Our real universe is macroscopically 4D. Hints come from every directions & show that it had to be so

Our real universe is macroscopically 4D. Hints come from every directions & show that it had to be so Stephane H. Maes1 April 23, 2023 Abstract: In the multi-fold theory, spacetime results from 2D (fractal) processes at very small spatial scales then growing to 4D at larger spatial scales, where we naturally recovered a 4D macroscopic, and at large enough microscopic scales. So far, we invoked stability of GR reconstruction to justify 4D. In a recent paper, we argued that we have almost all the elements for a theory of everything, based on the multi-fold least action principle and multi-fold space time matter induction and scattering. There, we essentially assumed 4D at large enough scales, rather than deriving it. This paper organizes past considerations before expanding and adding to them. The analysis is based both on conventional, and on multi-fold considerations. The conclusions are that the spacetime is 4D at large enough microscopic, and at macroscopic, scales, and only with 2D and 3D behaviors at the smallest spatial scales. At 4D, it can be continuous and equipped with notions of Hamiltonians, volume, areas or dot products / metrics / distances. It is not (asymptotic) AdS, and it has only one time dimensions. In the course of our analysis, we encounter a few nuggets. This paper provides a rigorous proof of why multi-fold spacetime reconstruction by random walk is 4D, and only 4D at large enough scales, and why (multi-fold) dark energy effects do not grow additional dimensions. Relying on random walks, and quantum cellular automata based on them, to model QFTs, we predict challenges in formulating QFTs at spacetime dimensions of 5 and above, except maybe for some CFTs, or when built using the random walks of extended objects like strings or branes in their AdS spacetime. This analysis extends to the QFT world. The case of dS universe is discussed. Our analysis of Kaluza Klein (KK) dimensions leads us to propose that the Higgs presence in the multi-fold is also understandable as related to Higgs as dilaton in KK, and in the double copy between gravity and gauge fields.. We also explain why, on the other hand, AdS could be generated via the random walks of strings or extended objects, or non-conservative random walks, up to way higher dimensions, where one can still encounter (unphysical) supersymmetric or conformant fields. It infers why that story stops at 10D/11D, and fields misbehave at 26D for bosonic strings. The paper includes some analyses of QCD and Electroweak interactions at spatial scales where spacetime appears 2D and 3D, and additional considerations on the mass gap in different dimensions. Coupled with the Multi-fold Least Action principle, our universe has to be 4D at large enough spatial scales. No other physical solution is possible. ____ 1. Introduction 1 [email protected] Cite as: Stephane H Maes, (2023), “Our real universe is macroscopically 4D. Hints come from every direction & show that it had to be so”, https://doi.org/10.5281/zenodo.17575694, https://shmaesphysics.wordpress.com/2023/04/23/our-real-universe-ismacroscopically-4d-hints-come-from-every-directions-show-that-it-had-to-be-so/, April 23, 2023. Note added on August 1, 2025: References in italic denote comments added on August1, 2025, unless if noted otherwise. It is intuitively obvious that we live in a 4D spacetime. However, once Physics gets involved, many other options may exist, and some may lead to questioning the 4D assertion. Are we in 4D, or in universes with more, but hidden dimensions, and if they are hidden, how are they hidden to our sense, and / or to most common Physics? If there were extra dimensions, are these extra dimensions small, e.g., compact or compactified, or large in a suitable embedding or tangent (dual) space? Or are they ghost dimensions, e.g., only interacting with dark matter r dark energy? Or could we live in a smaller dimension spacetime, yet get the impressions of living in 4D (Everything indicates a dimensionality reduction at high energies as discussed in [1,8-10,16,22,82,83,259,265,279,326])? Are there multiple time directions? Is our universe asymptotic de Sitter (dS), or anti de Sitter (AdS) (Note added on August 1, 2025: By now, we know that our real universe, and multi-fold universes, are not supersymmetric [1315,250,262,296,307,308], and therefore not AdS [1,8-20,22,62,80-83,250,262,268,296,307,308], and that the cosmological constant / dark energy effect of our real universe is strictly positive, even if possibly time varying [33,250,296,307,308])? In fact, is our spacetime continuous, or discrete, or even fractal, i.e., with non-integer dimensions (There are many indications that a multi-fold universe but also our real universe is discrete, noncommutative and fractal (See [1,8-10,22,30,31,60,64,259,265,276,279,282,296,296,307,308] and references therein))? Then, could it be that there are other universes in a multiverse, assuming that the option makes any sense (It doesn’t beyond the MWI (Many Worlds Interpretation) [177]) would have other dimensions? Can we move across all these dimensions, or multiverses, and experience changes in dimensions, etc.? Also, what to make of hints that physics would be of lower dimensions at small scales [1, 1,810,16,22,82,83,259,265,279,326] and references therein? Per [84,177], no move across multiverses. Yet, multi-fold mechanisms take some of a particle path integral paths across multi-folds in a 7D embedding space [1,23,49,51,62,77,268]. This subject sound like a bonanza for science fiction, or a minefield for your career, and sanity, even if some wellrespected physicists have spent efforts on this. Among the most notable ones, let us call out explicitly Ehrenfest [170,171], and Tegmark [167]. These famous papers are mostly focused on classical Physics, which makes sense for a macroscopic analysis. There are in fact ways to see that at large enough microscopic scales, the scales of the QFT, SM and SMG, spacetime is also 4D and it can be used to justify the macroscopic 4D spacetime. In comments on the web site tracking all the development of the multi-fold theory [8], we provided arguments on why we know that our real universe is macroscopically 4D, and why it had to be so. It was a review of existing related papers. Here we put all the arguments into a consistent story and add to it. Therefore, in this paper, we review experimental, simulation and theoretical justifications that spacetime is 4D at large enough scales, to convince the reader that our real universe is not only macroscopically 4D, but also that it just had to be 4D, except at very small scales, where we then need to understand what it means to be essentially processes of smaller dimensions, and some of the implications. Also, we will show that spacetime cannot be physically of higher dimensions, even if mathematically such spaces could exist. Embedding, tangent or compact dimensions may exist, we will see when and what that means, but their unphysicality must then be very clearly understood: no spacetime Physics takes place in these dimensions, again something to explain. Finally, we will argue against multiple time dimensions, or scales [96,166,167,172]. Note added on August 1, 2025: [351] has been recently pushed by the popular scientific press as discussed in [351]. In [351], another popular blog succinctly took it down as non-sense [328]. Throughout the paper, we will turn back to the spacetime reconstruction model by random walks, introduced in [1,63,89,177,265] for multi-fold universes but also encountered in what seems to be any GR-based universe, i.e., most probably our real universe [6,177,296,307]. We use it to unambiguously, in our view, justify a 4D spacetime (at spatial scales large enough for GR) as the only stable possibility, and provide a microscopic interpretation for the results from [122-124], invoked in [1,265], which simulated numerically GR spacetime (construction) with causal triangulation, and showed 4D as the emerging stable spacetime solution. We want to call out explicitly a key contribution of this paper. We use random walks, and interaction potentials discussed in Appendix B, to justify why quantum cellular automata, based on random walks, are suitable to equivalently model QFTs, and why QFTs become problematic in 5D spacetime sand above, except maybe for some CFT or supersymmetric constructs, which might be associated to the random walks of extended objects. (Note added on August [1]: By now, we know, that our real universe, and multi-fold universes, are not supersymmetric[1,8-20,22,62,80-83,250,262,268,296,307,308]). We also use random walks to predict 2D and 3D QED and QCD behaviors, e.g., QED confinement at high energies, which allow us to understand what happens at energies above the electroweak symmetry breaking, especially in terms of the chiral symmetry breaking and its impact on masses [1,4,29,52,53,60,63,259,265,279,289,296,303,307]. We will also show how such a model can equip spacetime with dot products, i.e., metrics, or distances, and with 2-forms, i.e., areas [b58] and become apparently continuous. Random walks of strings, and other extended objects, can create AdS [13-15,308], and be dense in way larger dimensions, so that fields built on such backgrounds can exist under certain circumstances as for example SUSY fields and CFTs, as supersymmetry and conformance are superstrings symmetries. But none of those are physically useful in multi-fold or conventional spacetime [1,8-20,22,62,80,81,250,259,265,308 ]. They are just mathematical fields, unphysical [1,8-20,22,62,80-83,250,262,265,296,307,308]. The good behavior does not extend to bosonic strings at 26D. It is for the same reasons, and discussed in Appendix C. In general, in this paper, we assume an asymptotically 2 de Sitter (dS) spacetime with positive curvature / cosmological constant, unless if / where specified explicitly otherwise. Note added on August 1, 2025: It is motivated by the strictly positive cosmological constant, or dark energy derived in [b47,b58]. We changed the sentence as follows we assume an asymptotically flat or (intentionally stroked through) an asymptotically de Sitter (dS) spacetime, because [296,307] have eliminated asymptotic flat spacetime as a physical option. 2. Experimental Indications Of A 4D spacetime In Our Macroscopic Universe 2.1 Our World And Our Physics We, humans, are clearly 3D spatial beings. We perceive 3D and time evolution, and already have challenges really imagining just a 4D spacetime. To date, we have not observed extra dimensions, whether large or compact, nor any macroscopic reductions in dimensionality. Assuming that other dimensions exist, it is unclear who or what would detect or perceive them, although some argued that they might under influence, other than maybe particles, or through physical effects at the Standard Model (SM) scales or below. For sure, superstrings assume such Physics beyond the SM [357]. Holographic effects might also be ways to perceive the impact of them [358]. 2 Although in many of the (earlier) papers, compiled in [8], we do not bother to add an asymptotic qualifier, it is rigorously needed when matter is present in the spacetime. Across all the papers compiled in [8], and here, it is always the intention, and justified for example because matter locally perturbs dS, and AdS, behaviors. To the best of our knowledge, so far, there has been no detection of any extra dimension (e.g., Kaluza Klein/(super)strings/Kasner/Wess–Zumino–Witten/supersymmetry) in any physics experiment. In particular, with particle physics and colliders like the LHC [99-102,342-344], where, so far, no loss/leakage of energy or momentum has been detected, nor the formation of microscopic black holes, easier to form if there were more dimensions, and therefore a potential sign of the existence of such extra dimensions – but also requiring new Physics beyond the SM, [100,102-105,107,178,179,316,317], or other signs or holographic mechanisms [358] or strings [101], or via gravitational waves [107] or gravitons [107-109]. It’s all about detecting leakages in energy or momentum, different behaviors (resonance, standing wave behavior, etc.) between gravitational waves and light waves, or unexpected particles appearing as the result from heavier KK particles, or microscopic black hole decays [100]. Also, no higher dimensional black hole, with different symmetry, or say topological stars, due to higher dimensions, have been observed either [100-102,179-181,100,359,360]. To our knowledge, no recent paper has reported changes since these references.. To the contrary, experimentations hint always at maximum 4D. We use maximum because, as already mentioned, we know that dimensions reduction seems to take place at the smallest spatial scales [1,8-10,16,22,82,83,259,265,279,326]. 2.2 The Standard Model Holds The Fort The Standard Model (SM) has passed most of the challenges thrown at it. Recently, some have hoped for cracks in the SM, but few have held [54-57,59]. In fact, in the multi-fold theory, we claim that most of the cracks are not cracks, and might be explained with the SM with gravity non negligible at its scales (SMG), or multi-fold mechanisms and effects [1-98,118,177,184,185,196]. Needless to say, the continued success of the SM is to the desperation of many Physicists looking for New Physics, especially the supersymmetry, Superstring and other GUTs afficionados. Indeed, no new Physics, and no supersymmetry, significantly reduces the theoretical arguments for additional dimensions predicted by superstrings and M-theory. Furthermore, it gives growing credence that supersymmetry and superstrings at dimensions higher than 6 are not compatible with the SM, something that we have also recovered in multi-fold theory. See [1,11,13,18,20,43] and references therein. Note added on August 1, 2025: In any case, we know by now that supersymmetry is not physical [1,8-20,22,250,259,262,265,279,296,307,308]. 2.3 Confirmations Of General Relativity Most people have heard of the alleged incompatibilities between General relativity and Quantum Physics, with the understanding that one is classic, the other quantum, or the former is with real numbers while the latter involves mathematical operators, and quantum frameworks like superposition, coherence or entanglement. For example, it is often suggested that superposition, or even coherence, may not coexist with GR/gravity, something that we do not agree with, beyond the usual effects of interactions on superposition or entanglement. See [78,183,261] and references therein. Superstring is seen by many as the quantum evolution of the GR framework [14], while Loop Quantum Gravity (LQG) is sold as a competing quantization of the Hilbert Einstein action and spacetime, as in [19]. None have gone anywhere, beyond fantastic theoretical mathematical frameworks, and many challenges as we pointed out for example in our multi-fold work [1,5,21,35,43,184]. In fact we have challenged their physicality cross the board [1,820,22,62,81,250,259,262,265,279,296,205,307,308]. Needless to say that most physicists believe and hope for signs of breaking GR, to make some progress. Yet, GR has survived almost all the tests thrown at it. An up-to-date list and entry points to classic and recent tests of GR can be found at [112,113], including very recent ones like [114-118,185,187-190]. Almost every few months, new confirmation variations are now reported. All these tests and results were for GR in 4D spacetime. 2.4 Experimental Proof Of 4D Spacetime 4D quantum Hall conductance effects [119-121] have been observed and they can be considered as a proof that our universe has a 4D spacetime 3 . Of course, the repeated confirmations of GR, as in the previous subsection, experimentally indicates a macroscopic 4D spacetime. 2.5 Simulations In [1,265], we already justified a 4D spacetime as the lowest number of dimensions where a stable spacetime at large enough scales, can be reconstructed using causal quantum gravity reconstruction [122-124]. The multi-fold spacetime reconstruction [1,6,265] is based on random walks, and through the top-down-up-andupper model, it recovers GR [1,6,63,89,177,265,296,303,307]. As a result, multi-fold universes can be seen as well approximated by causal quantum gravity reconstruction, as random walk will always be causal, by definition and construction. As the approach of [122-124] triangulates GR at small scales, and GR contains multi-folds at Planck and at small scales [6], this is a good argument for multi-fold universes. If one agrees that [6] implies that GR-based universes are therefore multi-fold, this paragraph implies that our real universe is 4D at large enough scales. Note added on August 5, 2025: The arguments presented in Appendix B of [307], show that one can easily triangulate by building on the path of the 2D random walks. Note also that if we consider nondifferentiable manifolds, 2D random walks remain suitable way to model GR, as discussed in [319,320], and references therein: one can also generalize GR with triangulation. Note that [319] and references therein focus on generalization of the singularity theorems, which is fine for conventional GR, but one needs to remember that in a multi-fold universe, we have no cosmological or gravitation singularities. If the reader is reluctant to buy these arguments, we still argue that [6,31,63,177,296,303,307] shows that a GR spacetime has a 2D then fractal random walk-like structure at small scales that must be causal (see the required progression between clumps of spacetime and linking constrictions in [6,63,296,303,307]). So, causal reconstruction, with triangularization compatible with Regge Calculus [125,126], are appropriate ways to simulate GR. [126] also assumes a causal discretization. As we will see later, 2D random walks are also equivalent in modeling relativistic QM, and QFT. 3 Some may argue that this remains compatible with dimensions ≥ 4, just as for 2D Hall effects. Upcoming sections address the cases with more dimensions 4. Note the effects of 4D quantum Hall conductance effects are not to be confused with 2D quantum Hall effects. 2.6 . The Huygens’ Principle Says It All For Our Macroscopic Spacetime The Huygens’ principle [131] is only valid in odd space dimensions (3 or larger, with 1 as degenerate case, where no other path exists) [129-131] (in particular [129], Chapter VI, page 689 in the 1989 edition). It would create a problems for Optics, and classical Electromagnetism, if our spacetime wasn’t 4D or less, for classical Physics, and its quantum origins at large enough scales. Note that, to some extent, the Huygens’ principle can be thought to be generalized by the path integrals formalism ([1,77] and references therein). That formulation is not subject to even vs. odd dimension restrictions, as it works off the wave function that captures all the required history and / or because of derivations as in [77]. Yet this is how topological material and effects for 2D systems can significantly vary, as for example with Quantum Hall effects. As an example, consider [168]. As we will revisit later, we have different behavior for QFTs in 2D and 3D, e.g., QED, with confinement and chiral anomalies/symmetry breaking, as discussed in [60,63,136,174,289,303]. These different behaviors confirm, in case there is any doubt remaining, that our macroscopic spacetime is not 2D or 3D; QED does not typically present confinement behavior, in macroscopic spacetime. So at this stage, at best, the remaining options for macroscopic spacetime dimensions would be 4D, 6D, 8D and above. 3. 4D And Only 4D In Macroscopic Spacetime Reconstruction And Dark Energy Effects 3.1 Integer Dimensions MUST Be 4D At the time of writing [1], we also argued spacetime reconstruction based on random walks up to 4D, and that 5D and above does not occur, because such spacetime is too large to support sufficient / strong enough interactions (through random walks). We will revisit it here, and after. In particular, Appendix B discuss potentials like the Coulomb potential in different dimensions. Figure 1. (a) sketches a 2D random walk from which random walk are started in the third dimension. With 2D random walks covering ever point of the 2D manifold, the 3D contributions can appear dense in 3D space. (a) is a good example of random walk with particle creations as in [1,265]. (b) shows the case from 3D spatial to 4D spatial (the slanted arrow). Because random walks are only dense in 3D, the coverage in 4D spatial is very sparse. It will get sparser and sparser as we raise in dimensions, e.g., repeating the process from (b), as (b) repeated it from (a). We can rigorously support the 4D and only 4D argument because, above spacetime 4D (≥ 3D spatial), random walks on discrete spacetime are not 100% recurrent, per Polya’s random walk theorem [127,128], a theorem already used, albeit differently, in [177], when arguing against the existence of multiverses as universe with any possible content, in any possible state, or with any possible Physics, e.g., physical laws and constants. For spatial D ≤ 2, random walks can expand to other dimensions with a stable construct: i.e., spatial D ≤ 3, as new particles can always come back to the same starting point, and feed more particles/paths into the new dimension, there and around. In the case of spatial D=3, it is the last integer spatial dimension that can be systematically fed from 2D random walks, as they can be dense in 2D. For any integer value larger than, or equal to, 4, as spatial dimensions, any attempt to create another spatial dimension is starved off by the lack of new random walks/particles fed into it in the neighborhood of a starting point in that dimension, and so, at best, there is too much diluted within it to have interactions or anything else taking place. The principle is sketched in Figure 1. This is always true, except, maybe under the right circumstances close enough to the seeding 3D spacetime, where there may be enough density. Comment added on August 1, 2025: Then, creating a continuouslooking spacetime, then with a dot product and therefore metrics, because of entanglement, and areas/Hamiltonian/conjugate/volumes, i.e., a symplectic-looking manifold as done in [307]. This reasoning works by construction with discrete spacetime, and non-commutative [b58], as well as non-differentiable manifolds [319,320], albeit, we have argued from a multi-fold point of view the foam should remain well behaved [5,19,21,184]. So for spatial D ≥ 3, any such expansion to another spatial dimension dilutes the density too much to build a stable spacetime where physical interactions take place: the coverage is not dense. Spatial D=3 or spacetime D=4 is therefore the only possible integer dimension can be stable, as lower spatial dimensions will automatically grow into larger dimensions, and beyond, no dense and stable spacetime can be created. Non-integer parts can exists to characterize the fractal nature of the random walks, but that matters only at microscopic scales. See section 3.2. It explains why, in [1,265], random walks, a 2D spacetime process must grow to 3D then 4D, and then stop without any growth beyond. Also, it explains why the multi-fold dark energy effects [1,8-10,22,27,62,259,265,279] expand spacetime but do not grow extra dimensions, even if pushing out of spacetime, into what can be seen as a larger embedding space (e.g., 5D or rather 7D) [1,27,62,296,303,307]. Note added on August 1, 2025: In [307], we link these dark matter effect to spacetime non-commutativity: they are one and the same, and need each other to exist and they underlie GR. This directly related to the quantum nature of gravity [273], albeit different from was some believe that it means, where non-commutativity is essential [30,64,77,250,282,296,301,303,307] (Note added on October 31, 2025:, as interestingly explained in [361]). And so, we were correct in [191] to state that if the dimensions where larger, not enough collisions would take place, and we would not have enough interactions for agglomeration/clumping of structures due to gravity, or creation of bound structure with gravity or electromagnetism etc. and so we would be challenged to explain the current large structures of the universe, or even possibly bound and composite structures like atoms and molecules. Again we will revisit in upcoming sections, and provide alternate ways to reach and prove the same conclusions. As already mentioned, considering random walks / moves of higher dimensional objects like strings or branes, can, for the same reasons, may support the generation of higher dimensional spacetime, and a priory these will be continuous, unless if the strings and branes were discrete, something less common in superstrings/Mtheory, even if they also encounter hints that spacetime is discrete, when extending to strings the reasoning of [64,250,282,289,296,303,307,362]. Interestingly, we believe that one could also argue that the lack of enough density at any spatial dimension 4 or above, will result into diluted and non-existent spacetime, except possibly in a/some region close to the underlying, say 3D spatial, manifold. This recovers another result that is widely known in Kaluza Klein and behind the String theories automatic compactification of the additional dimensions, and the string T-duality [192-195]. It is also well exemplified in [132], where it is argued that a fifth dimension must automatically compactified (and any higher ones). We just saw why: extra dimension can only occur this way, if density is sufficient, which may require additional context on how spacetime is constructed (that would justify feeding enough in such growth). For the reasons discussed so far and in upcoming sections, we argue that creation of a fifth dimension does not happen [289,296,303,307] in a typical universe conventional or multi-fold, but it might occur if extended objects like strings or branes are involved in the random walks. Note that this is not preventing, or constraining, the multi-fold mechanisms with kinematics and dynamics dictated by the motions of entangled particles [251]. Also, as discussed later on, binding forces like gravity, Coulomb potential and QCD interactions weaken with as spatial dimensions increase. (See Appendix B) Coupled with reduced density it makes it difficult for matter to interact in larger spatial dimensions d (d ≥ 4), and prevent orbits and bound elements: space is too sparse while attraction is also weaker. There would be no atoms, no molecules, no chemistry and no life in such universes. Although, relying on just a simple extension to Polya’s random walk theorem, and evolution of potentials like the Coulomb potential, discussed in Appendix B, we believe that such arguments of why our spacetime is macroscopically 4D (even if build by 2D random walks), and stable and not a smaller (it would always be able to grow additional dimensions if at D<4, due to multi-fold dark energy effects / non-commutativity [1,810,22,27,30,64,250,259,265,279,289,297,303,307]) or larger (won’t be able to grow into larger dimensions [132]). This is the answer as to why the multi-fold dark energy effects do not create new dimensions, a question that we received regularly after publication of [1,27]. These are original arguments and results presented this paper. It means that spacetime of 1D, 2D or 3D (with positive curvature / dark energy, to justify the random walk spacetime reconstruction, expanding the universe 4 ) will always become 4D, when left on its own unless if limited 4 The case of negative cosmological constant and asymptotic AdS spacetime is more tricky for our model. [1,810,22,63,250,259,265,276,279,296,307] show that multi-folds and random walks are only compatible with positive cosmological constant / curvature. (Note added on August 1, 2025: we have removed or null per [296,307]).We externally by other physical constraints into 1D or 2D (e.g., like spacetime available in topological materials). It is aligned with [77,177]. Again, because we recover GR from multi-fold spacetime reconstruction, and encounter multi-fold in GR (and Yang Mills [7,58])[1,6,265,307], we can argue that the same questions can be asked, and similarly answered, in conventional physics, i.e., non-multi-fold, and for conventional, and unexplained, dark energy. [1,6,265,296,303,306,307] ensures that the explanation is actually the same. We will recover more conventional, and multi-fold consequences in the upcoming sections. 3.2 What About (Multi-)Fractal Considerations? In [1,30,31,63,64,282,289,296,303,307], we argue that spacetime is discrete, non-commutative, and fractal at very small scales, a direct result of random walks with foraging / Levy walks, and, possibly, some entanglement between concretized spacetime locations [1,16]. And yes, it is also Lorentz symmetric and non-commutative, possibly non associative [1,265], this is not important here. In [1,31,63] and references therein, we also argue that, at large enough scales, such a fractal spacetime can appear to have integer dimensions, and then be continuous, as soon that the random walks and non-commutative effects become hidden by a high enough density of concretized spacetime locations, and quantum uncertainties [30,64,296]. Note added on August 1, 2025: In addition in [307], we explain how the resulting manifold can be equipped with dot product, metrics and areas, volumes, Hamiltonians / symplectic structure, on differentiable or non-differentiable manifolds. So, all of the discussions in section 3, and some of the considerations in section 2, can be with (n+ε) D dimensions instead of nD dimensions, with n ∊ ℕ, without having to bother about ε. The outcome are the ultimately same at large scale. Indeed, the fractal non-integer dimension component is relevant and visible only at very small microscopic scales (and otherwise possibly in the distribution of matter at cosmological scales [1,265]). This paper focuses on macroscopic considerations. In this paper, we will not bother with additional fractal concerns, considering them addressed by the comments made here. Related to this, the considerations on imaginary mass for the massless Higgs field (Tachyonic), and in space and time fractional quantum mechanics hints at the correctness of the model [31,63,89,289]: it happens with random walks of massless bosons, and only Hermicity is certain. 4. Implications Of Asymptotically Safe Gravity extend this to show incompatibility with superstrings in same spacetime, something also agreed by most in the string community. See [1,15,250,265,308] and references therein. A negative curvature, à la AdS, would require a background curvature shaped this way through initial conditions, or other processes, like expanding from a D-1 boundary that is flat or dS [62,197], or model/vacua down lifting (vs. the uplifting encountered with string theories and quintessence, where supporters try to encounter a positive cosmological constant, while strings are incompatible with such cosmological sign). It is consistent with [15,308] and references therein. To explain AdS(5) as in [1,265], the spacetime would rather be constructed by the multi-folds, who live in AdS(5)(+…), where the (+…) is to allow additional dimensions for superstrings, which could attempt model the gravitons or multi-folds [1,58,80,81]. We will revisit this later in section 10, where we will see that 5D+ can exist in an AdS space. This had to be as we have to support AdS(5) as tangent dual to multi-fold spacetime, as well as the mathematics of superstrings, supergravity and M-theory. The renormalizability and chirality may be circumvented by introducing superstrings, supergravity or the M-theory, but we are back to the same issues due to supersymmetry and dimensions > 6 still make the solution incompatible with the SM, if gravity is asymptotically safe, which we claim that it is in a multi-fold universe and in a conventional universe [1,6,13,16,17,63]. Note added on August 1, 2025: Then we now know that supersymmetry is not/never physical [250,296,307,308]. In addition, (a) dilaton particle(s) must be accounted for when the dimension compactifies, or the volume of compactified part varies [161]. No such dilaton is known in the SM, except maybe as Higgs field 7 , as proposed for example in papers like [162], a little bit like the inflaton proposals based also on the Higgs, as proposed (conventionally and in multi-fold theory) in [27,28], and references therein. There seems just no way out for constrained KK theories: we can’t be in a constrained (i.e., conventional) KK spacetime that supports the SM. We should not assume that conventional KK are physical, just as we already concluded that related superstrings and their Calabi-Yau manifolds [163], playing an analogous role to KK extra dimensions, are not physical, including, besides the challenges of incompatibility with the SM if gravity is asymptotically safe, the incompatibility of supersymmetry, and of superstrings, with de Sitter spacetime, i.e., spacetime with positive curvature, or the string swampland problem [1,11-18,20,81,250,265,296,307,308]. 7.2 The Multi-fold Space Time Matter Induction And Scattering Along With The Gravity Electroweak Symmetry Breaking: KK, The Rebirth The multi-fold theory proposes a variation on the 5D space time matter induction, which is an unconstrained KK, without compactification [166-168]. Let us summarize the principles (reusing text from [10]). Multi-folds generate at each location a 7D embedding space that can follow GR in 7D, and be flat or Einsteinian [1,49,60,62,268]. The effects of multi-folds are essentially with a spin-2 symmetry [1,23,265,268], which also explains the holographic principle of gravity [1,85,265], or the area laws of black holes. The spin-2 symmetry implies the embedding space effects are mostly 5D because paths on the multi-folds are essentially a grand circle on each fold. In the 4D multi-fold spacetime, the embedding space is only felt (inside out) through the multi-folds as ε infinitesimal and essentially 5D. No Physics takes place in the multi-folds, except for the massless and massive (when they exist) Higgs bosons and right-handed neutrinos, per [1,9,10,265,268] and references therein Particles in 4D spacetime feel essentially a 5D, but it is actually a 7D when it comes to the symmetries of the solutions/solitons induced or scatterings, spacetime through the ε region at entry, exit, or mapping points. It is an additional reason for the tenancy principle discussed in [1,9,10,265]: as each location only sees multi-fold due to their involvement with multi-folds, they do not see other particles, e.g., like the entangled ones, or other particles crossing the support between them, unless if they are already overlapping (wavefunction wise) in spacetime. The (massive) Higgs boson everywhere in spacetime and at the entrance and exit being the only exception, and due to 7 It may be a role played by the Higgs in multi-fold theory as we will discuss later. This would be the best possible justification of why the Higgs field appears, and exists in multi-folds [28,29,268,296,302,303]. So far, we had explained the consequences of the Higgs being associated to the multi-folds, but no so much why it was that way. The reader should assume that, going forward, this is a plausible aspect of the mainstream multi-fold theory. Note added on August 1, 2025: More details exist in [28,29,268,279,289,296,302,303]. the interaction with it to enter or exit. Then, let us also consider the discussion of dilaton from the previous footnote, and again towards the end of this section. Multi-fold 5D space time matter induction (actually effects of 7D, but mainly 5D when it comes to dominant solitons geometries, geometrical objects impacting the 4D spacetime), and scattering with 5D/7D objects, when feeling the embedding space in an ε region, and encountering a 5D/7D soliton, recovers particles and interactions in the 4D multi-fold spacetime that match the SM particles, fields, interactions and symmetries [23,29,30,49,51.62,64,77,177]. It can also be seen as an unconstrained Kaluza Klein theory. The 7D space can now support, and explain, the symmetries of the SM [23,51,62,77,17]. The multi-fold least action principle ensure that the SM, or SMG, is always what it is supposed to be [77]. In other words, we can recover the SM in multi-fold 4D spacetime via space time matter induction. The remaining challenges of chiral fermions, not available in 5D or 7D, is resolved in the 4D spacetime by the Multi-fold gravity electroweak symmetry breaking [4,9,10,29,30,52,53,60,64,63,296,303,307]: it (globally) orients spacetime, and makes some microscopic black hole particles rotate. Above that energy level, it only locally exist around massless particles as patterns of Higgs random walks. Note added on August 1, 2025: Consider also the details and interpretation described in [303]. The particles exist only in 4D spacetime, and only feel the multi-folds from such a 4D spacetime, therefore resolving the challenges of the absence of chirality in higher odd dimensions, of dimensions to compactify (embedding space is just no visible), or of incompatibilities between say 7D and the SM: spacetime is 4D even, chirality and Huygens’s principle are making sense, QFT are well defined and behaved, it is the normal number of dimensions for a GRbased stable spacetime (if flat or dS) etc. [318,331,377-381], yet taking advantage of KK induction and scattering effects from 7D, dominantly 5D, in a ε region. Gravity can be asymptotically safe [13,16,17,60,63,82,83]. Higgs and neutrinos are recovered together by scattering from within the multi-fold, as already discussed in previous sections [50,49,96,233]. Non-commutative theories in a multi-fold universe are key to ensure that we can fully recovers the SM [1,30,63,64]. Note added on August 1, 2025: QFTs on a discrete spacetime imply non-commutativity (because of the resulting discontinuous paths in the path integral), which is key to ensure the possibility physicality of fermions [6,30,64,282,294,296,299-301]. Note that we do not say that the 7D embedding space is physical, beyond the portions (ε neighborhood) seen offered (inside out) by the multi-folds, that the 4D spacetime particles feel at the points of entry, exit and mappings [1,265,268]. This way, 4D Physics is not 7D or 5D physics, and so chiral fermions are possible (as in 4D), and we do not have a challenge of explaining why 3 large, i.e., not compactified, dimensions would not be visible to us, which is one of the reason, (besides the automatic compactification discussed in section 3) why superstrings have had to compactify their extra dimensions because they do not have a mechanism to hide large extra dimensions and they need some Physics into them. Also it does not hurt that extra dimensions are expected to automatically compactify [132,192-195]. Such compactification is key to the superstring dualities. In the multi-fold case, we have no physics in the multi-fold (other than with the Higgs) and only feelings of ε neighborhoods, nothing to see or feel macroscopically, other than the 4D consequences [1,8-10,22,265,268,279]. As already mentioned, the dilaton is not needed in the multi-fold space time matter induction and scattering. However, we know that in the multi-fold theory, the Higgs boson appears in the multi-folds (See the tenancy model in [1,9,10,268]), including in front of (entangled) right-handed neutrinos, and their anti-particles at the entrance and exist of the multi-folds [29,41,49,96,233]. The latter ensures traversability of any wormhole implementation of multi-folds, if wormholes are to be involved [6,233], and stability of the underlying KK solution, because of the presence of fermions [96]. While there is no compactified dimension, and no volume is being modified in any dimension, are involved, multi-folds follow the entangled particles mapped in the embedding space, and the mutifolds have their own kinematics and dynamics of expanding to follow the attached entangled particles [1,8- 10,22,76,259,265,268,279]. So, in a multi-fold universe, there might still be a dilaton in waiting, and the Higgs could implement this dilaton, just as it can implement the inflaton in [28], or account for the dilaton/scalar of the double copy gravity when particles are massive [58,196,197], and 2D gravity [1,16,17,28,63,67,84,251,265,279,289,296,302,307], making it all consistent. It also has the unique advantage to explain why Higgs is naturally in the 4D spacetime and multi-folds [1,8-10,265,268,279,296,307,482]. This explanation is presented for the first time in this paper, even if mentioned, by topic, in passing in past papers. At this stage, we have established that in a multi-fold universe, spacetime is 4D at large enough scales, and it seems (/feels) embedded in a 7D spacetime generated / felt in an ε neighborhood at each entry, exit or points mapped to the multi-folds. It is 7D, which is required to support the symmetries of the SM or SMG[23], and support space time matter induction and scattering. As the embedding 7D spacetime is a ε neighborhood created by the multiple-folds, it is and will be a extra 3D spatial dimensions, dense enough to support the right fields there: the massless Higgs boson , i.e., the dilaton associated to the multi-fold dynamics following the attached entangled particles (or in the case of the W-type multi-fold hypothesis, following the evolution of the wavefunction [68]). 8. 2D, 3D, 4D? Can We Try To Get Our Acts Together? In all consistent theories of gravity, we see a dimension reduction of spacetime / gravity [1,82,83,218,219] to 2D or 3D. The 2D to 3D evolution is discussed in [1,82,83], and relates, for example, with the transformation essentially to everything massless above the muti-fold gravity electroweak symmetry breaking [53,63,60,303], give or take massiveness, due to chiral symmetry breaking and confinement as long that confinement exists [53,60,63,289,296,302,303], which justifies what seems to be a reduction to 3D that then evolves into a reduction to 2D. Around when reduced to 3D scales, conventional physics also tells us that spacetime is non-commutative [220], just as in the multi-fold theory [1,23,30,31,63,64,265,282,288,289,296,303,307]. A Random walk is inherently 2D (time and direction) with, at larger scale considerations, the plane where it moves then the volume, at even larger spatial scales, as illustrated in Figure 3. Figure 3. It illustrates how random walks are initially at lowest spatial scales a 2D process, then a 3D then eventually a 4D process. Also, per [83], when massless, 3D appears 2D as all particles move at c, making the 2D process dominant till larger spatial scales [1,265]. Note added on August 1, 2025: [289,303] shows that attempts at creating additional dimensions and noncommutativity are essentially equivalent, and a source to the multi-fold dark energy effects [1,810,22,27,30,33,64,75,259,265,270,279,296,305,307,308], which may be time varying. So multi-fold dark matter effects results (partially at least) from non-commutativity of a discrete spacetime [6,282,303,307]. So with 2D physics, we have asymptotic safety of gravity and renormalization/asymptotic safety of QFTs/Yang Mills/SM, or SMG as discussed in [16,17,30,31,53,63,73,289,296,303], along with UU [1,6,43,60,63,67]. And 2D Physics is all that matters [258]. All this means that spacetime is macroscopically 4D, not 2D, but when looked from the point of view of small enough spatial scales, it appears 2D (then 3D, when increasing the spatial scales), as well as for multi-fold universe: non-commutative while Lorentz invariant thanks to the randomness of the walks leading to realized locations according to Poisson distributions that preserve Lorentz invariance [1,23,30,31,32,63,64]. It matters. For example, when considering and applying the Polya’s random walk theorem, the spacetime is to be understood as 4D, not 2D. Indeed the 2D processes develop in a 4D spacetime (built in real time or by previous random walks; anything larger stalls and withers immediately), that is reconstructed and concretized [1,6,31,63,64,177], as well as not in a larger dimension spacetime (5D and above), per section 3. Note added om August 1, 2025: [296,303,307] also show how (entangled) random walks can then equip the resulting spacetime with dot products, distances, area and Hamiltonian/conjugate variables. Our reasoning in that paper (Appendix B in [307]), does not require differentiability, which makes the reasoning more generic than in the references relied on in [307], and suitable for a spacetime actually discrete, non-commutative, fractal and possibly not smooth [1,810,22,31,30,60,64,89,259,265,276,279,282,294-296,307,308,319,320]. Note added om August 1, 2025: Appendix B in [307] explains how spacetime with distances, areas and Hamiltonian, in a continuous smooth/differentiable or not, can emerge from dense enough 2D random walks. The fact that in our universe QED does not confine at SM and larger spatial scales, and spacetime appears continuous, shows that the processes of Appendix B in [307] must take place, otherwise QED would confine, as it does in 2D and 3D (see after and also appendix B here, and [60,63,296,303,307]). Physically this is because in Figure 3, we not just have motion in new dimensions (thwarted when going in the fourth spatial one), but also the density in each of the existing dimension is such that jumping along a path or across paths of random walks are equivalent, as hinted in Figure 4. When that is the case spacetime is really 4D and continuous at large enough macroscopic scales, and the constructs discussed in Appendix B of [307] can be developed. Figure 4: This figure shows a denser case of Figure 3, where, as hinted in purple/violet, distances between random walks concretized locations is equivalent/same order as the ones on a random walk path. Then jumps (think of [6], and figure 6) are no more linear but become 3D then 4D, then continuous. 9. Bound States, Stability, Orbits, Collisions And Escapes As we will see the go-to papers on this focused on classical / semi classical Physics [167,170,171]. We will extend the analysis to cover also quantum Physics, and QFT, relying on the 2D random walks. It is a key contribution of this work. 9.1 Ehrenfest’s Approach For The Conventional Universe Inspired by the papers of Ehrenfest [170,171,321], Tegmark provides his own analysis of the spacetime dimensionality [167]. These authors show that spacetime must be 4D if we want to have stable bound states with closed orbits, as encountered with, for examples, atoms and galaxies in our real universe. Here are a few key highlights: • Ehrenfest showed that [170,171]: o At spatial dimensions strictly larger than 3, no bound state (classical atoms, cosmic or quantum (Schrödinger)) can exist because interacting systems always end up colliding or escaping away from each other, never entering into stable / closed orbits [169,170,322,323] The system is always unstable 8 . o For spatial dimension of 3, there can exist stable orbits in Newton gravity {169,170], and in GR {170,171]. It is a miracle, in the words of Ehrenfest, that closed orbits exist in curved spacetime, and escapes to infinity are also possible, as is the hydrogen atom, including with relativistic effects as in [170,171] and references therein. Also, it is only in spatial 3D that the fine structure constant is dimensionless [170,171], per QED, our most precise physics theory so far. A fine structure constant function of the units selected is not what we observe in our universe. o For spatial dimension of 2, escape to infinity are not impossible, but the gravitational potential does not vanish/become constant at infinity, which excludes this option for our real universe. Also while one may have stable circular trajectories, they are not closed and hence not orbit [170,171]. o For spatial dimensions of 1, we recover 2D gravity like JT gravity (see section 12), orbits imply no relative motion, and therefore they are unstable. Only going from 2D to larger scales à la Multifold spacetime reconstruction makes it physical [1,6,265,296,303,307] • [171] and references therein also mention Withrow’s biological consideration, i.e., the need to be able to link neurons without intersections, something possible in our universe, as another reason why 2D spatial can’t support enough complexity: systems built in 2D cannot be complex enough for life, or many other systems. The need to support neurons crossing (and not intersecting) between complex bodies and brains is motivated for example in [234]. Without this capability, no perception of a 3D world would be manageable with 2D neural network representations, as seemingly encountered in the brain. All this indicates that our spacetime must be 4D, i.e., 3D spatial. As discussed at the smallest scales it is 1D spatial evolving to 2D spatial then 3D and stopping there. Appendix B provides some considerations on the interaction potentials e.g., Coulomb potential, in different dimensions. 9.2 A Random Walk Qualitative Perspective On Stability And Bound States For QFTs In Higher Dimensions 8 We note that [169] criticizes using stability as criterion. The authors argue that systems, or particles, which exist and are stable in a larger dimensional spacetime, may be unstable in 4D spacetime, and therefore that this may not be a valid criteria to decide on the spacetime, or a system, dimensionality. It may be adequate for their examples and considerations, but it does not apply here. Indeed, such an argument seems unapplicable to the discussion here as Ehrenfest showed that there is just no stability for any spatial dimension above 3D spatial: we don’t have an issue of stable system becoming unstable at a lower spatial dimension. [169] also argues that higher dimensions remove singularities, think of black holes, which may be a criteria against 3D spatial when black holes are singular. It is unclear if this really helps, as such higher dimension black holes would have to form without enough gravitation interactions (see Appendix B), and stable orbits. In any case [169] propose another experimentation, which may be realizable in the future. We believe however that the point is moot with the results reported in sections 2.3 and 2.4. Note added on August 1, 2025: Furthermore, we know that multi-fold universes have no cosmological or gravitational singularities, and argue that our universe would not have any naked singularity. So singularities may not be the best criteria either [1,4,66,182,b16,b29,b35,b40]. Section 9.1 analyzes bound states for classical and simple quantum mechanical systems. As we also focus on QFTs in different dimensions (e.g., se section 5), it would be good to validate the implications of the above for QFTs, if at all. The absence of guaranteed recurrences of random walks in D ≥ 4 spacetime, means that interactions weaken rapidly at these dimensions (and closed orbits are impossible). While the paths may still be dense in D=4, as explained in earlier sections, they certainly aren’t for dimensions above 4, unless maybe if associated to SUSY, CFTs. Topological fields or strings/branes (i.e., extended objects, discussed earlier, which elevate the density to higher dimensions). Therefore, virtual particles, i.e., carriers of QFT interactions, do not always reach the other parties, hence reducing the intensity of the interaction as the spatial dimension increases. Actual dependencies in the distance between particles are discussed in Appendix B. As a result, stable closed orbits become impossible above a certain dimension, which we would expect to be above D=4 spacetime (as no more dense enough) for QFT (without extended objects). It is what section 9.1 obtains. While [1,60,98] argue for a mass gap and Yang Mills viability in a 4D *discrete* spacetime [60], here we conjecture that around 5D we would not have stable orbits, and therefore no gluon balls and no mass gap: Yang Mills in 5D would probably only exist via spacetime fluctuations (leakage) due to quantum uncertainties [14,86,197], not really because 5D force carriers would be sufficient, they need to be complemented by the leakage effects, and won’t exist far away between 5D (generalized) charge carriers. Overall, we see some relation to results like [173]. At spatial 2D, i.e., D=3, the only other reasonable spatial dimension to consider, interactions are maximized. Escape becomes harder and we would rather have confinement. Again this is consistent with section 9.1. Also, it is consistent with for example 3D QED, and the Schwinger model, now behaving similarly to the strong interaction with confinement [60,63,136,174-176] (and axial chiral symmetry breaking, this being more a consequence of the apparition of confinement (See discussions in [60,296,303,307] and references therein). It motivates UU [1,8-10,22, 6,43,59,60,63,67,177,259,265,279,296303,307], and the dark matter conjecture [59,303]. With this reasoning, and stronger possibilities to form bound states, we expect QCD at 3D and 2D to have a mass gap way more naturally than in 4D [1,60,98], but we would need further work to decide if discreteness remains a requirement. It may be the object of future work. If Physics is a guidance, discreteness of the 2D, and 3D, spacetimes, implies that it remains probably a requirement. Also, the absence of actual closed orbits may not favor orbits as in figure 5 of [60]. We suspect that it prevents guaranteeing a mass gap, without involving stable gluon balls. This analysis is complementing our mass gap resolution papers [60,98]. 9.3 About QCD And QED/Electroweak Below The Gravity Electroweak And Chiral Symmetry Breakings At Higher Energies In [1,4,29,52,53,60,63,b10,b16,b30,b40,b47,b54,b58], we distinguish between behaviors below and above the (multi-fold) gravity electroweak symmetry breaking. When raising in energy, or looking at smaller and smaller spatial scales, we loosely model a transition from mostly massive particles (with Higgs condensation) to massless particles resulting from random walk patterns of massless Higgs, and recognizing some interim plasma state if density is high enough at high enough energy, so that confinement breaks, or is irrelevant as we can’t distinguish freedom from confinement if all particles are densely packed, before potentially reaching a very densely packed BEC [60,63,296,303,307,308,315]. It is well known that confinement and associated chiral symmetry breaking convey mass to particles or environment by adding energy content to the soup of quarks present in particle (e.g., hadrons or nucleons) or plasma. See [60,221] and references therein. Note added on August 1, 2025: The mechanisms and microscopic interpretations are described in [60,63,296,303,307,308,315]. Also, in 2D QED, the Schwinger process shows exactly how interacting massless fermions cancel out massless bosons, leaving a massive boson / photon), due to chiral symmetry breaking and associated confinement. See [60,63,136,175,176] and references therein. Also, in [63,137], we see that fermions are key to the existence of Maxwell and Yang Mills interactions, via these massive bosons that reflect confinement. Going smaller in spatial scales, confinement and chiral symmetry breaking continues until densities / pressures render confinement meaningless, or until quark gluon plasma forms with loosened confinement (and hence with massless particles (Note added on August 1, 2025: it is consistent with [296,303,307], where plasma formation can be seen as a path to forcing masslessness)) [60,221,222], or when one reach dimensions smaller than the fundamental particles and UU starts to dominate [1,6,43,60,63,67], and everything at these scales appears massless. These are slight additional details added to the story told so far in previous papers [1, 6,43,60,63,67]. Here, what is important is to understand that, above the gravity electroweak symmetry breaking energy scales, we do not have a Higgs condensate any more, and particles instead consist of random walk patterns, but they may keep inertial mass coming from the energy associated to the confinement/chiral symmetry breaking and/or anomalies (think the extra energy resulting from the axial chiral current [b93] impacting the random walk patterns; this is where our tentative image of spin may also help [1,64], as it may allow us to imagine this as the energy of an extra vortex. With the caveat that we are not claiming that such vortex is how to see axial chirality current, symmetry breaking, and possible associated anomalies. Note added on August 1, 2025: See [296,303,307] for more details on what we propose that actually happens). 10. About AdS vs. dS 10.1 Spacetime with Negative Curvature / Cosmological Constant There are many indications that our spacetime is slightly asymptotically dS (de Sitter), with a strictly positive spacetime curvature and cosmological constant. It is therefore not asymptotically AdS. Here are some entry points of experimental confirmations [1,18,27,223,259,265,279] and references therein, although we must admit that the subject remains controversial, and, at times, some argue that it is actually flat. Note added on August 1, 2025: by now we have shown that the cosmological constant must be strictly positive [250,289,296,307]. Flatness is not an option. In [1,8-20,62,81], we discussed how AdS[5)(+…) 9 can be seen as the space created by multi-folds and where multifolds, or possibly gravitons (as implemented by multi-folds [1,58,80,81,197]) and superstrings (as approximation of the multi-folds) live. It is involved in the AdS/CFT correspondence conjecture, and can relate to our spacetime via the AdS/(C)QFT correspondence (AdS/CFTYMC2G) [YMADS} [197], or the multi-fold factual AdS/CFT correspondence [1,8-20,62,81,197]. It has been shown, see references in [1,8-10,14,15,16,250,265,279,308], that superstrings (and supersymmetry) can only exist in spacetimes with negative (or flat) cosmological constant. It has also been shown that it is not possible to compactify gravity from superstrings or supergravity to a 4D (asymptotic) spacetime) [224,225]. The 9 (+…) is added to allow for extra dimensions needed by superstrings, supergravity or M-theory as in the conventional AdS/CFT correspondence conjecture. However, it is not needed in the multi-fold theory and its factual AdS/CFT correspondence [1,8-20,259,265,279]. combination of this with the 2 paragraphs above indicates that our spacetime is macroscopically 4D asymptotic dS, and not (asymptotic) AdS (4 or 5)(with or without (+…)). 10.2 (Asymptotic) dS Spacetime Fields can be defined on asymptotic dS(4) spacetime, including some supersymmetric ones [226], but the latter would not be unitary, which is a quantum theory challenge, albeit something that may be acceptable with hermicity considerations instead, as discussed in [1,63,65,77] and references therein. Note added on August 1, 2025: We know by now that supersymmetry is non-physical, so these are only mathematical constructs. Note also that a unitary supersymmetric field has now been found [329], but it is non-interacting, as it should be per [341]. Free-only unitary fields do not match our observed universe where we have (at least) 4 interactions. The lack of time like killing spinors (Simply because energy is not conserved as the metric changes over time, at the difference of AdS which is static. A more rigorous analysis can be found, for example, in [365]. It is also why unitarity can be a challenge [341]. While a challenge for all QFT models, for supersymmetric field, we need repelling or nonconservative random walks, as the most fundamental underlying physical interpretation [59,250,369,370], something forbidden as unitary fields can’t be interacting [341]. Indeed, this means that no local perturbation or rescaling with dS isometry can address this lack of interaction: Physically meaningful supersymmetry can’t exist. This is a strong new argument to add to those compiled in [250,296,307].), and of a well-defined S-matrix (due to horizons, and the absence of asymptotic states) in dS(4) means that standard renormalization group (RG) techniques and unitarity arguments fail. This differ from flat space, or AdS(4), and undermines the construction of interacting SUSY QFTs, which rely on these properties for consistency [330,341,362-366]. Again, we have an unphysical purely mathematical theory. [364] provides another topological example of supersymmetric field in dS, but at larger dimensions (9+1). Note that there are some unitary possibilities for some supersymmetric-like half spin particles [367,368], but again this are purely unphysical considerations per all our analyses, and they do not explicitly encounter supersymmetry but rather unitary representations of a Spin group. CFTs, also related to supersymmetry and the AdS/CFT correspondence conjecture, also present problems in dS. To be fair, such a dS spacetime also presents problems, as already discussed for example with black holes in asymptotic dS/expanding universes as in [75], a topic still confusing to many, as exemplified in several references in [75]. Note added on August 1, 2025: [182] should put this to rest. We also know by now that non-commutativity and dS spacetime are closely linked [307]. Non-commutativity, related to spacetime discreteness, contributes to ensuring no singularities at all. We expect that the real universe has no cosmological or gravitational singularity. Another puzzling set of challenges comes from Witten [227], who argues against achievability of realistic precision Physics in (asymptotic 10 ) de Sitter universe, unless if we can precisely explain the cosmological constant. We will not discuss here such challenges, only point out that, in our view, the multi-fold theory can achieve the required precise explanation, at least qualitatively for now [1,27]. We may revisit in a future paper. Note added on August 1, 2025: See [6,27,64,307,325] for more on this. So far, our conclusions are that our universe is macroscopically dS(4), because of the strictly positive dark energy effects, constant or time-varying, it does not matter [1,8-22,27,265,268,279,296,307]. It means a finite closed universe, instead of an infinite universe as with AdS(4). Note added on August 1, 2025: It also means a universe which is stable with matter [318,331,377-381], vs. the instabilities of AdS [1,14,18,265,332]. [318,381] implies initially a state with only massless ultra relativistic fields, which is consistent with 2D random walks of massless Higgs bosons, and UU. The problem of radiation at the horizon, and constraints to stability for instabilities within the horizon is in our view related to the challenge to selecting a god-like observer of the dS universe. When 10 Realistic is for the asymptotic case. considering dS as a whole, within and outside the cosmological horizon, we argue that the stability holds and Hawkings radiation at the horizon are not relevant: the horizon is fictitious or said otherwise, what seems to be radiated inwards never occurs because its out-falling component can’t catch up with the horizon expanding at c [1,8-10,22,32,66,259,265,279].To understand, consider Hawkings popular explanation and the multi-fold hawking radiation proposal [1,8-10,22,32,66,88,238,239,259,265,279]. We may further detail the latter in an upcoming paper. Figure 5: In an expanding (asymptotic) dS universe, the cosmological horizon expands at c. The entangles pairs move apart with a direction orthogonal to the horizon that is smaller, or equal, to c. The horizon expands and catches up with most particles that would have been beyond the cosmological horizon, separated from the other particle in the pair. Eventually it would do so for all of them. There is no Hawking effect that would render the spacetime unstable. 10.3 AdS QFTs and all that As already mentioned, there are supersymmetric, (super)conformant, topological and Chern-Simons fields at higher dimensions, typically supersymmetric, and many associated to AdS spaces. A quick reading of section 5, skipping the footnote where we already hinted of what is to come here, should surprise the reader: how can such fields exist if we have shown that random walks does not cover such spacetime densely enough? We explained how 5D+~ fields could exists thank to leakage mechanisms [86] due to quantum fluctuations, or CFTs could exists close to the seeding D-2 11 spatial space with random walk translation of that seeding space. But it has limits. That latter statement contains an alternate model that we already mentioned as the random walk of extended objects: if spacetime was to be generate by superstrings (think also of branes), then these superstrings, or branes, e.g., as in [14,15,308], provide a background field of their dimensions, or their own random walks can generate a denser coverage of larger dimensions spaces, as we now have extended object “walking” (and undulating as they do so). So, it should not be surprising that AdS(5), and higher dimensions space (10, 11, 26) could exist, (some) with associated fields, always expected to be supersymmetric, conformant (and/or topological). Indeed other cases would not be justifiable by this arguments as superstrings are supersymmetric and conformant, at least not if not accompanied by a sensible symmetry breaking justifications. An example of not making sense is discussed in Appendix C. 11 One of the -2 is for the time dimension. Appendix B: SM (Coulomb, QCD, (Electro)Weak), and Gravity potentials in Different Spatial Dimensions At the core of Ehrenfest arguments is the modeling of the Coulomb potential for QED / Electromagnetism, and its corresponding distance dependency for the weak (/electroweak) and strong interactions, as for example discussed in [307]. For QCD, we are similarly inspired as in [60], while the weak interaction is dominated with the exponential weakening à la Yukawa, at energies below the gravity electroweak symmetry breaking (For energy above, the dependency can be as for QED, as they unify in one unified interaction, carried by massless bosons). At large scale, where GR / Newton gravity is a good model, the gravity potential has similar behaviors [1,265,357]. Accordingly, when decreasing the spatial scale, the coulomb potentials evolves in ln(1/r), then r, as spacetime dimensions become essentially 3D then 2D [324,357], resembling QCD. As a result, QED and QCD, i.e., the SM interactions, essentially confine [60,63], unless if/when percolating in a very dense plasma state where confinement becomes meaningless because of the density. Going to smaller spatial scales, GR based gravity on the other hand becomes independent of the distance when in 2D spacetime [325]. As a result, only gravity remains relevant. It is the essence of the Ultimate Unification (UU) [1,6,8-10,22,31,43,59,60,63,67,259,265,279,296,303,304,307], and why 2D gravity like JT / dilaton gravity is such a good model for some studies of quantum gravity [1,16,28,43,63,67,84,251,259,265,279,296,302]. At larger scales, the gravity & Coulomb potentials evolve in 1/rD-3 [357]. As a result, as D increases, the interactions between charges decrease, amplifying the lower density effects due to 2D random walks (the Polya’s theorem [127,128]), discussed in section 3, and (further) preventing QFTs to be defined in high dimensions. Appendix C: What about D=26 for Bosonic Strings? Based on this paper, one may be surprised that bosonic strings (open and closed) live in a 26D space (with 1 time dimension). Reasoning and derivations are mentioned to, and relied on, in [14], based on [371-376], and many other materials on quantum gravity, strings and supersymmetry. When imposing that the Weyl invariance, inherent to, and apparent only in the Polyakov formulation of the string action, must hold and that string on a background spacetime / background of field must be independent of its curvature/behavior, at low energy, one cancel the conformance anomaly introduced by quantization, if D = 26. D=26 is also required to ensure Lorentz invariance. At other D, conformance symmetry is lost, and our criterion of independence from above fails. In such a space, open strings include models of Tachyons and massless bosons modeled by Yang Mills interactions, while closed strings model a Tachyon and a massless spin-2 particle, reminiscent of the graviton, and the GR equation is encountered. In [14], we argued that this, encountering GR and gravitons behaviors, (and Yang Mills with Yang Mills carriers)) is not surprising. The tachyon and the presence of ghosts is a concern. Ghosts and tachyon instability still need to be addressed. These discovery were the origin of the claims that strings is a good candidate model for quantum gravity, the SM and for a TOE (Theory of Everything). Interestingly, in multi-fold theory, multi-fold seem to play the role of gravitons as quasi particles (sometimes massive when associated to entangled massive particles), and becoming closed string within the dual/cotangent AdS(5) (+…) space [1,8-20,22,58,62,80,81,250,251,259,265,279]. What lives in that space is not physical. When super-symmetrizing the action, by adding a minimally coupled fermion contribution for each boson, and repeating the steps above, the superstrings now requires a spacetime D=10, where ghosts are well treated, and the conformance anomaly and tachyons disappear. And we have Lorentz invariance. It is the reason for involving supersymmetry in string theory/M-Theory, along with super gravity [250]. The good behavior, including putative renormalizability, because of the Weyl Conformance, and the fact that the action includes gravitons for GR, bosons, described by Yang Mills, and super symmetric fermions (and conversely for bosons) is the main reason while the Physics community drank the cool aid, with many claiming that superstring is the best theory we have so far for gravity and TOE. Alas, it was not to be, as discussed in [1,8-20,22,58,62,80,81,250,251,259,265,279], and proven in [250,296,307,308] and reference therein. No experiment has ever encountered any sign of supersymmetry or any supersymmetric particle. Note added on August 1, 2025: [250,296,307] also showed that supersymmetry breaking are not of any help, as the main arguments against supersymmetry apply especially well at the smallest possible spatial dimensions, i.e., the highest possible energies: there was never supersymmetry in our universe, so nothing to break. Based on our analysis in this paper, the random walk of extended objects (D-branes) in D =10 can justify 10D spaces (and 11D for the M-theory when adding supergravity). It can be supersymmetric, but it is meaningless as it contains no Physics and no particles (other than, in some cases, within the multi-fold) outside 4D. So AdS(5) (+…) works up to 10D or 11D. Any extra dimension can be mathematically added, and have misbehaving strings and extended objects, which are unphysical and misbehaved, per the string analysis mentioned above. 26D, and other dimensions are possible, but misbehaved: when D≠26. They have no well behaved path of extended objects random walk as far away from D = 10 or 11. Therefore, when D≠26, fields can’t be modeled by any type of random walks. And so, it is not surprising that they also includes ghosts, tachyon, instabilities and a Weyl anomaly. At D=26, only the Weyl anomaly, and Lorentz invariance, can be addressed. As argued, yes one can build mathematical “fields” but they are just not physical at such high dimensions, even if, because suited to model gravity, that they obvious include [14], they can hint at some physical behavior within such spaces like multi-folds as hints of gravitons as quasi particle, while no graviton particle actually exists in our 4D spacetime [1,820,22,58,62,80,81,250,251,259,265,279]. ____ References [1]: Stephane H. Maes, (2020-2022) “Quantum Gravity Emergence from Entanglement in a Multi-Fold Universe”, HIJ, Vol 2, No 4, pp 136-219, Dec 2022, https://doi.org/10.55672/hij2022pp136-219, https://shmaesphysics.wordpress.com/2020/06/09/paper-published-as-preprint-quantum-gravity-emergencefrom-entanglement-in-a-multi-fold-universe/, https://shmaesphysics.wordpress.com/2022/11/09/quantumgravity-emergence-from-entanglement-in-a-multi-fold-universe-2/, and viXra:2006.0088, (June 9, 2020). Errata/improvements/latest updates at https://zenodo.org/doi/10.5281/zenodo.7792911. [2]: Wikipedia, "Reissner–Nordström metric", https://en.wikipedia.org/wiki/Reissner%E2%80%93Nordstr%C3%B6m_metric. Retrieved on March 21, 2020. [3]: Wikipedia, "Kerr–Newman metric", https://en.wikipedia.org/wiki/Kerr-Newman_metric. Retrieved on March 21, 2020. [4]: Stephane H Maes, (2021), “More on Multi-fold Particles as Microscopic Black Holes with Higgs Regularizing Extremality and Singularities”, viXra:2210.0004v1, https://shmaesphysics.wordpress.com/2021/02/28/more-on- multi-fold-particles-as-microscopic-black-holes-with-higgs-regularizing-extremality-and-singularities/, February 25, 2021. [5]: Stephane H Maes, (2020), “Multi-folds, The Fruit From The Loops? Fixing “Oops for The Loops” May Encounter Multi-folds in General Relativity And The E/G Conjecture”, viXra:2212.0206v1, https://shmaesphysics.wordpress.com/2021/12/31/multi-folds-the-fruit-from-the-loops-fixing-oops-for-loopsencounters-multi-folds-and-the-e-g-conjecturein-general-relativity/, January 1, 2022. [6]: Stephane H Maes, (2022), “Deriving the Multi-fold Theory from General Relativity at Planck scale”, viXra:2302.0129v1, https://shmaesphysics.wordpress.com/2022/02/22/deriving-the-multi-fold-theory-fromgeneral-relativity-at-planck-scale/, February 22, 2022. [7]: Stephane H Maes, (2022), “From Quantum Relational Equivalence to Multi-folds Encounter in the Real Universe and Confirmation of the E/G conjecture”, viXra:2302.0108v1, https://shmaesphysics.wordpress.com/2022/02/12/from-quantum-relational-equivalence-to-multi-foldsencounter-in-the-real-universe-and-confirmation-of-the-e-g-conjecture/, February 7, 2022. [8]: Stephane Maes, (2020-25), “Web Site Tracking all Publications around the Multi-fold universe”, Navigation page listing all papers, https://shmaesphysics.wordpress.com/shmaes-physics-site-navigation/. [9]: Stephane H Maes, (2021), ”The Multi-fold Theory: A synopsis”, viXra:2112.0144v1, https://shmaesphysics.wordpress.com/2021/12/24/the-multi-fold-theory-a-synopsis-so-far-v2-end-of-2021/, December 24, 2021. Note that additional links will always be available at https://shmaesphysics.wordpress.com/2021/05/03/the-multi-fold-theory-a-synopsis-so-far/ to track the latest and interim versions of the synopsis, as they may be published under different tittle or URL/publication numbers. [10]: Stephane H Maes, (2022), “Understanding the Multi-fold theory principles and the SM_G”, osf.io/xc74t, https://shmaesphysics.wordpress.com/2022/03/11/understanding-the-multi-fold-theory-principles-and-the-sm_g/, March 11, 2022. Also as Stephane H Maes, (2022), “A tutorial on the Multi-fold theory principles and the SM_G”, viXra:2303.0154v1, https://shmaesphysics.wordpress.com/blog-2/a-tutorial-on-the-multi-fold-theoryprinciples-and-the-sm_g/, March11, 2022. [11]: Stephane H. Maes, (2022), “Comment on LQG, Superstrings, Supersymmetry and most GUTs/TOEs, all have big problems exposed by the Multi-fold Theory”, https://shmaesphysics.wordpress.com/2021/12/27/the-multifold-theory-a-synopsis/#comment-3293. Published on January 9, 2022. [12]: Stephane H. Maes, (2020), “Comment on why no supersymmetry”, https://shmaesphysics.wordpress.com/2020/10/11/circular-arguments-in-string-and-superstring-theory-from-amulti-fold-universe-perspective/#comment-934. Published on October 12, 2020. [13]: Stephane H Maes, (2020), “Renormalization and Asymptotic Safety of Gravity in a Multi-Fold Universe: More Tracking of the Standard Model at the Cost of Supersymmetries, GUTs and Superstrings”, viXra:2102.0137v1, https://shmaesphysics.wordpress.com/2020/09/19/renormalization-and-asymptotic-safety-of-gravity-in-a-multifold-universe-more-tracking-of-the-standard-model-at-the-cost-of-supersymmetries-guts-and-superstrings/, September 18, 2020. [14]: Stephane H Maes, (2020), “Circular Arguments in String and Superstring Theory from a Multi-fold Universe Perspective”, viXra:2103.0195v1, https://shmaesphysics.wordpress.com/2020/10/11/circular-arguments-in-stringand-superstring-theory-from-a-multi-fold-universe-perspective/, October 5, 2020. [15]: Stephane H Maes, (2021), “The String Swampland and de Sitter Vacua: A Consistent Perspective for Superstrings and Multi-fold Universes”, viXra:2208.0078v1, https://shmaesphysics.wordpress.com/2021/01/12/the-string-swampland-and-de-sitter-vacua-a-consistentperspective-for-superstrings-and-multi-fold-universes/, January 9, 2021. [16]: Stephane H Maes, (2021), “Quantum Gravity Asymptotic Safety from 2D Universal Regime and Smooth Transition to Dual Superstrings”, viXra:2208.0151v1, https://shmaesphysics.wordpress.com/2021/02/07/quantumgravity-asymptotic-safety-from-2d-universal-regime-and-smooth-transition-to-dual-superstrings/, January 29, 2021. [17]: Stephane H Maes, (2020), “A Non-perturbative Proof of the Asymptotic Safety of 4D Einstein Gravity, With or Without Matter”, https://doi.org/10.5281/zenodo.7953796, https://shmaesphysics.wordpress.com/2022/05/04/anon-perturbative-proof-of-the-asymptotic-safety-of-4d-einstein-gravity-with-or-without-matter/, May 4, 2022, viXra:2305.0138. [18]: Stephane H Maes, (2020), “Dualities or Analogies between Superstrings and Multi-fold Universe”, viXra:2006.0178v1, https://shmaesphysics.wordpress.com/2020/06/14/dualities-or-analogies-betweensuperstrings-and-multi-fold-universes/, June 14, 2020. [19]: Stephane H Maes, (2020), “Alignments and Gaps Between Multi-fold Universes And Loop Quantum Gravity”, viXra:2006.0229v1, https://shmaesphysics.wordpress.com/2020/06/19/multi-fold-universes-analysis-ofloop-quantum-gravity/, June 18, 2020. [20]: Stephane H Maes, (2020), ”Superstrings Encounter of the Second, Third or Fourth Types?”, viXra:2010.0140v1, https://shmaesphysics.wordpress.com/2020/07/19/superstrings-encounter-of-the-second-third-or-fourth-types/, July 5, 2020. [21]: Stephane H Maes, (2022), “Oops For The Loops II: Real Oops; LQG Does Not Optimize the Hilbert Einstein Action”, viXra:2301.0036v1, https://shmaesphysics.wordpress.com/2022/01/05/oops-for-the-loops-ii-real-oopslqg-does-not-optimize-the-hilbert-einstein-action/, January 5, 2022. [22]: Stephane H. Maes, (2022), “What is the Multi-fold Theory? Its Main Characteristics in a Few Words”, vixra:2207.0172v1, https://shmaesphysics.wordpress.com/2022/07/28/what-is-the-multi-fold-theory-its-maincharacteristics-in-a-few-words/, July 28, 2022. [23]: Stephane H. Maes, (2022), “Justifying the Standard Model U(1) x SU(2) x SU(3) Symmetry in a Multi-fold Universe”, https://doi.org/10.5281/zenodo.8422911, https://shmaesphysics.wordpress.com/2022/08/08/justifyingthe-standard-model-u1-x-su2-x-su3-symmetry-in-a-multi-fold-universe/, August 8, 2022, (viXra:2310.0040v1). [24]: Stephane H Maes, (2020), “The E/G conjecture: entanglement is gravity and gravity is entanglement”, viXra:2010.0139v1, https://shmaesphysics.wordpress.com/2020/10/15/the-e-g-conjecture-entanglement-isgravity-and-gravity-is-entanglement/, October 15, 2020. [25]: Stephane H Maes, (2020), “Gravity-like Attractions and Fluctuations between Entangled Systems?”, viXra:2010.0010v1, https://shmaesphysics.wordpress.com/2020/06/25/gravity-like-attractions-and-fluctuationsbetween-entangled-systems/, June 24, 2020. [26]: Stephane H Maes, (2020), ”Massless and Massive Multi-Gravity in a Multi-fold Universe”, viXra:2010.0095v1, https://shmaesphysics.wordpress.com/2020/06/30/massless-and-massive-multi-gravity-in-a-multi-fold-universe/, June 19, 2020. [27]: Stephane H Maes, (2020), ”Explaining Dark Energy, Small Cosmological Constant and Inflation Without New Physics?”, viXra:2006.0261v1, https://shmaesphysics.wordpress.com/2020/06/19/explaining-dark-energy-smallcosmological-constant-and-inflation-without-new-physics/, June 19, 2020. [28]: Stephane H Maes, (2020), “Multi-fold Higgs Fields and Bosons”, viXra:2204.0146v1, https://shmaesphysics.wordpress.com/2020/11/10/multi-fold-higgs-fields-and-bosons/, November 6, 2020. [29]: Stephane H Maes, (2021), “Multi-fold Gravity-Electroweak Theory and Symmetry Breaking”, viXra:2211.0100, https://shmaesphysics.wordpress.com/2021/03/28/multi-fold-gravity-electroweak-theory-and-symmetrybreaking/, March 16, 2021. [30]: Stephane H Maes, (2021), “Multi-fold Non-Commutative Spacetime, Higgs and The Standard Model with Gravity”, viXra:2212.0037v1, https://shmaesphysics.wordpress.com/2021/04/18/multi-fold-non-commutativespacetime-higgs-and-the-standard-model-with-gravity/, April 11, 2021. [31]: Stephane H Maes, (2022), “Multi-fold Discrete Fractal Spacetime, and the Viability of Local vs. Non-Local Hidden Variables”, https://doi.org/10.5281/zenodo.10344634, https://shmaesphysics.wordpress.com/2022/10/30/multi-fold-discrete-fractal-spacetime-and-the-viability-of-localvs-non-local-hidden-variable-viability/, October 30, 2022, osf.io/qevys, viXra:2312.0065v1. [32]: Stephane H Maes, (2022), “Unruh effects, Hawking Black Hole Evaporation, Quantum Corrected Larmor Formula, Numbers of Particles in Curved Spacetime: “Same-Same, but Just A Bit Different””, https://doi.org/10.5281/zenodo.8306942, https://shmaesphysics.wordpress.com/2022/07/25/unruh-effectshawking-black-hole-evaporation-quantum-corrected-larmor-formula-numbers-of-particles-in-curved-spacetimesame-same-but-just-a-bit-different/, July 25, 2022, (viXra:2309.0005). [33]: Stephane H. Maes, (2022), “Time-Varying Multi-fold Dark Energy Effects and Implications for the Hubble Tension”, https://doi.org/10.5281/zenodo.10396357, https://shmaesphysics.wordpress.com/2022/11/13/timevarying-multi-fold-dark-energy-effects-and-implications-for-the-hubble-tension/, November 13, 2022, osf.io/g2vzy/, viXra:2312.0083v1. Also as Stephane H. Maes, (2022), “The Possibility of a Multi-fold Time-Varying Hubble Constant”, viXra:2312.0083v1. [34]: Stephane H Maes, (2020), ”Explaining Dark Matter Without New Physics?”, viXra:2007.0006, https://shmaesphysics.wordpress.com/2020/06/21/explaining-dark-matter-without-new-physics/, June 21, 2020. [35]: Stephane H Maes, (2020), “Multi-Fold Universe Dark Matter Successful Explanation and the “Too Thin Universe” but “Too Strong Gravity Lensing by Galaxy Clusters””, viXra:2102.0079v1, https://shmaesphysics.wordpress.com/2020/09/15/multi-fold-universe-dark-matter-successful-explanation-andthe-too-thin-universe-but-too-strong-gravity-lensing-by-galaxy-clusters/, September 14, 2020. [36]: Stephane H Maes, (2020), ”Multi-Fold Universe Dark Matter Effects Survive Low-Mass Galaxies with Dark Matter Deficits and Excesses”, viXra:2105.0042v1, https://shmaesphysics.wordpress.com/2020/10/14/multi-folduniverse-dark-matter-effects-survive-low-mass-galaxies-with-dark-matter-deficits-and-excesses/, October 14, 2020. [37]: Stephane H Maes, (2020), ”Multi-Fold Dark Matter Effects and Early Supermassive Black Holes”, viXra:2105.0041v1, https://shmaesphysics.wordpress.com/2020/10/15/multi-fold-dark-matter-effects-and-earlysupermassive-black-holes/, October 15, 2020. [38]: Stephane H Maes, (2022), “Hints of Multi-fold Dark Matter Effects in the Universe”, osf.io/krw7g, https://shmaesphysics.wordpress.com/2022/03/14/hints-of-multi-fold-dark-matter-effects-in-the-universe/, March 14, 2022, https://zenodo.org/record/7791678. [39]: Stephane H Maes, (2022), “Multi-fold Dark Matter and Energy Effects Fit The Ratios to Normal Matter in the Universe”, https://zenodo.org/doi/10.5281/zenodo.10071554, https://shmaesphysics.wordpress.com/2022/08/14/multi-fold-dark-matter-and-energy-effects-fit-the-ratios-tonormal-matter-in-the-universe/, August 14, 2022, (https://osf.io/mahsu, viXra:2311.0018v1). [40]: Stephane H Maes, (2020), ”Derivation of the Equivalence Principle in a Multi-fold Universe”, viXra:2010.0090v1, https://shmaesphysics.wordpress.com/2020/06/29/derivation-of-the-equivalence-principle-ina-multi-fold-universe/, June 19, 2020. [41]: Stephane H Maes, (2020), “Gravity Induced Anomalies Smearing in Standard Model so that Protons May Never Decay, Except in Black holes“, viXra:2006.0128v1, https://shmaesphysics.wordpress.com/2020/06/13/gravity-induced-anomalies-smearing-in-standard-model-sothat-protons-may-never-decay-except-in-black-holes/, June 13, 2020. [42]: Stephane H Maes, (2022), ”Gravity or Magnetic Monopoles? You Cannot Have Both! II“, viXra:2006.0190v2, https://shmaesphysics.wordpress.com/2022/08/20/gravity-or-magnetic-monopoles-you-cannot-have-both-2/, August 20, 2022; Stephane H Maes, (2020), ”Gravity or Magnetic Monopoles? You Cannot Have Both!“, viXra:2006.0190, https://shmaesphysics.wordpress.com/2020/06/15/gravity-or-magnetic-monopoles-you-cannothave-both/, June 15, 2020. [43]: Stephane H Maes, (2020), ”Ultimate Unification: Gravity-led Democracy vs. Uber-Symmetries”, viXra:2006.0211v1, https://shmaesphysics.wordpress.com/2020/06/16/ultimate-unification-gravity-led-democracyvs-uber-symmetries/, June 16, 2020. [44]: Stephane H Maes, (2020), ”Right-handed neutrinos? Mass? Ask Gravity”, viXra:2007.0018v1, https://shmaesphysics.wordpress.com/2020/06/21/right-handed-neutrinos-ask-gravity/, June 23, 2020. [45]: Stephane H Maes, (2020), ”Strong CP Violation Tamed in The Presence of Gravity”, viXra:2007.0025v1, https://shmaesphysics.wordpress.com/2020/06/23/strong-cp-violation-tamed-in-the-presence-of-gravity/ , June 21, 2020. [46]: Stephane H Maes, (2020), “Gravity Dictates the Number of Fermion Generations: 3”, viXra:2007.0068v1, https://shmaesphysics.wordpress.com/2020/06/24/gravity-dictates-the-number-of-fermion-generations-3/, June 24, 2020. [47]: Stephane H Maes, (2020), “Gravity Stabilizes Electroweak Vacuum – No Bubble of Nothing to Worry About!”, viXra:2007.0173v1, https://shmaesphysics.wordpress.com/2020/06/24/gravity-stabilizes-electroweak-vacuum-nobubble-of-nothing-to-worry-about/, June 24, 2020. [48]: Stephane H Maes, (2020), ”More Matter Than Antimatter, All Falling Down”, viXra:2010.0121v2, https://shmaesphysics.wordpress.com/2020/07/05/more-matter-than-antimatter-all-falling-down/, July 5, 2020. (V2: April 8, 2021) [49]: Stephane H Maes, (2020), “Tracking Down The Standard Model With Gravity In Multi-Fold Universes”, viXra:2011.0208v1, https://shmaesphysics.wordpress.com/2020/08/30/tracking-down-the-standard-model-withgravity-in-multi-fold-universes/, August 20, 2020. [50]: Stephane H Maes, (2020), “No Conventional Sterile Neutrinos In a Multi-fold Universe: just SMG business as usual”, viXra:2103.0202v1, https://shmaesphysics.wordpress.com/2020/10/02/no-conventional-sterile-neutrinosin-a-multi-fold-universe-just-smg-business-as-usual/, October 1, 2020. [51]: Stephane H. Maes, (2020), “Particles of The Standard Model In Multi-Fold Universes”, viXra:2111.0071v1, https://shmaesphysics.wordpress.com/2020/11/05/particles-of-the-standard-model-in-multi-folduniverses/, November 4, 2020. [52]: Stephane H Maes, (2022), “Can Chirality Flips Occur in a Multi-Fold Universe? What About Conservation Laws? II”, viXra:2204.0152v2, https://shmaesphysics.wordpress.com/2022/08/20/can-chirality-flips-occur-in-amulti-fold-universe-what-about-conservation-laws-ii/, August 20, 2022 & Stephane H Maes, (2020), “Can Chirality Flips Occur in a Multi-Fold Universe? What About Conservation Laws?”, viXra:2204.0152, https://shmaesphysics.wordpress.com/2020/12/07/can-chirality-flips-occur-in-a-multi-fold-universe-what-aboutconservation-laws/, December 6, 2020. [53]: Stephane H Maes, (2020), “Viable Lattice Spacetime and Absence of Quantum Gravitational Anomalies in a Multi-fold Universe”, viXra:2205.0143v1, https://shmaesphysics.wordpress.com/2020/12/13/viable-latticespacetime-and-absence-of-quantum-gravitational-anomalies-in-a-multi-fold-universe/, December 4, 2020. [54]: Stephane H Maes, (2021), “New Physics with LHCb to explain loss of lepton universality, or just gravity?”, viXra:2103.0191v1, https://shmaesphysics.wordpress.com/2021/03/29/new-physics-with-lhcb-toexplain-loss-of-lepton-universality-or-just-gravity/, March 29, 2021. [55]: Stephane H. Maes, “A bold prediction on the muon anomalous magnetic moment, and expected results to be published on April 7, 2021 by the Fermilab Muon g-2, and its explanation”, viXra:2104.0030v1, https://shmaesphysics.wordpress.com/2021/04/01/a-bold-prediction-on-the-muon-anomalous-magnetic-momentand-expected-resulted-to-be-published-on-april-7-2021-by-the-fermilab-muon-g-2-and-its-explanation/, April 1, 2021. [56]: Stephane H Maes, (2021), “New Physics is often not so new”, osf.io/z3sj6, https://shmaesphysics.wordpress.com/2021/04/27/new-physics-is-often-not-so-new/, April 27, 2021, https://zenodo.org/records/7791704. [57]: Stephane H Maes, (2022), “Direction of Possible Multi-folds Corrections to the W Boson Mass”, osf.io/qvewa, https://shmaesphysics.wordpress.com/2022/04/08/direction-of-possible-multi-folds-corrections-to-the-w-bosonmass/, April 8, 2022, viXra:2304.0020. [58]: Stephane H Maes, (2022), “Multi-folds in Yang Mills Feynman Diagrams”, osf.io/y8fpd, https://shmaesphysics.wordpress.com/2022/04/05/multi-folds-in-yang-mills-feynman-diagrams/, April 5, 2022, viXra:2303.0161. [59]: Stephane H. Maes, (2022), Stephane H. Maes, (2022), “A Conjecture: No Dark Matter will be discovered at LHC, or elsewhere”, (v2), https://doi.org/10.5281/zenodo.8175806, https://shmaesphysics.wordpress.com/2022/07/08/a-prediction-no-dark-matter-will-be-discovered-at-lhc-orelsewhere/, July 8, 2022, viXra:2307.0119. [60]: Stephane H. Maes, (2022), “Invalidation and Proof of the Mass Gap, and Viability of The Standard Model on a Discrete Spacetime”, https://doi.org/10.5281/zenodo.8237456, https://shmaesphysics.wordpress.com/2022/07/15/invalidation-and-proof-of-the-mass-gap-and-viability-of-thestandard-model-on-a-discrete-spacetime/, July 15, 2022. (viXra:2308.0059). [61]: Stephane H. Maes, (2022), “Multi-fold Gravity can Violate P-Symmetry. It is Aligned With Observations of Asymmetry of the Orientation of Tetrahedra of Galaxies”, https://doi.org/10.5281/zenodo.10443847, https://shmaesphysics.wordpress.com/2022/12/10/multi-fold-gravity-can-violate-p-symmetry-it-is-aligned-withobservations-of-asymmetry-of-the-orientation-of-tetrahedra-of-galaxies/, December 10, 2022. Also published as Stephane H. Maes, (2022), “Multi-fold Gravity can Violate Parity Symmetry”, https://shmaesphysics.wordpress.com/2022/12/10/multi-fold-gravity-can-violate-p-symmetry-it-is-aligned-withobservations-of-asymmetry-of-the-orientation-of-tetrahedra-of-galaxies/, December 10, 2022. [62]: Stephane H Maes, (2021), “Multi-fold Embeddings, Space Time Matter Induction or Gravity Asymptotically Safe and The AdS/CFT Correspondence Conjecture, they all can recover the Standard Model”, viXra:2212.0120v1, https://shmaesphysics.wordpress.com/2021/12/20/multi-fold-embeddings-space-time-matter-induction-orgravity-asymptotically-safe-and-the-ads-cft-correspondence-conjecture-they-all-can-recover-the-standard-modelor-smg/, December 20, 2021. [63]: Stephane H Maes, (2022), “2D Random Walks of Massless Higgs Bosons as Microscopic Interpretation of the Asymptotic Safety of Gravity, and of the Standard Model”, https://doi.org/10.5281/zenodo.10467452, https://shmaesphysics.wordpress.com/2022/12/28/2d-random-walks-of-massless-higgs-bosons-as-microscopicinterpretation-of-the-asymptotic-safety-of-gravity-and-of-the-standard-model/, December 28, 2022, (osf.io/udhbf). Also published as: Stephane H. Maes, (2022), “2D Random Walks of Massless Higgs Bosons”, viXra:2401.0073v1, https://shmaesphysics.wordpress.com/2022/12/28/2d-random-walks-of-massless-higgs- bosons-as-microscopic-interpretation-of-the-asymptotic-safety-of-gravity-and-of-the-standard-model/, December 28, 2022. [64]: Stephane H. Maes, (2022), “Multi-folds, Non-Commutative Spacetime, Spin, and All That”, https://doi.org/10.5281/zenodo.11114501, https://shmaesphysics.wordpress.com/2022/12/31/the-principles-ofquantum-mechanics/, December 31, 2022. Also as https://shmaesphysics.wordpress.com/2022/12/31/multi-foldsnon-commutative-spacetime-spin-and-all-that/, (osf.io/au7wc, viXra:2405.0022v1). [65]: Stephane H Maes, (2022), “Comments on Multi-fold mechanisms as Hermitian vs. Unitary processes”, https://shmaesphysics.wordpress.com/2020/06/25/gravity-like-attractions-and-fluctuations-between-entangledsystems/#comment-4359, July 27, 2022. [66]: Stephane H Maes, (2020), “Multi-Fold Black Holes: Entropy, Evolution and Quantum Extrema”, viXra:2105.0136v1, https://shmaesphysics.wordpress.com/2020/11/01/multi-fold-black-holes-entropy-evolutionand-quantum-extrema/, October 31, 2020. [67]: Stephane H. Maes, (2022), “A Better Quantum Extremal Surface and Island Interpretation that explains the Associated Massive Gravity”, https://doi.org/10.5281/zenodo.10437116, https://shmaesphysics.wordpress.com/2022/12/03/a-better-quantum-extremal-surface-and-island-interpretationthat-explains-the-associated-massive-gravity/, December 3, 2022, (https://osf.io/dn3kh). [68]: Stephane H Maes, (2020), “The W-type Multi-Fold Hypothesis and Quantum Physics Interpretation of wave Functions and QFT”, viXra:2207.0118v1, https://shmaesphysics.wordpress.com/2020/12/24/the-w-type-multi-foldhypothesis-and-quantum-physics-interpretation-of-wave-functions-and-qft/, December 20, 2020. [69]: Stephane H Maes, (2020), “Implicit Multi-Fold Mechanisms in a Neural Network Model of the Universe”, viXra:2012.0191v1, https://shmaesphysics.wordpress.com/2020/09/12/implicit-multi-fold-mechanisms-in-a-neuralnetwork-model-of-the-universe/, September 12, 2020. [70]: Stephane H Maes, (2020), “Interpretation of “Neural Network as the World””, viXra:2012.0197v1, https://shmaesphysics.wordpress.com/2020/09/14/interpretation-of-neural-network-as-the-world/, September 14, 2020. [71]: Stephane H Maes, (2020), “Entangled Neural Networks from Multi-fold Universes to Biology”, viXra:2207.0174v1, https://shmaesphysics.wordpress.com/2020/12/31/entangled-neural-networks-from-multifold-universes-to-biology/, December 25, 2020. [72]: Stephane H Maes, (2020), “Area Laws Between Multi-Fold Universes and AdS”, viXra:2010.0207v1, https://shmaesphysics.wordpress.com/2020/08/10/area-laws-between-multi-fold-universes-and-ads/, August 10, 2020. [73]: Stephane H Maes, (2022), “Trans-Planckian Censorship Conjecture: Factual in Multi-fold Universes as well as GR Universes”, viXra:2303.0025v1, https://shmaesphysics.wordpress.com/2022/03/13/trans-planckian-censorshipconjecture-factual-in-multi-fold-universes-as-well-as-gr-universes/, March 12, 2022. [74]: Wikipedia, “Lambda-CDM model”, https://en.wikipedia.org/wiki/Lambda-CDM_model. Retrieved on August 14, 2022. [75]: Stephane H. Maes, (2023), “Yeah or Nay on Black Holes as Explanation for Dark Energy?”, osf.io/369pd, https://shmaesphysics.wordpress.com/2023/03/01/yeah-or-nay-on-black-holes-as-explanation-for-dark-energy/, V3, March 26, 2023. (V2: March 12, 2023, V1: Stephane H. Maes, (2023), “Yeah or Nay on Black Holes as Explanation for Dark Energy?”, viXra:2303.0031, https://shmaesphysics.wordpress.com/2023/03/01/yeah-or-nayon-black-holes-as-explanation-for-dark-energy/, March 1, 2023). [76]: Stephane H. Maes, (2023), “Dynamic sources, Dynamic Multi-folds, and General Relativity Lense-Thirring and Frame Dragging Effects”, https://doi.org/10.5281/zenodo.14737010, https://shmaesphysics.wordpress.com/2023/03/12/dynamic-sources-dynamic-multi-folds-and-general-relativitylens-thirring-and-frame-dragging-effects/, March 12, 2023, https://osf.io/ytmw6/download/ [77]: Stephane H. Maes, (2023), “The Multi-fold Least Action Principle, a Quasi Theory Of Everything”, https://doi.org/10.5281/zenodo.14542569, https://shmaesphysics.wordpress.com/2023/02/19/themulti-fold-least-action-principle-a-quasi-theory-of-everything/, February 19, 2023. (osf.io/2ncqf/, viXra:2412.0145v1). [78]: Stephane H Maes, (2020), “No Gravity Induced Wave Function Collapse in a Multi-fold Universe”, viXra:2012.0152v1, https://shmaesphysics.wordpress.com/2020/09/11/no-gravity-induced-wave-function-collapsein-a-multi-fold-universe/, September 11, 2020. Also as: Stephane H Maes, (2020), “No Gravity Superposition Induced Wave Function Collapse in a Multi-fold Universe”, viXra:2012.0152v1, https://shmaesphysics.wordpress.com/2020/09/11/no-gravity-induced-wave-function-collapse-in-a-multi-folduniverse/, September 11, 2020. [79]: Stephane H. Maes, (2023), “Maybe, black holes do not systematically decohere quantum states”, https://shmaesphysics.wordpress.com/2020/11/01/multi-fold-black-holes-entropy-evolution-and-quantumextrema/#comment-6315, March 7, 2023. [80]: Stephane H Maes, (2020), “Multi-fold Gravitons In-N-Out Spacetime”, viXra:2010.0155v1, https://shmaesphysics.wordpress.com/2020/07/27/multi-fold-gravitons-in-n-out-spacetime/, July 27, 2020, (posted September 6, 2020). [81]: Stephane H Maes, (2022), “Gravitational Bootstrap, S-matrix, Superstrings, and The Plausible Unphysicality of Gravitons”, viXra:2301.0155v1, https://shmaesphysics.wordpress.com/2022/02/06/gravitational-bootstrap-smatrix-superstrings-and-the-plausible-unphysicality-of-gravitons/, February 6, 2022. [82]: Stephane H Maes, (2021), “Spacetime and Gravity are 2D around Planck Scales: A Universal Property of Consistent Quantum Gravity”, viXra:2211.0001v1, https://shmaesphysics.wordpress.com/2021/03/23/spacetimeand-gravity-are-2d-around-planck-scales-a-universal-property-of-consistent-quantum-gravity/, March 20, 2021. [83]: Stephane H Maes, (2021), ““Quantum Gravity Emergence from Entanglement in a Multi-Fold Universe”: 2D or 2+1D spacetime at small scales”, viXra:2103.0142, https://shmaesphysics.wordpress.com/2021/03/20/quantumgravity-emergence-from-entanglement-in-a-multi-fold-universe-2d-or-21d-spacetime-at-small-scales/, March 20, 2021. [84]: Stephane H. Maes, (2023), “No electroweak / Higgs mass hierarchy problem in multi-fold theory”, https://shmaesphysics.wordpress.com/2021/03/28/multi-fold-gravity-electroweak-theory-and-symmetrybreaking/#comment-6794, March 30, 2023. [85]: Stephane H Maes, (2022), “The Replica Trick, Wormholes, Island formula, and Quantum Extremal Surfaces, and How the AdS/CFT Correspondence Conjecture, and Hence the M-theory, Encounters Multi-folds”, https://doi.org/10.5281/zenodo.10207057, https://shmaesphysics.wordpress.com/2022/09/20/the-replica-trickits-wormholes-islands-and-quantum-extremal-surfaces-and-how-the-ads-cft-correspondence-conjecture-andhence-the-m-theory-encounters-multi-folds/, September 26, 2022, (osf.io/xwf6q/). Also published as: Stephane H Maes, (2022), “The Replica Trick, Wormholes, Island formula, and Quantum Extremal Surfaces”, September 26, 2022 (viXra:2311.0154v1). [86]: Alexander D. Popov, (2015), “String theories as the adiabatic limit of Yang-Mills theory”, arXiv:1505.07733. [87]: Stephane H. Maes, (2022), “Explaining Imbalance of Tidally Ejected Stars from Open Stars Clusters Without MOND”, https://doi.org/10.5281/zenodo.10421124, https://shmaesphysics.wordpress.com/2022/11/19/explaining-imbalance-of-tidally-ejected-stars-from-open-starsclusters-without-mond/, November 19, 2022, https://osf.io/bp64c. [88]: Stephane H. Maes, {2022), “Black holes effects outside the black holes do not mean that Hawking radiation is not occurring at its horizon”, https://shmaesphysics.wordpress.com/different-approaches-to-compute-hawkingblack-holes-decay/#comment-5027, November 23, 2022. [89]: Stephane H Maes, (2022), “Multi-fold Discrete Fractal Spacetime, and the Viability of Local vs. Non-Local Hidden Variables”, https://doi.org/10.5281/zenodo.10344634, https://shmaesphysics.wordpress.com/2022/10/30/multi-fold-discrete-fractal-spacetime-and-the-viability-of-localvs-non-local-hidden-variable-viability/, October 30, 2022, osf.io/qevys, viXra:2312.0065v1. [90]: Stephane H. Maes, (2021), “Comment on 4D spacetime and follow-up comments”, https://shmaesphysics.wordpress.com/2020/09/19/renormalization-and-asymptotic-safety-of-gravity-in-a-multifold-universe-more-tracking-of-the-standard-model-at-the-cost-of-supersymmetries-guts-andsuperstrings/#comment-1416, January 16, 2021. Retrieved on February 21, 2021. [91]: Stephane H. Maes, (2021), “Comment on 4D spacetime and follow-up comments: https://shmaesphysics.wordpress.com/2020/09/19/renormalization-and-asymptotic-safety-of-gravity-in-a-multifold-universe-more-tracking-of-the-standard-model-at-the-cost-of-supersymmetries-guts-andsuperstrings/#comment-1579, February 18, 2021. Retrieved on February 21, 2021. [92]: Stephane H. Maes, (2021), “Comment on 2D spacetime and follow-up comments”, https://shmaesphysics.wordpress.com/2020/09/19/renormalization-and-asymptotic-safety-of-gravity-in-a-multifold-universe-more-tracking-of-the-standard-model-at-the-cost-of-supersymmetries-guts-andsuperstrings/#comment-1695, March 3, 2021. Retrieved on March 31, 2021. [93]: Stephane H. Maes, (2021), “Comment on 4D spacetime and follow-up comments”, https://shmaesphysics.wordpress.com/2020/09/19/renormalization-and-asymptotic-safety-of-gravity-in-a-multifold-universe-more-tracking-of-the-standard-model-at-the-cost-of-supersymmetries-guts-andsuperstrings/#comment-1891, March 30, 2021. Retrieved on March 31, 2021. [94]: Stephane H. Maes, (2021), “Comment on 4D spacetime and follow-up comments”, https://shmaesphysics.wordpress.com/2020/09/19/renormalization-and-asymptotic-safety-of-gravity-in-a-multifold-universe-more-tracking-of-the-standard-model-at-the-cost-of-supersymmetries-guts-andsuperstrings/#comment-1906, April 1, 2021. Retrieved on December 27, 2022. [95]: Stephane H. Maes, (2022), “Additional arguments for 4D spacetime for our real universe”, https://shmaesphysics.wordpress.com/2020/09/19/renormalization-and-asymptotic-safety-of-gravity-in-a-multifold-universe-more-tracking-of-the-standard-model-at-the-cost-of-supersymmetries-guts-andsuperstrings/#comment-4679, September 21, 2022. Retrieved on December 27, 2022. [96]: Stephane H. Maes, “Right-handed neutrinos in the multi-fold stabilize the multi-fold unconstrained KK space time matter induction and scattering”, https://shmaesphysics.wordpress.com/2021/04/03/right-handed-neutrinosand-traversable-wormholes-the-key-to-entanglement-gravity-and-multi-folds-extensions-to-erepr/comment-page1/#comment-6875. [97]: Stephane H. Maes, (2022-2023), “Confusing mathematical duality to predict quantum computing algorithm, with building a wormhole”, https://shmaesphysics.wordpress.com/2020/10/11/circular-arguments-in-string-andsuperstring-theory-from-a-multi-fold-universe-perspective/comment-page-1/#comment-5093, and following related comments, November 30, 2022. [206]: Wigner, E. P. (1960). “The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959”. Communications on Pure and Applied Mathematics. 13: 1–14. [207]: nLab, “hadrons as KK-modes of 5d Yang-Mills theory -- references”, https://ncatlab.org/nlab/show/hadrons+as+KK-modes+of+5d+Yang-Mills+theory+--+references. Retrieved on April 22, 2023. [208]: Alexei M. Frolov, (2022), “On Maxwell Electrodynamics in Multi-Dimensional Spaces”, Universe 2022, 8, 20. [209]: Marc Henneaux, Cedric Troessaert, (2019), “The asymptotic structure of electromagnetism in higher spacetime dimensions”, arXiv:1903.04437v1. [210]: Ernesto A Matute, (1997), “Geometry–matter duality and electromagnetism in higher dimensions”, Class. Quantum Grav., 14, 2771–2783. [211]: Surya, S. The causal set approach to quantum gravity. Living Rev Relativ 22, 5 (2019). [212]: Philippe Francesco , Pierre Mathieu , David Sénéchal, (1997), “ Conformal Field Theory”, Springer. [213]: Roland Bauerschmidt, (2018), “Supersymmetry for probabilists”, http://www.statslab.cam.ac.uk/~rb812/teaching/toronto2018/toronto.pdf. [214]: Belitsky, V., & Schütz, G. M., (2019), “Duality, supersymmetry and non-conservative random walks”, Journal of Statistical Mechanics: Theory and Experiment, (5), 054004. [215]: S. Bera, B. Chakrabarti, A. Gammal, M. C. Tsatsos, M. L. Lekala, B. Chatterjee, C. Lévêque & A. U. J. Lode, (2019), “Sorting Fermionization from Crystallization in Many-Boson Wavefunctions”, Scientific Reports volume 9, Article number: 17873. [216]: Joshua M. Wilson, Neel Malvania, Yuan Le, Yicheng Zhang, Marcos Rigol, David S. Weiss, (2019), “Observation of Dynamical Fermionization”, arXiv:1908.05364v1. [217]: Witten, E., (1982), “Instability of the Kaluza-Klein vacuum”, Nuclear Physics B, 195(3), 481–492. [218]: G. ‘t Hooft, (1993), “Dimensional Reduction in Quantum Gravity”, arXiv:gr-qc/9310026v2. [219]: Steven Carlip, (2010), “The Small Scale Structure of Spacetime“, arXiv:1009.1136v1. [220]: Laurent Freidel, Etera R. Livine, (2005-2006), “3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory”, arXiv:hep-th/0512113v2. [221]: David Tong, (2018), “Gauge Theory”, Cambridge University, https://www.damtp.cam.ac.uk/user/tong/gaugetheory/gt.pdf. [222]: Takahiro Doi, (2017), “Lattice QCD Study for the Relation Between Confinement and Chiral Symmetry Breaking”, Springer. [223]: Wikipedia, “Cosmological constant”, https://en.wikipedia.org/wiki/Cosmological_constant. Retrieved for this paper on April 23, 2023. [224]: De Witt, B., Smit, D. J., & Hari Dass, N. D., (1987), “Residual supersymmetry of compactified d = 10 supergravity”, Nuclear Physics B, 283, 165–191. [225]: Juan Maldacena, Carlos Nunez, (2000), “Supergravity description of field theories on curved manifolds and a no go theorem”, arXiv:hep-th/0007018v2. [226]: Tarek Anous, Daniel Z. Freedman, Alexander Maloney, (2014), “de Sitter Supersymmetry Revisited”, arXiv:1403.5038v1. [227]: Edward Witten, (2001), “Quantum Gravity In De Sitter Space”, arXiv:hep-th/0106109v1. [228]: Wikipedia, “Proton decay”, https://en.wikipedia.org/wiki/Proton_decay. Retrieved for this paper on April 23, 2023. [229]: Michael Schirber , 2013), “Constraining the Photon Lifetime. Photons could conceivably decay, but new analysis of the cosmic microwave background shows that a visible wavelength photon is stable for at least 10^18 years”, Physics 6, s96, https://physics.aps.org/articles/v6/s96, July 11, 2013. [230]: Wikipedia, “Tachyon”, https://en.wikipedia.org/wiki/Tachyon. Retrieved for this paper on April 23, 2023. [231]: Julian Heeck, (2013), “How stable is the photon?”, arXiv:1304.2821v2 [232]: Stephane H Maes, (2020), “Entanglement Concretizes Time in a Multi-fold Universe”, viXra:2010.0083v1, https://shmaesphysics.wordpress.com/2020/06/28/entanglement-concretizes-time-in-a-multi-fold-universe/, June 28, 2020. Also published as: Stephane H Maes, (2020), “Entanglement and Random Walks Concretize Time in a Multi-fold Universe”, viXra:2010.0083v1, https://shmaesphysics.wordpress.com/2020/06/28/entanglementconcretizes-time-in-a-multi-fold-universe/, June 28, 2020. [233]: Stephane H Maes, (2021), “Right-handed Neutrinos and Traversable Wormholes: the key to entanglement, gravity and multi-folds extensions to ER=EPR?”, viXra:2211.0173v1, https://shmaesphysics.wordpress.com/2021/04/03/right-handed-neutrinos-and-traversable-wormholes-the-keyto-entanglement-gravity-and-multi-folds-extensions-to-erepr/, April 3, 2021. [234]: Shinbrot, T., & Young, W., (2008). “Why Decussate? Topological Constraints on 3D Wiring. The Anatomical Record: Advances in Integrative Anatomy and Evolutionary Biology”, 291(10), 1278–1292. [235]: Stephane H Maes, (2021), “Pointers to Nowhere with Geometric Unity Theory, or Some Ways Forward in Multi-fold Universes?”, viXra:2210.0081v1, https://shmaesphysics.wordpress.com/2021/03/07/pointers-tonowhere-with-geometric-unity-theory-or-some-ways-forward-in-multi-fold-universes/, March 7, 2021. [236]: Stephane H Maes, (2020), “Call for Collaboration”, https://shmaesphysics.wordpress.com/2020/09/07/doyou-want-a-phd-or-who-knows-a-nobel-price-in-physics/, September 6, 2020. [237]: Stephane H Maes, (2020), “Particles, Especially Virtual Particles, in a Multi-fold Universe vs. QFT”, viXra:2010.0133v1, https://shmaesphysics.wordpress.com/2020/07/11/particles-especially-virtual-particles-in-amulti-fold-universe-vs-qft/ , July 10, 2020. [238]: Stephane H Maes, (2020), “Comments to “Yes, Stephen Hawking Lied To Us All About How Black Holes Decay””, https://osf.io/v7thb/, https://shmaesphysics.wordpress.com/2020/07/11/comments-to-yes-stephenhawking-lied-to-us-all-about-how-black-holes-decay/, July 11, 2020. [239]: Stephane H Maes, (2020), “Different approaches to compute Hawking Black Holes Decay”, viXra:2208.0009v1, https://shmaesphysics.wordpress.com/different-approaches-to-compute-hawking-black-holesdecay/, August 1, 2022. (Originally published July 11, 2020). [240]: Stephane H Maes, (2020), “No Gravity Shield in Multi-folds Universes”, viXra:2010.0032v1, https://shmaesphysics.wordpress.com/2020/06/26/no-gravity-shields-in-multi-folds-universes/ , June 26, 2020. [241]: Stephane H. Maes, (2022), “Comments on radiation black hole simulation on a lattice”, https://shmaesphysics.wordpress.com/2022/07/25/unruh-effects-hawking-black-hole-evaporation-quantumcorrected-larmor-formula-numbers-of-particles-in-curved-spacetime-same-same-but-just-a-bitdifferent/#comment-5099, December 2, 2022. [242]: Stephane H. Maes, (2021), “Neutrons are forming an external skin in Nuclei and Neutron Stars”, https://zenodo.org/doi/10.5281/zenodo.14582585, https://shmaes.wordpress.com/2021/05/08/neutronsare-forming-an-external-skin-in-nuclei-and-neutron-stars/, May 8, 2021. (V1) (V3 is January 7, 2024). (osf.io/zdy4s/, viXra:2501.0029). [243]: Stephane H. Maes, (2022), “Schwinger effect and charged black holes”, https://shmaesphysics.wordpress.com/2020/11/01/multi-fold-black-holes-entropy-evolution-and-quantumextrema/#comment-4686, September 25, 2022. [244]: Stephane H. Maes, “Comments on asymmetry of distributions of ejected star from gas clusters”, https://shmaesphysics.wordpress.com/2020/06/21/explaining-dark-matter-without-new-physics/#comment4813 and subsequent comments, October 27, 2022 [245]: Stephane H. Maes, (2022), “CO2 and CH4 absorption powered by nuclear fusion, via fission, is the only way to manage climate change and the Planet’s trigger points”, viXra:2211.0154v1, https://shmaes.wordpress.com/2022/04/09/co2-and-ch4-absorption-powered-fission-is-the-only-way-to-manageclimate-change-and-the-planets-trigger-points/, April 9, 2022. [246]: Stephane H Maes, (2021), “How the ER = EPR, GR = QM and AdS/CFT correspondence conjectures, can be explained in multi-fold theory, along with the E/G conjecture. A call to the Physics Community!”, viXra:2111.0144v2, https://shmaesphysics.wordpress.com/2021/11/28/how-the-er-epr-gr-qm-and-ads-cftcorrespondence-conjectures-can-be-explained-in-multi-fold-theory-and-the-e-g-conjecture-explains-and-realize-ina-multi-fold-universe-a-call-to-the-physics-comm/, December 28, 2021. [247]: Stephane H Maes, (2020), “A Multi-fold Universe Genesis Inspired By Explosive Total Collision: The Source Of The Big Bang?”, viXra:2208.0082v1, https://shmaesphysics.wordpress.com/2021/01/17/a-multi-fold-universegenesis-inspired-by-total-explosion-collision-the-source-of-the-big-bang/, January 12, 2021. [248]: Stephane H. Maes, (2022), “JWST and the Big Bang invalidation”, https://shmaesphysics.wordpress.com/2021/01/17/a-multi-fold-universe-genesis-inspired-by-total-explosioncollision-the-source-of-the-big-bang/#comment-4577, and following comments. August 21, 2022. [249]: Stephane H. Maes, (2022), “Schwinger effect dominates near the horizon of charged black holes near extremality and reduces the charge”, https://shmaesphysics.wordpress.com/2022/07/25/unruh-effects-hawkingblack-hole-evaporation-quantum-corrected-larmor-formula-numbers-of-particles-in-curved-spacetime-same-samebut-just-a-bit-different/#comment-4687, September 23, 2022. References added on August 1, 2025 [250]: Stephane H. Maes, (2023), “No supersymmetry”, https://shmaesphysics.wordpress.com/2023/11/21/nosupersymmetry/, November 21,2023. [251]: Stephane H. Maes, (2023), “Justification for the multi-fold mappings, and dynamic multi-fold mechanism”, https://shmaesphysics.wordpress.com/2020/12/24/the-w-type-multi-fold-hypothesis-and-quantum-physicsinterpretation-of-wave-functions-and-qft/comment-page-1/#comment-8092, October 29, 2023. [252]: Stephane H Maes, (2023), “Comments of the universe is too smooth”, https://shmaesphysics.wordpress.com/2020/06/21/explaining-dark-matter-without-new-physics/#comment-6086, February 9, 2023, and https://shmaesphysics.wordpress.com/2020/06/21/explaining-dark-matter-without-newphysics/#comment-6974, April 12, 2023. [253]: Stephane H Maes, (2023), “No Gravitational Evaporation of Everything à la Schwinger, only for Black Holes”, https://shmaesphysics.wordpress.com/2023/07/15/no-gravitational-evaporation-of-everything-a-la-schwingeronly-for-black-holes/, July 15, 2023. [254]: Stephane H Maes, (2023), “Unstable QFT and SM with Gravity except in a Multi-fold Universe”, https://shmaesphysics.wordpress.com/2023/07/19/unstable-qft-and-sm-with-gravity-except-in-a-multi-folduniverse/, July 19, 2023. [255]: Stephane H. Maes, (2023), “Comments about massive galaxies without dark matter”, https://shmaesphysics.wordpress.com/2020/10/14/multi-fold-universe-dark-matter-effects-survive-low-massgalaxies-with-dark-matter-deficits-and-excesses/#comment-7430, July 20, 2023. [256]: Stephane H Maes, (2023), “Less Cracks in the Standard Cosmology in a Multi-fold Universe with its Quantum Random walks”, https://shmaesphysics.wordpress.com/2023/06/20/less-cracks-in-the-standard-cosmology-in-amulti-fold-universe-with-its-quantum-random-walks/, June 19, 2023. [257]: Stephane H. Maes, (2023), “Ad Astra With Warp Drives? Probably Not”, https://shmaesphysics.wordpress.com/2023/12/09/ad-astra-longe-with-warp-drives-probably-not/, December 9, 2023. [258]: Stephane H Maes, (2023), “2D gravity and 2D Yang Mills Physics is all what matters”, https://shmaesphysics.wordpress.com/2023/04/23/our-real-universe-is-macroscopically-4d-hints-come-fromevery-directions-show-that-it-had-to-be-so/comment-page-1/#comment-7588, August 5, 2023. [259]: Stephane H Maes (2023), “The Multi-fold Theory – Draft Raw Compendium of Research Papers (till August, 2023)”, https://doi.org/10.5281/zenodo.8242021, https://shmaesphysics.wordpress.com/2023/08/12/the-multifold-theory-draft-raw-compendium-of-research-papers-till-august-2023/, August 12, 2023, (https://osf.io/swqmb). [260]: Stephane H Maes, (2023), “Barnett’s resolution of the Minkowski – Abraham dilemma holds, no 4-vector issue”, https://zenodo.org/records/10071847, https://shmaes.wordpress.com/2023/08/11/barnetts-resolution-ofthe-minkowski-abraham-dilemma-holds-no-4-vector-issue/ August 13, 2023, (https://osf.io/bd8ju, viXra:2311.0023v1). [261]: Stephane H. Maes, (2023), “Persisting on No Decoherence due to Gravity, Black Holes, or Spacetime Curvature Superpositions”, https://shmaesphysics.wordpress.com/2023/08/18/persisting-on-no-decoherence-dueto-gravity-black-holes-or-spacetime-curvature-superpositions/, August 18, 2023. [262]: Stephane H. Maes, (2023), “No supersymmetry at D<=4 with a positive cosmological constant”, https://shmaesphysics.wordpress.com/2022/07/08/a-prediction-no-dark-matter-will-be-discovered-at-lhc-orelsewhere/#comment-7563. July 23, 2023. [263]: Stephane H. Maes, (2023), “The universe is exactly the only thing that it could be if it is a 4D multi-fold universe! No fine-tuning problem, no invocation of God or multiverses”, https://shmaesphysics.wordpress.com/2023/04/08/multi-fold-universes-multi-folds-and-many-worlds/commentpage-1/#comment-8037, October 7, 2023. [264]: Stephane H. Maes, (2020-2023), “Quantum Gravity Emergence from Entanglement in a Multi-Fold Universe – V3: Update to section 4.1 – Multi-folds for Entanglement and EPR”, https://shmaesphysics.wordpress.com/quantum-gravity-emergence-from-entanglement-in-a-multi-fold-universev3-update-to-section-4-1-multi-folds-for-entanglement-and-epr/. [265]: Stephane H. Maes, (2020-2023), “Quantum Gravity Emergence from Entanglement in a Multi-Fold Universe”, V3, https://zenodo.org/doi/10.5281/zenodo.7792911, October 29, 2023. [266]: Stephane H. Maes, (2023), “Path integrals and wormholes impact on the cosmological constant”, https://shmaesphysics.wordpress.com/2022/09/20/the-replica-trick-its-wormholes-islands-and-quantumextremal-surfaces-and-how-the-ads-cft-correspondence-conjecture-and-hence-the-m-theory-encounters-multifolds/comment-page-1/#comment-7978, September 3, 2023. [267]: Stephane H. Maes, (2023), “Microscopic interpretation of mass acquisition from massless Higgs bosons”, https://shmaesphysics.wordpress.com/2021/02/28/more-on-multi-fold-particles-as-microscopic-black-holes-withhiggs-regularizing-extremality-and-singularities/#comment-8412, November 5, 2023. [268]: Stephane H. Maes, (2023), “Justifying the Multi-folds Mechanisms, Mapping, Tenancy and More”, https://shmaesphysics.wordpress.com/2023/11/10/justifying-the-multi-folds-mechanisms-mapping-tenancy-andmore/, November 10, 2023. [269]: Stephane H. Maes, (2023), “In multi-fold theory, the expansion of the universe is not a mirage”, https://shmaesphysics.wordpress.com/2020/06/19/explaining-dark-energy-small-cosmological-constant-andinflation-without-new-physics/#comment-7242, June 20, 2023. [270]: Stephane H. Maes, “Multi-fold dark energy is also a fluctuation of quantum vacuum fluctuations”, https://shmaesphysics.wordpress.com/2020/06/19/explaining-dark-energy-small-cosmological-constant-andinflation-without-new-physics/#comment-6111, February 18, 2023. [271]: Stephane H. Maes, (2023), “It’s experimentally validated: antimatter falls down, no antigravity”, https://shmaesphysics.wordpress.com/2020/07/05/more-matter-than-antimatter-all-falling-down/#comment8018 and subsequent comments, September 27, 2023. [272]: Stephane H. Maes, (2023), “Particle internal symmetries and anti-particles when modeled as microscopic black holes or random walk patterns”, https://shmaesphysics.wordpress.com/2021/02/28/more-on-multi-foldparticles-as-microscopic-black-holes-with-higgs-regularizing-extremality-and-singularities/#comment-8634, November 28, 2023. [273]: Stephane H. Maes, (2023), “Information has no mass”, https://shmaesphysics.wordpress.com/2023/12/14/information-has-no-mass/, December 14, 2023 [274]: Stephane H. Maes, (2023), “Gravity is Quantum”, https://shmaesphysics.wordpress.com/2023/12/19/gravityis-quantum/, December 19, 2023. [275]: Stephane H. Maes, (2023), “Multi-folds for Entanglement and EPR”, https://zenodo.org/doi/10.5281/zenodo.10059877, https://shmaesphysics.wordpress.com/2023/11/01/multifolds-for-entanglement-and-epr/, October 29, 2023, (viXra:2311.0001v1), also as “Update to section 4.1 of “Quantum Gravity Emergence from Entanglement in a Multi-Fold Universe” – Multi-folds for Entanglement and EPR”, https://shmaesphysics.wordpress.com/2023/10/29/update-to-section-4-1-of-quantum-gravity-emergencefrom-entanglement-in-a-multi-fold-universe-multi-folds-for-entanglement-and-epr/, (https://osf.io/54ycm/). [276]: Stephane H. Maes, (2023), “A Fractal spacetime just leads to rescaled cosmological constant. Yet that may provide a time varying effect”, https://shmaesphysics.wordpress.com/2022/10/30/multi-fold-discrete-fractalspacetime-and-the-viability-of-local-vs-non-local-hidden-variable-viability/comment-page-1/#comment-8896. December 14, 2023. [277]: Stephane H. Maes, (2023), “Multi-Fold dark Matter effects & Rotation Curve Differences in Galaxies in Clusters, Yet Respect of the Strong Equivalence Principle”, https://doi.org/10.5281/zenodo.13766006, https://shmaesphysics.wordpress.com/2023/01/29/multi-fold-dark-matter-effects-rotation-curve-differences-ingalaxies-in-custers-yet-respect-of-the-strong-equivalence-principle/, January 29, 2023, (osf.io/texvj, vixra:2409.0088v1). [278]: Stephane H. Maes, (2024), “Collapses, Singularities, Censorship, Conjectures, and More”, https://shmaesphysics.wordpress.com/2024/07/16/collapses-singularities-censorship-conjectures-and-more/, July 16, 2024. [279]: Stephane H. Maes, (2024), “June 2024 Status of the Multi-fold Theory”, https://doi.org/10.5281/zenodo.13345964, https://shmaesphysics.wordpress.com/2024/08/19/june-2024-statusof-the-multi-fold-theory/, June 22, 2024. [280]: Stephane H. Maes, (2024), “About binaries alleged gravity anomalies”, https://shmaesphysics.wordpress.com/2023/01/29/multi-fold-dark-matter-effects-rotation-curve-differences-ingalaxies-in-custers-yet-respect-of-the-strong-equivalence-principle/#comment-9726, September 10, 2024. [281]: Stephane H Maes, (2024), “A different and more generic proof based on the multi-fold theory, that confinement implies mass effects and chiral symmetry breaking”, https://shmaesphysics.wordpress.com/2021/02/28/more-on-multi-fold-particles-as-microscopic-black-holes-withhiggs-regularizing-extremality-and-singularities/comment-page-1/#comment-9952, November 3, 2024. [282]: Stephane H. Maes, (2024), “A discrete multi-fold spacetime realized by random walk, implies a noncommutative spacetime”, https://shmaesphysics.wordpress.com/2022/12/31/multi-folds-non-commutativespacetime-spin-and-all-that/#comment-9820, September 23, 2024. [283]: Stephane H Maes, (2021), “Comments on “No issue of unnaturalness and mass hierarchy with the Higgs mass””, https://shmaesphysics.wordpress.com/2021/04/27/new-physics-is-often-not-so-new/comment-page1/#comment-3026, December 24, 2021. [284]: Stephane H. Maes, (2024), “Physics Salvages The Third Law Of Black Hole Thermodynamics”, https://shmaesphysics.wordpress.com/2024/11/24/physics-salvages-the-third-law-of-black-hole-thermodynamics/, November 24, 2024. [285]: Stephane H. Maes, “No Issue with the Quantization of Electrostatic Fields”, https://shmaesphysics.wordpress.com/2024/12/31/no-issue-with-the-quantization-of-electrostatic-fields/, December 31, 2024. [286]: Stephane H. Maes, (2025), “Looks like we were right. Neutrinos are probably not Majorana Fermions”, https://shmaesphysics.wordpress.com/2020/06/21/right-handed-neutrinos-ask-gravity/#comment-10501, March 23, 2025. [287]: Stephane H. Maes, (2024), “Gödel's incompleteness theorems implies no full theory is possible”, https://shmaesphysics.wordpress.com/2023/02/19/the-multi-fold-least-action-principle-a-quasi-theory-ofeverything/#comment-10066, November 30, 2024. Based on: Stephane H. Maes, (1989), “Feynman Path Integrals”, and communication to Prof. J. Weyers, Quantum Physics Seminar as part of BS in Physics, FYMA, UC Louvain. [288]: Stephane H. Maes, (2024), “Spin as angular momentum of massless Higgs bosons in Higgs condensate or random walks”, https://shmaesphysics.wordpress.com/2022/12/31/multi-folds-non-commutative-spacetime-spinand-all-that/#comment-10027, November 26, 2024. [289]: Stephane H. Maes, (2025), “No Extremality or Singularity for Particles as Multi-fold Black Holes”, https://shmaesphysics.wordpress.com/2025/03/27/no-extremality-or-singularity-for-particles-as-multi-fold-blackholes/, March 27, 2025. [290]: Stephane H. Maes, (2024), “Explaining the mass anisotropy of certain semi-Dirac Fermions in semimetals”, https://shmaesphysics.wordpress.com/2021/02/28/more-on-multi-fold-particles-as-microscopic-black-holes-withhiggs-regularizing-extremality-and-singularities/comment-page-1/#comment-9951, November 3, 2024. [291]: Stephane H. Maes, (2024), “Gravity in SMG contributes in the right direction to the discrepancies of CP violation in B-mesons with the SM”, https://shmaesphysics.wordpress.com/2022/07/08/a-prediction-no-darkmatter-will-be-discovered-at-lhc-or-elsewhere/#comment-10078, December 6, 2024. [292]: Stephane H. Maes, (2024), “As we predicted, still no sterile neutrino”, https://shmaesphysics.wordpress.com/2020/10/02/no-conventional-sterile-neutrinos-in-a-multi-fold-universe-justsmg-business-as-usual/#comment-10039, November 26, 2024. [293]: David Tong, (2018), “Gauge Theory”, Cambridge University, https://www.damtp.cam.ac.uk/user/tong/gaugetheory/gt.pdf. [294]: Stephane H. Maes, (2024), “Continuous mathematics to model Physics are just degenerate approximations of finite / discrete mathematics”, https://shmaesphysics.wordpress.com/2023/11/21/nosupersymmetry/#comment-9457, July 13, 2024. [295]: Stephane H. Maes, (2022), “Background independence implies discreteness”, https://shmaesphysics.wordpress.com/2021/04/18/multi-fold-non-commutative-spacetime-higgs-and-thestandard-model-with-gravity/comment-page-1/#comment-3304, January 11, 2022. [296]: Stephane H. Maes, "Consistencies and Implications of 2D Massless Random Walks: Discrete Noncommutative Spacetime, and No Flat Supersymmetry", https://shmaesphysics.wordpress.com/2024/12/12/consistencies-and-implications-of-2d-massless-random-walksdiscrete-non-commutative-spacetime-and-no-flat-supersymmetry/, December 12, 2024. [297]: nLab, “Skyrmions”, https://ncatlab.org/nlab/show/skyrmion. Retrieved for this paper on December 10, 2024. [298] : Wikipedia, “Skyrmion”, https://en.wikipedia.org/wiki/Skyrmion. Retrieved for this paper on December 10, 2024. [299]: Stephane H. Maes, (2024), “QFT on discrete spacetime is OK”, https://shmaesphysics.wordpress.com/2020/12/13/viable-lattice-spacetime-and-absence-of-quantumgravitational-anomalies-in-a-multi-fold-universe/comment-page-1/#comment-10322, December 30, 2024. [300]: Stephane H. Maes, (2025), “Mathematics, Physics / QFT on discrete spacetime is more general than Mathematics and Physics / QFT on continuous spacetime”, https://shmaesphysics.wordpress.com/2022/10/30/multi-fold-discrete-fractal-spacetime-and-the-viability-of-localvs-non-local-hidden-variable-viability/#comment-9455, July 13, 2024. [301]: Stephane H. Maes, (2025), “QFT on discrete and / or non-commutative spacetime”, https://shmaesphysics.wordpress.com/2024/12/12/consistencies-and-implications-of-2d-massless-random-walksdiscrete-non-commutative-spacetime-and-no-flat-supersymmetry/#comment-10326, January 7, 2025. [302]: Stephane H. Maes, (2025), “Preons as Massless Higgs Bosons”, https://shmaesphysics.wordpress.com/2025/01/09/preons-as-massless-higgs-bosons/, January 9, 2025. [303]: Stephane H. Maes, (2025), “Microscopic Interpretation of The Gravity Electroweak Symmetry Breaking”, https://doi.org/10.5281/zenodo.15099220, https://shmaesphysics.wordpress.com/2025/03/27/microsc opic-interpretation-of-the-gravity-electroweak-symmetry-breaking/, March 27, 2025. (https://osf.io/q5erz). [304]: Stephane H. Maes, (2025), “Gravity From Relative Entropic Action Is Not Necessarily Entropic Gravity”, https://shmaesphysics.wordpress.com/2025/04/06/gravity-from-relative-entropic-action-is-not-necessarilyentropic-gravity/, April 6, 2025. [305]: Stephane H Maes, (2025), “Time-Varying Dark Energy Effect, How to Beat a Dead Horse. No It Not Provide A First Evidence of String Theory”, https://shmaesphysics.wordpress.com/2020/10/11/circular-arguments-in-stringand-superstring-theory-from-a-multi-fold-universe-perspective/#comment-10609, April 5, 2025. [306]: Stephane H. Maes, (2021), “Comments on CPT / anti-universe”, https://shmaesphysics.wordpress.com/2020/10/02/no-conventional-sterile-neutrinos-in-a-multi-fold-universe-justsmg-business-as-usual/#comment-1489 and comments after, January 30, 2021. [307]: Stephane H. Maes, (2025), “2D Random Walks Imply a Strictly Positive Cosmological Constant, Possibly Variable in Time”, https://shmaesphysics.wordpress.com/2025/04/24/2d-random-walks-imply-a-strictly-positivecosmological-constant-possibly-variable-in-time/, April 24, 2025. [308]: Stephane H. Maes, (2025), “No Hilbert Einstein Action With Positive Dark Energy / Cosmological Constant From A String Action”, https://zenodo.org/doi/10.5281/zenodo.15385159, https://shmaesphysics.wordpress.com/2025/05/08/no-hilbert-einstein-action-with-positive-dark-energycosmological-constant-from-a-strings-action/, May8, 2025, (https://osf.io/7nh45/download/). [309]: Stephane H. Maes, (2025), “Hopefully somebody will tell Vopson that he misunderstands Landauer”, https://shmaesphysics.wordpress.com/2023/12/14/information-has-no-mass/#comment-10716, April 26, 2025. [310]: Stephane H Maes, (2022), “Why is The Multi-fold Theory on viXra, and not peer-reviewed (yet)?”, https://shmaesphysics.wordpress.com/why-is-the-multi-fold-theory-on-vixra-and-not-peer-reviewed-yet/, July 8, 2022. [311]: Stephane H. Maes, (2025), “Adaptive Co-Design of Quantum Machine Learning Algorithms and Error Correction Protocols using Reinforcement Learning”, https://zenodo.org/doi/10.5281/zenodo.15428357, https://shmaes.wordpress.com/2025/05/15/adaptive-co-design-of-quantum-machine-learning-algorithms-anderror-correction-protocols-using-reinforcement-learning/, May 15, 2025, (https://osf.io/5jte9/download/). [312]: Stephane H. Maes, (2025), “Preserving the Power of Preprints: Why Minimal Oversight is Key to Scientific Progress”, https://zenodo.org/doi/10.5281/zenodo.15617193, https://shmaes.wordpress.com/2025/06/05/preserv ing-the-power-of-preprints-why-minimal-oversight-is-key-to-scientific-progress/, June 5, 2025. [313]: Stephane H Maes, (2025), “Rotating Black holes based on charged black holes”, https://shmaesphysics.wordpress.com/2024/11/24/physics-salvages-the-third-law-of-black-holethermodynamics/#comment-11016, June 28, 20265. [314]: Stephane H. Maes, (2025), “Information Energy Momentum Tensor, E/G Conjecture vs. Alleged Massive Information”, https://shmaesphysics.wordpress.com/2025/06/11/information-energy-momentum-tensor-e-gconjecture-vs-alleged-massive-information/, June 11, 2025. [315]: Stephane H. Maes, (2025), “No Naked Singularity, Whatever The Physical Collapse”, https://doi.org/10.5281/zenodo.16181569, https://shmaesphysics.wordpress.com/2025/07/19/nonaked-singularity-whatever-the-physical-collapse/, July 19, 2025. [316]: Marcus Bleicher, Piero Nicolini, Martin Sprenger, Elizabeth Winstanley, (2011), “Micro black holes in the laboratory”, arXiv:1111.0657v2. [317]: D Seitova, M V Savina and S V Shmatov, (2019),” The microscopic black hole production at the LHC with the CMS experiment”, J. Phys.: Conf. Ser. 1337 012010. [318]: Stephane H. Maes, (2025), “Early inflation dS instabilities, require a mechanisms like the multi-fold spacetime reconstruction with 2D random walks of massless bosons”, https://shmaesphysics.wordpress.com/2024/12/12/consistencies-and-implications-of-2d-massless-random-walks- discrete-non-commutative-spacetime-and-no-flat-supersymmetry/comment-page-1/#comment-11204, November 4, 2025. [319]: Steve Nadis, (2025), “A New Geometry for Einstein’s Theory of Relativity. A team of mathematicians based in Vienna is developing tools to extend the scope of general relativity.”, Quanta Magazine, https://www.quantamagazine.org/a-new-geometry-for-einsteins-theory-of-relativity-20250716/, July 16, 2025. [320]: Wikipedia, “Quantum foam”, https://en.wikipedia.org/wiki/Quantum_foam. Retrieved on May 24, 2020. [321]: Paul Ehrenfest, (1959), “Collected scientific papers”, North-Holland, January 1, 1959 [322]: Wikipedia, “Bertrand’s theorem”, https://en.wikipedia.org/wiki/Bertrand%27s_theorem. Retrieved for this paper on March 16, 2025. [323] Physics Stack Exchange, (2013), “No stable closed orbits for a Newtonian gravitational field in d≠3 spatial dimensions”, https://physics.stackexchange.com/questions/66417/no-stable-closed-orbits-for-a-newtoniangravitational-field-in-d-neq-3-spatial/. Retrieved on March 16, 2025. [324]: John Donne, (2017), “Answer to “Coulomb Potential in 1+1 and 1+2 dimensions?””, Physics StackExchange, https://physics.stackexchange.com/questions/372291/coulomb-potential-in-11-and-12-dimensions, December 3, 2017. [325]: John Donne, (2016), “Question and Answers to “Does Gravity Depend on Spatial Dimension?””, Physics StackExchange, https://physics.stackexchange.com/questions/279054/does-gravity-depend-on-spatial-dimension, September 8, 2016, and after. [326]: G. ‘t Hooft, (1993), “Dimensional Reduction in Quantum Gravity”, arXiv:gr-qc/9310026v2. [327]: Vadim Kaplunovsky, (2019), "Renormalizability and Dimensional Analysis", UT Physics Lecture Notes, https://web2.ph.utexas.edu/~vadim/Classes/2019s-qft/diman2.pdf. [206<328]: Wigner, E. P. (1960). “The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959”. Communications on Pure and Applied Mathematics. 13: 1–14. [328]: Sabine Hossenfelder, (2025), “Time has 3 dimensions and that explains particle masses, physicist claims”, YouTube, https://www.youtube.com/watch?v=LWzK6nITCK0. Retrieved on June29, 2025. [329]: Atsushi Higuchi, Vasileios A. Letsios, (2025), “Unitary Rigid Supersymmetry for the Chiral Graviton and Chiral Gravitino in de Sitter Spacetime”, arXiv:2503.04515v3. [330]: Nicolás Abate, Gonzalo Torroba, (2025), “Irreversibility of quantum field theory in de Sitter: the C, F and A theorems”, arXiv:2411.08961v1. [331]: Conghan Dong, Antoine Song, (2023-2024), “Stability of Euclidean 3-space for the positive mass theorem”, arXiv:2302.07414v3. [332]: Georgios Moschidis, (2018), “A proof of the instability of AdS for the Einstein–massless Vlasov system”, arXiv:1812.04268v1. [333]: G N Ord, (1983), “Fractal space-time: a geometric analogue of relativistic quantum mechanics”, J. Phys. A: Math. Gen. 16, 1869-1884. [334]: Stephane H. Maes, (2023), “Equivalency between 2D random walks and (relativistic) QM/ QFT” , https://shmaesphysics.wordpress.com/2022/11/09/quantum-gravity-emergence-from-entanglement-in-a-multifold-universe-2/#comment-8083, October 21, 2023. [335]: Chen Ly, (2024), “How a simple physics experiment could reveal the “dark dimension”. Could the universe's missing matter be hiding in a "dark" extra dimension? We now have simple ways to test this outlandish idea - and the existence of extra dimensions more generally.”, New Scientist, https://www.newscientist.com/article/mg26334993-000-how-a-simple-physics-experiment-could-reveal-the-darkdimension/, July 10, 2024. [336]: Miguel Montero, Cumrun Vafa, Irene Valenzuela, (2022-2023), “The Dark Dimension and the Swampland”, arXiv:2205.12293v3. [337]: Cumrun Vafa, (2024), “Swamplandish Unification of the Dark Sector”, arXiv:2402.00981v2. [338]: Steve Nadis, (2024), “In a ‘Dark Dimension,’ Physicists Search for the Universe’s Missing Matter. An idea derived from string theory suggests that dark matter is hiding in a (relatively) large extra dimension. The theory makes testable predictions that physicists are investigating now.”, Quanta Magazine, https://www.quantamagazine.org/in-a-dark-dimension-physicists-search-for-missing-matter-20240201/, February 1, 2024. [339]: Latham Boyle, Kieran Finn, Neil Turok, (2018), “CPT-Symmetric Universe”, arXiv:1803.08928v3. [340]: Latham Boyle, Kieran Finn, Neil Turok, (2022), “The Big Bang, CPT, and neutrino dark matter”, [341 [c26]: Emil T. Akhmedov, P. V. Buividovich, (2008), “Interacting Field Theories in de Sitter Space are NonUnitary”, arXiv:0808.4106v2. [342]: Michael de la Force, (2025), ” THE FOUR-DIMENSIONAL GHOST HAUNTING CERN’S PARTICLE ACCELERATOR”, Facebook, https://www.facebook.com/michael.delaforce/posts/the-four-dimensional-ghost-haunting-cernsparticle-acceleratordeep-within-the-wo/10164182529693900/, September 17, 2025. Retrieved on October 28, 2025. [343]: Albert De Roeck, Greg Landsberg, (2017), “The LHC’s extra dimension. Searches at ATLAS and CMS constrain models of extra dimensions.”, CERN Courier, https://cerncourier.com/a/the-lhcs-extra-dimension/, 13 January 2017 [344]: R.L. Workman et al. (Particle Data Group), (2022), “85. Extra Dimensions”, Prog. Theor. Exp. Phys. 2022, 083C01. [345]: Andrey Feldman, (2024), “CERN scientists search for new physics in unusual energy patterns linked to hidden particles. Researchers at CERN's Large Hadron Collider explore subtle energy signals to search for new physics beyond the Standard Model.”, Advanced Science News, https://www.advancedsciencenews.com/cern-scientistssearch-for-new-physics-in-unusual-energy-patterns-linked-to-hidden-particles/, December 27, 2024. [346]: Stephane H. Maes, (2023), “2D / JT gravity are well behaved, and without graviton. A sign of Physicality, 2D random walks and gravity by entanglement”,https://shmaesphysics.wordpress.com/2023/04/23/our-real-universeis-macroscopically-4d-hints-come-from-every-directions-show-that-it-had-to-be-so/#comment-7588, August 5, 2023. [347]: Kevin Hartnett, (2016), “A Unified Theory of Randomness. Researchers have uncovered deep connections among different types of random objects, illuminating hidden geometric structures.”, Quanta Magazine, https://www.quantamagazine.org/a-unified-theory-of-randomness-20160802/, August 2, 2016.