith/arXiv arXiv 1995

  10. [10]

    Higher-Dimensional Algebra and Planck-Scale Physics

    J. Baez, “Higher-Dimensional Algebra and Planck-Scale Physics”, inPhysics Meets Philosophy at the Planck Length, Cambridge University Press, Cambridge, 177 (2001),arxiv:gr-qc/9902017

    Pith/arXiv arXiv 2001

  11. [11]

    Mikovi´ c and M

    A. Mikovi´ c and M. Vojinovi´ c,State-Sum Models of Piecewise Linear Quantum Gravity, World Scientific, Singapore (2023)

    2023

  12. [12]

    Girelli, H

    F. Girelli, H. Pfeiffer and E. M. Popescu,Jour. Math. Phys.49, 032503 (2008),arXiv:0708.3051

    Pith/arXiv arXiv 2008

  13. [13]

    J. F. Martins and A. Mikovi´ c,Adv. Theor. Math. Phys.15, 1059 (2011),arXiv:1006.0903

    Pith/arXiv arXiv 2011

  14. [14]

    Mikovi´ c and M

    A. Mikovi´ c and M. A. Oliveira,Gen. Relativ. Gravit.47, 58 (2015),arXiv:1409.3751

    Pith/arXiv arXiv 2015

  15. [15]

    Mikovi´ c, M

    A. Mikovi´ c, M. A. Oliveira and M. Vojinovi´ c,Class. Quant. Grav.33, 065007 (2016),arxiv:1508.05635

    Pith/arXiv arXiv 2016

  16. [16]

    S. K. Asante, B. Dittrich, F. Girelli, A. Riello and P. Tsimiklis,Class. Quant. Grav.37, 205001 (2020),arxiv:1908.05970

    Pith/arXiv arXiv 2020

  17. [17]

    Mikovi´ c, M

    A. Mikovi´ c, M. A. Oliveira and M. Vojinovi´ c,Adv. Theor. Math. Phys.26, 3783 (2022),arXiv:1610.09621

    Pith/arXiv arXiv 2022

  18. [18]

    Mikovi´ c, M

    A. Mikovi´ c, M. A. Oliveira and M. Vojinovi´ c,Class. Quant. Grav.36, 015005 (2019),arXiv:1807.06354

    Pith/arXiv arXiv 2019

  19. [19]

    Polyhedron phase space using 2-groups: kappa-Poincare as a Poisson 2-group

    F. Girelli, M. Laudonio and P. Tsimiklis, “Polyhedron phase space using 2-groups: kappa-Poincare as a Poisson 2-group”, arxiv:2105.10616

    Pith/arXiv arXiv

  20. [20]

    Mikovi´ c and M

    A. Mikovi´ c and M. Vojinovi´ c,Class. Quant. Grav.29, 165003 (2012),arXiv:1110.4694

    Pith/arXiv arXiv 2012

  21. [21]

    Mikovi´ c and M

    A. Mikovi´ c and M. Vojinovi´ c,Europhys. Lett.133, 61001 (2021),arXiv:2008.06354

    Pith/arXiv arXiv 2021

  22. [22]

    Witten,Comm

    E. Witten,Comm. Math. Phys.117, 353 (1988),MR 0953828

    1988

  23. [23]

    M. F. Atiyah,Publications Math´ ematiques de l’IH ´ES68, 175 (1988),MR 1001453

    1988

  24. [24]

    Quinn,Lectures on axiomatic topological quantum field theory, inGeometry and Quantum Field Theory(eds

    F. Quinn,Lectures on axiomatic topological quantum field theory, inGeometry and Quantum Field Theory(eds. D. S. Freed and K. K. Uhlenbeck), pp. 325, IAS/Park City Mathematical Series, American Mathematical Society, University of Texas, Austin (1995)

    1995

  25. [25]

    3d TQFTs and 3-manifold invariants

    K. Sozer and A. Virelizier, “3d TQFTs and 3-manifold invariants”, inEncyclopedia of Mathematical Physics 2nd ed, Elsevier (2024)

    2024

  26. [26]

    Baez,Lett

    J. Baez,Lett. Math. Phys.38, 129 (1996),arxiv:q-alg/9507006

    Pith/arXiv arXiv 1996

  27. [27]

    D. N. Yetter, inQuantum Topology, World Scientific, Singapore (1993)

    1993

  28. [28]

    Radenkovi´ c and M

    T. Radenkovi´ c and M. Vojinovi´ c,JHEP10, 222 (2019),arXiv:1904.07566. 42

    Pith/arXiv arXiv 2019

  29. [29]

    Radenkovi´ c and M

    T. Radenkovi´ c and M. Vojinovi´ c,Ann. Univ. Craiova Phys.30, 74 (2020),arXiv:2103.08037

    Pith/arXiv arXiv 2020

  30. [30]

    Radenkovi´ c and M

    T. Radenkovi´ c and M. Vojinovi´ c,Symmetry12, 620 (2020),arXiv:2004.06901

    Pith/arXiv arXiv 2020

  31. [31]

    Radenkovi´ c and M

    T. Radenkovi´ c and M. Vojinovi´ c,Class. Quant. Grav.39, 135009 (2022),arXiv:2101.04049

    Pith/arXiv arXiv 2022

  32. [32]

    -Dor -devi´ c, T

    M. -Dor -devi´ c, T. Radenkovi´ c, P. Stipsi´ c, and M. Vojinovi´ c,Universe9, 281 (2023),arXiv:2305.00117

    Pith/arXiv arXiv 2023

  33. [33]

    Stipsi´ c and M

    P. Stipsi´ c and M. Vojinovi´ c,Jour. Phys. A: Math. Theor.58, 215201 (2025),arXiv:2402.17675

    Pith/arXiv arXiv 2025

  34. [34]

    Porter,J

    T. Porter,J. London Math. Soc.58, 723 (1998),MR 1678163

    1998

  35. [35]

    Radenkovi´ c and M

    T. Radenkovi´ c and M. Vojinovi´ c,JHEP7, 105 (2022),arXiv:2201.02572

    Pith/arXiv arXiv 2022

  36. [36]

    Radenkovi´ c and M

    T. Radenkovi´ c and M. Vojinovi´ c,Jour. Phys. A: Math. Theor.58, 345203 (2025),arXiv:2412.21032

    Pith/arXiv arXiv 2025

  37. [37]

    J. F. Martins and R. Picken,Differ. Geom. Appl. Journal29, 179-206 (2011),arXiv:0907.2566

    Pith/arXiv arXiv 2011

  38. [38]

    Wang,Jour

    W. Wang,Jour. Math. Phys.55(4), 043506 (2014)

    2014

  39. [39]

    Saemann and M

    C. Saemann and M. Wolf,Lett. Math. Phys.104, 1147 (2014),arxiv:1305.4870

    Pith/arXiv arXiv 2014

  40. [40]

    Stipsi´ c and M

    P. Stipsi´ c and M. Vojinovi´ c,Class. Quant. Grav.42, 195009 (2025),arXiv:2506.17722

    arXiv 2025

  41. [41]

    Blagojevi´ c,Gravitation and Gauge Symmetries, Institute of Physics Publishing, Bristol (2002)

    M. Blagojevi´ c,Gravitation and Gauge Symmetries, Institute of Physics Publishing, Bristol (2002)

    2002

  42. [42]

    Vasili´ c and M

    M. Vasili´ c and M. Vojinovi´ c,Phys. Rev. D78, 104002 (2008),arXiv:1010.1861

    Pith/arXiv arXiv 2008

  43. [43]

    J. F. Plebanski,Jour. Math. Phys.18, 2511 (1977)

    1977

  44. [44]

    G. D. Smith,Numerical solution of partial differential equations: finite difference methods, Oxford University Press, Oxford (1985)

    1985

  45. [45]

    Shashkov,Conservative Finite-Difference Methods on General Grids, CRC Press, Boca Raton, Florida (1996)

    M. Shashkov,Conservative Finite-Difference Methods on General Grids, CRC Press, Boca Raton, Florida (1996)

    1996

  46. [46]

    K. W. Morton and D. F. Mayers,Numerical Solution of Partial Differential Equations, An Introduction, Cambridge University Press, Cambridge (2005)

    2005

  47. [47]

    Lemeshevsky, P

    S. Lemeshevsky, P. Matus and D. Poliakov,Exact Finite-Difference Schemes, De Gruyter, Berlin (2016)

    2016

  48. [48]

    Gerdt, R

    V. Gerdt, R. Horan, A. Khvedelidze, M. Lavelle, D. McMullan and Yu. Palii,J. Math. Phys.47, 112902 (2006), arXiv:hep-th/0511245

    Pith/arXiv arXiv 2006

  49. [49]

    Mikovi´ c, M

    A. Mikovi´ c, M. Vojinovi´ c,Class. Quant. Grav.28, 225004 (2011),arXiv:1104.1384

    Pith/arXiv arXiv 2011

  50. [50]

    Mikovi´ c,Universe8, 268 (2022),arXiv:2203.12313

    A. Mikovi´ c,Universe8, 268 (2022),arXiv:2203.12313

    Pith/arXiv arXiv 2022