Edited by: Darya L. Zabelina, University of Arkansas, United States
Reviewed by: Marc Wittmann, Institute for Frontier Areas of Psychology and Mental Health (IGPP), Germany; Rui Ferreira Afonso, Albert Einstein Israelite Hospital, Brazil
This article was submitted to Cognition, a section of the journal Frontiers in Psychology
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Meditation is an umbrella term, which subsumes a huge number of diverse practices. It is still unclear how these practices can be classified in a reasonable way. Earlier proposals have struggled to do justice to the diversity of meditation techniques. To help in solving this issue, we used a novel bottom-up procedure to develop a comprehensive classification system for meditation techniques. In previous studies, we reduced 309 initially identified techniques to the 20 most popular ones. In the present study, 100 experienced meditators were asked to rate the similarity of the selected 20 techniques. Using multidimensional scaling, we found two orthogonal dimensions along which meditation techniques could be classified:
Meditation and mindfulness belong to two of the currently most popular and hyped research topics in psychology, psychiatry, medicine, and neuroscience (
Recently, researchers have begun to compare selected meditation techniques (
Therefore, in an attempt to clarify and simplify these issues, we chose to develop a new classification system in a bottom-up way, relying on the judgments of experienced meditators. A similar approach has already been successfully employed in a study deducing a working definition of meditation by repeatedly asking a panel of seven experts in meditation research (
Neuroscientific research has repeatedly shown differing brain activation and deactivation patterns during diverse meditative states following different meditative practices (
This limitation is probably due to the historical development of meditation research. While the 70’s saw considerable research efforts in examining the effects of Transcendental Meditation, the 90’s brought a huge interest into mindfulness meditation which keeps growing to the present (
Still, comparative studies have mainly focused on the above-mentioned four types of meditation, i.e., focused attention, open monitoring, loving kindness or compassion meditation, and mantra meditation. Studies empirically comparing some of these meditation techniques found differences in, e.g., dispositional mindfulness (
Diverse meditation techniques have distinct effects. This finding has led to a few new proposals in classifying meditation including a greater diversity of meditation techniques from various backgrounds.
Yet, as reasonable as such considerations may be, these proposals have largely been derived top-down and, thus, might be limited by researchers’ personal expertise and experience. Consistent with this assumption, previous proposals omit several important and commonly practiced meditation techniques, especially from the Hindu context. Additionally, experienced meditators from the respective traditions might not agree with these classifications as the proposed clusters might be misguided attempts at throwing together “apples and oranges”.
Other approaches acknowledged these problems and devised phenomenological features or taxonomic keys to help researchers and practitioners describe what they are doing during meditation (
When people talk about meditation they often refer to someone sitting silently in a cross-legged position with closed eyes and searching for some inner silence or truth. This may be due to the historical development of meditation and meditation research in the West (see above) but cannot account for the immense variety of meditation practices found across different spiritual traditions. Interestingly, especially those approaches coming from our own Western Christian context, or from related Abrahamic traditions like Sufi mysticism and the Jewish Merkabah, have gotten less attention. Only now, there is an increasing interest into a more broad scientific exploration of meditation in its many forms, including rather atypical practices like Osho’s dynamic meditation (
“The term
“Meditation is an art of being serene and alert in the present moment, instead of constantly struggling to change or to become” (
“Three main criteria have been defined as essential to any meditation practice: the use of a defined technique, logic relaxation (i.e., not intending to analyze, judge or expect), and a self-induced state/mode. Other criteria deemed important (by meditation experts) involve a state of psycho-physical relaxation, the use of a self-focus skill or anchor, the presence of a state of suspension of logical thought processes, a religious/spiritual/philosophical context, or a state of mental silence” (
“A complex neural practice that induces changes in neurophysiology and neurochemistry of brain resulting in altered neurocognition and behavior in the practitioner” (
“An exercise in which the individual turns attention or awareness to dwell upon a single object, concept, sound, image, or experience, with the intention of gaining greater spiritual or experiential and existential insight, or of achieving improved psychological well-being” (
“A contemplative practice (e.g., meditation) is multi-generational, embedded in a community, has certain features which include an alteration of body and/or mind, and a certain kind of purpose or goal. There is a recipe (i.e., instructions) to achieve this goal, plus criteria for progress toward this goal which can be evaluated by evaluators from the community” (
These six definitions are representative of opposing inclusion and exclusion criteria deemed important for labeling a practice meditation, or not. Some definitions are very specific (1, 3, 5), whereas others are rather broad (2, 4, 6). Specific definitions may be appropriate for investigating clear-cut research questions, they might, however, not account for the diversity of practices labeled “meditation”. Let’s consider the Sufi whirling technique (i.e., spinning around one’s own axis with arms spread out). This practice is generally considered a meditation technique aimed at “gaining greater spiritual or experiential insight” (5), it is thought to train awareness (1), and is a self-induced state of suspension of logical thought processes taking place within the context of a spiritual tradition (3). However, it does not necessarily involve a psycho-physiological relaxation (3), and does not necessarily focus on bringing mental processes under greater voluntary control (1), and might not be considered as dwelling upon a single object or experience (5).
On the other hand, very broad definitions could be very inclusive of diverse meditation techniques, but might broaden the scope too far by including practices generally not considered to be meditation techniques. This proves to be a tricky question, though. Can dancing, prayer, CrossFit or mindfully doing the dishes be considered meditation techniques or not? Where do we draw the line? According to definitions (2), (4), and (6) almost all the practices mentioned above would count as meditation. However, inducing “changes in neurophysiology and neurochemistry of brain resulting in altered neurocognition and behavior in the practitioner” (4) would also be true for experiences involving taking hallucinatory drugs or doing any kind of sports. As
This was the starting point for our research. We decided to approach the above-mentioned difficulties from a completely different perspective involving experienced meditators from diverse traditions in the process of gathering, selecting and grouping meditation techniques. We wanted to include as many different contexts, schools and traditions as possible. This bottom-up methodological approach differs fundamentally from any previous study, and stands in line with several researchers demanding a more rigorous investigation into the diversity of meditation techniques (
As mentioned above, meditation techniques are often taught in a specific context, tradition or belief system. This context can influence the effects of meditation immensely (
Two preparatory studies were carried out to evaluate and deduce basic meditation techniques to be classified in the current study. In the first study (Matko et al., unpublished) we collected all meditation techniques we could find through literature search and by conducting guided interviews with 20 experienced meditators from diverse traditions such as Tibetan Buddhism, Theravada Buddhism, Zen Buddhism, Yoga, Hinduism, Tantra, Sri Chinmoy, Kundalini Yoga, Osho-Meditation, Christianity, Sufism, Brahma Kumaris and Qi Gong. Interviews focused on the central question “When you meditate, what exactly do you do?” The literature search included meditation manuals from different schools as well as research papers that included detailed descriptions of meditation practices (e.g.,
The second preparatory study (Matko et al., unpublished) focused on exploring the prevalence, popularity, and comprehensiveness of our selection of 50 meditation techniques, and examined their underlying factor analytic structure. In a broad online survey, 637 experienced meditators from diverse meditation backgrounds provided data on how much experience they had with each of these 50 techniques. We found that all techniques were commonly used and could be grouped into seven factors. These factors represent groups of techniques that are commonly practiced together and correlate with the respective traditions they were derived from, but also span different traditions. In addition, we identified the 20 most popular meditation techniques widely practiced across many traditions (see section “Materials”,
List of 20 basic meditation techniques used in the present study, in their abbreviated and full descriptions.
Repeating syllables | Repeating syllables, words or phrases either mentally or loudly |
Manipulating the breath | Voluntary manipulation of breath, e.g., reducing the strength of breathing or “pranayama” including holding one’s breath |
Contemplating on question | Contemplating on a spiritually important question (e.g., “Who am I?”) |
Walking and observing senses | Walking and being mindful of sensory perceptions (movement of the feet, legs, clothing, air, hair, etc.), coordinating it with the breath if necessary |
Lying meditation | Lying down and going into a state of deep relaxation while being fully conscious |
Concentrating on energy centers or channeling | Concentrating on one or subsequent locations in the body/“energy centers” (e.g., abdomen or Chakra, Dan Tien), including “channeling energy” through certain pathways (e.g., spine) |
Observing the body | Observing how bodily sensations arise without adhering to them |
Singing sutras or mantras | Singing sutras/mantras/invocations, alone or together with others |
Contradiction or paradox | Concentrating the mind on something contradictory or complex without thinking discursively about the contradiction (e.g., Koan, Mahavakyas) |
Body scan | Scanning the entire body (e.g., body scan), including perceiving and releasing occurring emotions and tensions |
Concentrating on an object | Sustained concentration on an object or a visualized object (e.g., Kasina, geometrical pattern, picture of the master) |
Meditation with movement | Carrying out predetermined, meditative sequences of movements |
Sitting in silence | Sitting in silence (e.g., Shikantaza) |
Observing thoughts or emotions | Observing how thoughts or emotions arise without adhering to them |
Breath abdomen | Being mindful of the rise and fall of the abdomen while breathing |
Opening up to blessings | Opening oneself up to blessings and inspiration |
Meditation with sound | Meditation with sound (e.g., humming, or singing bowls) |
Cultivating compassion | Cultivating compassion, sympathetic joy, equanimity, loving kindness1 (for oneself, friends, neutral people, enemies, the whole world), including Tonglen |
Breath nose | Being mindful of the sensations arising in the nose during inhalation and exhalation |
Visualizations | Visualization practices (e.g., heart as an opening rose blossom, body expanding in all directions, combining inhalation and exhalation with visualizations of energy, light, smoke, etc.) |
This final selection of 20 techniques formed the basis of the current study, which focused on examining the structure underlying these diverse techniques. These structural investigations were based on intuitive similarity ratings of general effects that might be expected when meditators engage in practicing these meditation techniques. We decided to focus on general effects, because we were interested in the most general intuitions associated with these techniques. To make similarity judgments not too difficult (and to avoid activating textbook-knowledge about meditation), we did not further discriminate phenomenological, psychological or behavioral effects in our investigation.
We chose to pursue a purely statistical approach in this venture rather than referring to pre-existing concepts based on traditions or theoretical approaches. On the one hand, we were interested in identifying dimensions along which these 20 techniques could be classified and differentiated. On the other hand, we took an interest in potential clusters of similar meditation techniques that could be identified within these dimensions. The dimensions and clusters should form the basis of a new, empirically derived classification system for meditation techniques.
The current study used multidimensional scaling (MDS) as a tool for uncovering latent dimensions of diverse meditation techniques (
The procedures followed in this study and the results are discussed below. The data were collected in accordance with ethical guidelines pertaining to the use of human subjects.
We devised an online survey to judge the 20 most popular meditation techniques identified in the two above-mentioned preliminary studies (see section “Materials”,
The survey was sent to all participants of the second preparatory study mentioned above (Matko et al., unpublished) who had provided their e-mail addresses and consented to participate in further studies. A total of 102 experienced meditators completed the survey. Two participants were excluded because one did not provide sufficient data on his/her meditation routine, and one filled all answer fields with the same number. The final sample comprised 100 experienced meditators. The mean age was 52.90 years (
Of all participants, 55.0% reported holding a university degree, 18.0% had completed higher education, 8.0% had completed their doctorate, and 11.0% had acquired a professional qualification. Regarding their occupation, 37.6% of participants were working as employees, 28.7% were self-employed, and 16.8% were retired.
Participants had practiced meditation from 2 years up to 46 years, the mean meditation experience being 15.10 years (
Participants were asked to select the tradition(s), the meditation techniques they practiced, were affiliated with. They reported practicing in the following traditions:
Zen (
Theravada, Vipassana (
Tibetan Buddhism (
Yoga, Kundalini Yoga (
Osho meditation (
Other Hindu traditions, such as Vaishnavism, Sri Chinmoy, Sri Aurobindo, Mother Meera, Ramana Maharshi, Deepak Chopra, and Transcendental Meditation (
Mindfulness, MBSR (
Christianity (
Sufism (
Qigong, Tai Chi (
Judaism, Merkabah (
No Tradition, Free Meditation (
Other (
Several participants had been practicing in different spiritual traditions, therefore, the total number of allocated traditions (
Participants were asked to rate the similarity of the 20 basic meditation techniques listed below.
Multidimensional scaling can be applied to any similarity matrix. Thus, each participant’s ratings could serve as the basis for analysis. However, as an individual’s ratings can be very subjective or limited to his or her personal experience, we calculated the means of the similarity judgments across all participants. On the basis of the resulting similarity matrix, we performed a multidimensional scaling analysis using SPSS’s program PROXSCAL. Following recommendations by
Overall multidimensional scaling (MDS) solution, based on average similarity judgments of
The statistical method of multidimensional scaling returns a dimensional output with potentially meaningful clusters, which are open to interpretation by the researcher. Thus, we thoroughly inspected
Dimension 1 has cultivating compassion and other brahmaviharas (see footnote 1), contemplating on a spiritual question, concentrating on a contradiction or paradox, and singing sutras or mantras on one extreme. At the other end are scanning the body, observing the abdomen or the nostrils while breathing, lying meditation, and manipulating the breath. Meditation techniques with a more abstract or conceptual focus received lower scores, while those with a higher amount of body-orientation received higher scores. Therefore, we decided to label this dimension “amount of body orientation”.
Dimension 2 has sitting in silence, concentrating on a contradiction or paradox, lying meditation, and observing thoughts or emotions at one end of the spectrum, while meditation with movement, walking and observing senses, and manipulating the breath are at the other end. Lower scores reflect a more passive, still and contemplative kind of meditation practice, while higher scores reflect more (bodily) active kinds of meditation practices. This dimension was labeled “activation”.
We identified seven clusters of meditation techniques by visual inspection (
Overall multidimensional scaling (MDS) solution with indicated clusters and labels.
Four smaller clusters were identified on the other side of the diagram, toward the more conceptual or object-oriented end. One cluster comprises concentrating on a contradiction or paradox and contemplating on a spiritual question and was labeled “contemplation”. The second cluster includes visualizations, and concentrating on an object or a visualized object, and was labeled “visual concentration”. The third cluster comprises opening oneself up to blessings, and cultivating compassion, loving-kindness, sympathetic joy, or equanimity, and can be seen as a cluster of “affect-centered techniques”. The forth of the smaller clusters includes repeating syllables, words or phrases, singing sutras or mantras, and meditation with sound, and was labeled “mantra meditation”.
These two dimensions, plus the seven clusters of meditation techniques, constitute our proposed new classification system of meditation techniques.
Results from one of the preliminary studies (Matko et al., unpublished) identified differences in usage and popularity of certain meditation techniques between meditators of two major traditions, i.e., Buddhist and Hindu meditators. Therefore, we decided to conduct another two multidimensional scaling analyses for these two subgroups. We wanted to see whether meditators from these two traditions have different conceptions about clusters and dimensions of basic meditation techniques.
Participants who stated practicing in one or more Buddhist traditions (i.e., Zen, Theravada, Vipassana, Mindfulness, or MBSR), but in no other tradition from another spiritual background, were allocated to the group of Buddhist meditators (
In accordance with the results mentioned above, we selected two-dimensional models with Kruskal’s stress values of 0.054 (Buddhist), and 0.048 (Hindu), respectively. These values indicate an adequately good, but not perfect fit between model and data.
Multidimensional scaling (MDS) solution for Buddhist meditators (
Multidimensional scaling (MDS) solution for Hindu meditators (
First, both figures indicate a high congruence between ratings. Both solutions, Buddhist and Hindu, bear similarity not only to each other, but also to the overall solution described above. Moreover, both solutions exhibit similar dimensions, namely “amount of body orientation” as Dimension 1, and “activation” as Dimension 2, and similar clusters of techniques. However, and importantly, some of the techniques have slightly shifted their position and/or affinity to the afore-mentioned clusters (printed in bold type).
The solution for Buddhist meditators shows basically the same cluster structure as the overall solution, with two small peculiarities. First, the technique walking and observing senses shifted from the “meditation with movement” to the “body-centered meditation” cluster. This appears reasonable when looking at Buddhist traditional practices where walking meditation is commonly practiced alternating with breathing meditation (
Looking at the solution of Hindu meditators, both dimensions can be replicated, again. Looking closer, certain shifts in location lead to changes in some clusters. Contrary to the Buddhist solution, opening oneself up to blessings and cultivating compassion remain in the same cluster. However, both techniques moved further away from the “visual concentration” cluster, and now appear to be closer to the cluster of “mantra meditation”. Second, the body scan has left the cluster of “body-centered techniques” and joined lying meditation and observing thoughts and emotions. This appears reasonable with regard to Hindu practice traditions, especially in the Yoga context where the body scan is commonly practiced in a supine position (
All in all, there is remarkable conformance between the original solution and both solutions from Buddhist and Hindu meditators, respectively. At the same time, both solutions reveal tradition-specific particularities that can easily be attributed to traditional frameworks and modes of practice. This gives further evidence to the general validity of the proposed classification system.
The present study arrives at a novel classification system for meditation techniques and seems to be the first attempt to have been devised in an empirical and systematic bottom-up way. Drawing upon results from extensive preparatory studies (Matko et al., unpublished), we employed multidimensional scaling (MDS) to the similarity ratings of 100 experienced meditators for 20 well-known and diverse meditation techniques. Thus, our approach is unique not only in its methodology, but also in the variety of meditation techniques that were included in the analyses.
During the past years, the scope of scientific research has expanded continually to include a wider range of meditation practices (
Based on our results, we propose a two-dimensional system of classifying meditation according to (1) the amount of body orientation in the technique, and (2) the level of activation in the technique. Furthermore, we propose seven main clusters of meditation techniques, namely: (1) Body-centered meditation, (2) mindful observation, (3) contemplation, (4) mantra meditation, (5) visual concentration, (6) affect-centered meditation, and (7) meditation with movement.
Taking a closer look at the dimensions and clusters, implicit assumptions of experienced meditators differ fundamentally from afore-mentioned theoretical proposals. Former proposals have focused on cognitive variables to describe and differentiate meditation techniques with the popular “focused attention” (FA) and “open monitoring” (OM) distinction (
Quite on the contrary, our MDS solution does not depict cognitive, but rather embodied dimensions. Both dimensions, amount of body orientation and level of activation, are closely related to bodily processes. They have been taken into account in previous descriptive or taxonomic systems (
It seems that, according to experienced meditators, meditation is inherently somatic. This is in line with research on “embodied cognition” (
Meditation places the focus of attention onto those ascending and descending inner processes, making them more salient in consciousness. Many, if not all, meditation practices emphasize directing attention to interoceptive and/or exteroceptive signals. Whether meditators observe all incoming (sensory or mental) stimuli, develop compassionate feelings for others, silently repeat a mantra, or explicitly focus on bodily mechanisms such as the breath: the body remains a constant companion in all their endeavors. Likewise, Buddhist teachings emphasize that body and mind are equally valid objects of meditation, and encourage practitioners to use awareness of the whole body as a somatic anchor for mindfulness, or, in other words, cultivate an embodied form of mindfulness (
It is surprising, though, that meditators implicitly classify meditation techniques on embodied dimensions, although we had requested them to judge the similarity of general effects of these techniques. We do not know whether participants judged techniques according to similar phenomenological experiences likely to occur during the practice of the specific technique or according to similar psychological outcomes following the prolonged practice of the technique. It might well be that they considered the one or the other, or both, or something completely different. But, we can probably assume that these diverse interpretations of the question were leveled out by agglomerating the judgments of 100 participants. Overall, it seems that similarity or dissimilarity of meditation techniques seems to be implicitly attributed to differences in the two above-mentioned embodied dimensions, i.e., level of activation and amount of body orientation.
Yet, one issue that should be looked at more closely in further research is whether similarity on these two dimensions corresponds to differences in actual effects, too. Future studies should evaluate whether meditation techniques judged high in one dimension, e.g., level of activation, lead to similar phenomenological experiences, neuroscientific signatures, and/or psychological and behavioral outcomes. They could also compare techniques judged high versus techniques judged low in one dimension and investigate whether there is a linear increase or decrease of specific effects along this dimension. A close-up examination of diverse techniques could reveal similar or dissimilar mechanisms and processes underlying the practice of these techniques and take into account individual variation between participants.
The commonly made distinction between FA and OM practices could not be replicated in the present study, confirming previously voiced considerations (
Still, it is easier to connect the cluster of “mindful observation” techniques with OM practices than to make connections to the FA concept. The mindful observation cluster includes three main practices in which the present-moment experience is approached with an open and receptive attitude (
Furthermore, observing the breath might be considered concentrative for novice meditators, but might progress into a more passive and observational mode with growing experience, or even change back and forth from concentrative to receptive during the same meditation session. This would also be true for other practices clustered together in our solution as “body-centered meditation,” i.e., scanning or observing the body, and concentrating on a location in the body or on “energy centers”. The only identifiable cluster of techniques with a strong concentrative focus is the group of “visual concentration” techniques. Conversely, these have a very specific visual focus (concentrating on an object such as a picture or disk, or visualization techniques). Thus, they can be considered to be a very specific form of FA.
In conclusion, we would suggest that it might eventually be helpful to discard the rather unspecific category of FA meditation and replace it by the more specific categories presented in our empirically derived MDS solution. This notion needs further empirical investigation, though. Future experimental intervention studies should evaluate whether the alleged differences between clusters can be replicated in empirical findings. According to our model, meditation techniques that are closer to each other in the MDS solution should yield more similar effects than techniques which are further apart from each other.
We encourage researchers to evaluate this new classification system through comparative empirical studies. These studies could investigate short-term and long-term effects of each technique or cluster of techniques taking into account phenomenological, psychological, behavioral and neuroscientific aspects. They could also try to capture individual experiences with and reactions to these techniques. Single-case research designs (
We are well aware that our choice of practices might have been limited to the regional availability of meditation teachers and traditions. Still, the comprehensiveness of our selection was confirmed by a broad sample of experienced meditators in one of the preparatory studies (Matko et al., unpublished). This allowed us to deliberately choose the 20 most popular and commonly known techniques for the current study. Additionally, the MDS solutions of ratings of primarily Buddhist or Hindu meditators were astonishingly congruent with the overall solution, while, at the same time, revealing tradition-specific particularities. This shows how different traditional background knowledge can frame responses, even though the question we asked our participants was very general in nature. We might have received different answers if our question had been more specific, e.g., specifying phenomenological, psychological or behavioral effects. Yet, this was not the aim of the present study, which rather focused on detecting general structures and intuitive typologies. Future studies could evaluate more specific typologies of meditation.
One could argue that the 20 techniques, which were investigated in this study, were artificially constructed and taken out of context. Traditionally, meditation techniques are practiced in a specific order, in the framework of a specific tradition, or in combination with other practices. Observing the breath, e.g., is often combined with visualizations or with the repetition of a mantra. Conversely, little is known about the effects of combined meditation techniques compared to simple techniques. Therefore, it seems promising to investigate and compare both, simple and combined techniques, and see if there are, indeed, any additive or interactive effects.
The same is true for the sequence of practices and the specific framework or traditional context of practice. To date, there is a scarcity of studies into sequence or framework effects (
Another argument could be that some of the 20 meditation techniques employed in this study are not simple techniques but already rather broad categories in themselves. For example, voluntarily manipulation of breath, visualizations, or meditation with movement are all conglomerates subsuming a lot of diverse techniques. This was our conscious choice in the interest of brevity. During our preparatory studies we came across a great variety of techniques (
Nonetheless, these broad categories of techniques should be eventually investigated in greater detail. For instance, manipulating the breath, also often referred to as “pranayama,” can take many forms. These can range from reducing the strength of breathing, to alternate nostril breathing with holding one’s breath, or even very rapid breathing (
The other two broad categories mentioned above can be very diverse, too. Visualizations can focus on imagining light or fire at different body parts, imagining the body expanding in all directions, or merging with a visual representation of a deity (a typical Tibetan Buddhist practice, see, e.g.,
In the long run, all of these efforts could contribute to establishing one or more theories of meditation. This endeavor is not only imperative for the future of scientific research into meditation (
A broad range of diverse meditation techniques was effectively depicted in the novel classification system presented in this paper. This classification system is the first to be derived empirically by requesting experts’ evaluations. The dimensions depicted in our classification system shed new light on previous categorizations and shift the focus from cognitive to embodied variables of interest. We hope that our classification system will be useful for future studies and the development of one or more profound theories of meditation.
The datasets generated for this study are available on request to the corresponding author.
The studies involving human participants were reviewed and approved by Ethikkommission, Fakultät für Human- und Sozialwissenschaften, Technische Universität Chemnitz. The patients/participants provided their written informed consent to participate in this study.
KM designed and executed the studies, analyzed the data, and wrote the first draft of the manuscript. PS conceptualized the studies and supervised the data analyses. Both authors worked on the final version of the manuscript.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
We thank Ulrich Ott for his valuable contribution to our preparatory studies. We also thank him, Fynn-Mathis Trautwein, and Ritesh Mariadas for their very helpful comments on a previous version of the manuscript.