The theory of relational accommodation postulates that our universe is a specific set of coherently accommodating relations between logical probabilities. This set of accommodating probabilities exists in a bigger framework: the ground state of everything. In this ground state all logical probabilities and their relations exist simultaneously in superposition. This ground state cannot be absolutely nothing, because without even potential, nothing could logically exist. The ground state cannot be some specific probabilities because then it would logically be something. So from a strictly logical perspective the only way something can be nothing is when it is all logical probabilities at once. Because it is not differentiated it is nothing specific and therefore akin to nothing. It is pure potential. Without dimensions. The probabilities in the ground state must be logical. If they are not logical then endless unpredictable realities would arise and no stable reality can form. In this ground state of pure potential there are relations between probabilities. If a relation changes then they all change to accommodate for the change. If a set of relations is coherent then all relations in the set can interact in a way that is coherent with the set. For the set a specific reality forms: the coherence with the set. If a set of relations is stable then it exists further. Our universe is such a set of relations. As long as probabilities and relations are coherent with our set of accommodating relations then they are real to us. The rest is filtered out. They could be part of another set of coherent relations but that set doesn’t share coherence with our set, so we can’t see the other set. To go even further: it would then not exist to us. If one accepts this conclusion, one starts to see that everything must be an accommodated set of relations between probabilities that is part of the total set that is our universe. Once this conclusion has been drawn the next step is to see that particles or massive objects are in fact an enormous number of accommodating relations that must be processed to maintain coherence within the set. Therefore it seems logical that mass is a set of accommodating relations between probabilities. This means that to process a certain amount of mass it would take an amount of time to process the relations. This would mean there are more or less dense areas of processing. This different amount of time it takes to process relations, creates differences in dimensions. Therefore dimensions are not fundamental. They emerge when a coherent set of relations needs to process to stay coherent. I found that there is even a formula to describe this. The system accommodation load of a mass (S) in rest is related to the smallest amount of relations that has dimensions. This is the Planck unit consisting of the Planck time and the Planck length. S(m) = m ∙ l_P / t_P / r (or since l_P / t_P = c:) S(m) = m ∙ c / r. It is in fact the proportion of mass and volume (radius) versus the smallest unit of relations. The system accommodation load is expressed in kg/s. The system accommodation load (S) in itself has relevance if one correlates this to the frame of dimensions it causes. I call this frame A_(xyzt). What is frame A? Frame A is the capacity for creating space and time that is left over when the relations of a specific mass have been processed. The maximum amount of relations a Planck unit can process, is also known in existing physics. Its S = c^3 / G. It is the light speed to the third power divided by the gravitational constant. This number represents the maximum accommodating capacity in kg/s of a Planck unit. Therefore frame A_(xyzt) = 1 – S(m) / S_max. To calculate the dimension frame of a mass and therefore relate distance of time to this mass one can use A. Another addition is that if the object has speed more relations have to be accommodated. This can be added by multiplying with the Lorentz factor (gamma v) γ_v = 1 / √ 1 – v^2 / c^2 which leads to formula: S(m) = (m ∙ c / r) ∙ γ_v. If an object is moving through a space with multiple masses with different speeds the formula gets like this. S_total = S_obj1 + S_obj 2 + S_obj x + … (relative r to obj1). With frame A_total = 1 – S_total / S_max. The results of this calculation are remarkably similar to General Relativity. Except for very heavy objects, when a small deviation is seen. It would be an object for research to analyse why this difference exists. Another factor which can be added is temperature. The reason for that is that raising temperature means more speed for particles. This is an extra gamma factor, which I suspect could be γ_T = 1 / √ 1 – v^2_Th / c^2 or γ_T = 1 + Q / mc^2 or S_Q = Q / rc (S = S_m + S_Q). Adding γ_T leads to formula S(m) = (m ∙ c / r) ∙ γ_v ∙ γ_T expressed in S(kg/s) where m : v : T is an exchange ratio.
The theory of relational accommodation postulates that our universe is a specific set of coherently accommodating relations between logical probabilities. This set of accommodating probabilities exists in a bigger framework: the ground state of everything. In this ground state all logical probabilities and their relations exist simultaneously in superposition. This ground state cannot be absolutely nothing, because without even potential, nothing could logically exist. The ground state cannot be some specific probabilities because then it would logically be something. So from a strictly logical perspective the only way something can be nothing is when it is all logical probabilities at once. Because it is not differentiated it is nothing specific and therefore akin to nothing. It is pure potential. Without dimensions. The probabilities in the ground state must be logical. If they are not logical then endless unpredictable realities would arise and no stable reality can form. In this ground state of pure potential there are relations between probabilities. If a relation changes then they all change to accommodate for the change. If a set of relations is coherent then all relations in the set can interact in a way that is coherent with the set. For the set a specific reality forms: the coherence with the set. If a set of relations is stable then it exists further. Our universe is such a set of relations. As long as probabilities and relations are coherent with our set of accommodating relations then they are real to us. The rest is filtered out. They could be part of another set of coherent relations but that set doesn’t share coherence with our set, so we can’t see the other set. To go even further: it would then not exist to us. If one accepts this conclusion, one starts to see that everything must be an accommodated set of relations between probabilities that is part of the total set that is our universe. Once this conclusion has been drawn the next step is to see that particles or massive objects are in fact an enormous number of accommodating relations that must be processed to maintain coherence within the set. Therefore it seems logical that mass is a set of accommodating relations between probabilities. This means that to process a certain amount of mass it would take an amount of time to process the relations. This would mean there are more or less dense areas of processing. This different amount of time it takes to process relations, creates differences in dimensions. Therefore dimensions are not fundamental. They emerge when a coherent set of relations needs to process to stay coherent. I found that there is even a formula to describe this. The system accommodation load of a mass (S) in rest is related to the smallest amount of relations that has dimensions. This is the Planck unit consisting of the Planck time and the Planck length. S(m) = m ∙ l_P / t_P / r (or since l_P / t_P = c:) S(m) = m ∙ c / r. It is in fact the proportion of mass and volume (radius) versus the smallest unit of relations. The system accommodation load is expressed in kg/s. The system accommodation load (S) in itself has relevance if one correlates this to the frame of dimensions it causes. I call this frame A_(xyzt). What is frame A? Frame A is the capacity for creating space and time that is left over when the relations of a specific mass have been processed. The maximum amount of relations a Planck unit can process, is also known in existing physics. Its S = c^3 / G. It is the light speed to the third power divided by the gravitational constant. This number represents the maximum accommodating capacity in kg/s of a Planck unit. Therefore frame A_(xyzt) = 1 – S(m) / S_max. To calculate the dimension frame of a mass and therefore relate distance of time to this mass one can use A. Another addition is that if the object has speed more relations have to be accommodated. This can be added by multiplying with the Lorentz factor (gamma v) γ_v = 1 / √ 1 – v^2 / c^2 which leads to formula: S(m) = (m ∙ c / r) ∙ γ_v. If an object is moving through a space with multiple masses with different speeds the formula gets like this. S_total = S_obj1 + S_obj 2 + S_obj x + … (relative r to obj1). With frame A_total = 1 – S_total / S_max. The results of this calculation are remarkably similar to General Relativity. Except for very heavy objects, when a small deviation is seen. It would be an object for research to analyse why this difference exists. Another factor which can be added is temperature. The reason for that is that raising temperature means more speed for particles. This is an extra gamma factor, which I suspect could be γ_T = 1 / √ 1 – v^2_Th / c^2 or γ_T = 1 + Q / mc^2 or S_Q = Q / rc (S = S_m + S_Q). Adding γ_T leads to formula S(m) = (m ∙ c / r) ∙ γ_v ∙ γ_T expressed in S(kg/s) where m : v : T is an exchange ratio.
The framework rests on eight foundational postulates — eight statements about how reality is structured. Each postulate makes a specific claim. Together, they constrain everything that can happen. In plain English, the eight postulates say: 1. There is a real, physical time at the deepest level of reality. Time flows. 2. Time and space are not symmetric. (This sounds technical but just means time is special — it has a direction, space does not have a preferred direction.) 3. Time emerges from the substrate dynamics. It is not a separate thing — it comes from how the substrate vibrates. 4. There exist tiny excitations of the substrate, called time quanta. They are everywhere, all the time, propagating at the speed of light. 5. Reality has two layers. There is the underlying quantum stuff (call it Frame 1), and there are the definite outcomes we actually observe (Frame 2). A filter connects them. 6. Matter is, in a sense, the absence of substrate. Where the substrate field drops to zero, mass appears.7. The substrate has a particular shape — a Mexican-hat potential — that determines the physics of inflation, vacuum energy, and how the universe can be stable. 8. The substrate carries an extra electromagnetic-like force — a hidden gauge symmetry — with very specific properties. Time Quanta: The Tiny Observers Postulate 4 says that the substrate carries excitations called time quanta. These are like the photons of light, but they are excitations of the substrate field rather than the electromagnetic field. A few key facts about time quanta: • They are physically real, not a mathematical fiction • They exist everywhere, all the time • They propagate at the speed of light • They are unimaginably tiny — about one Planck length in size, which is something like a hundred-quintillionths of the diameter of a proton • They carry energy on the order of the Planck energy — extraordinarily large for one particle, but they are nearly massless when you average them. Where is the key insight: time quanta are constantly interacting with everything. Every atom, every electron, every macroscopic object is being constantly bombarded by time quanta from all directions. It is like rain. If you stand outside in a downpour, you are constantly being hit by water droplets. You feel them as pressure on your skin, as wetness in your hair. Each individual droplet is small, but the cumulative effect is large. Time quanta are like that, except they are everywhere, not just outside, and they are constant — there is no umbrella, no shelter from them. Every system in the universe is being continuously rained on by time quanta.
A perspective on Everett's relative state formulation is proposed leading to a relational quantum mechanics. There are inevitably a large number of different versions of the universe in which a specific observer could exist, and in the universe of the unitary wave function they are all existing and coincident. If these different versions of the universe are superposed the result is a universe in which the superposition of all of the identical copies sums to a single observer. The effective universe in the functional frame of reference of this observer would be highly indeterminate but determinate where observed by this observer. This would naturally relativise the universe of the conventional view since each observer would inhabit an effective universe in which different aspects were determinate. Although the identity of the observer as a physical body does not readily fit this concept, it appears to apply inevitably to the functional identity of an observer as depicted by Everett. In this relational quantum mechanics a collapse dynamics applies only to the functional frame of reference of the observer and raises no incompatibility with the linear dynamics.
Common introduction to all the records of this series. The content of this record follows below. Mathematical Materiality (MM) in brief. Why are the laws of physics the same everywhere and at every instant, even though nothing forces matter to obey them? MM proposes an answer: the laws are not rules imposed on matter from the outside; rather, matter itself is made of mathematical relations. And mathematics cannot change: a relation binds two distinct terms everywhere and always. In logic, nothing exists on its own: to exist means to be in relation to another logical entity, and outside this web of relations nothing can exist, not even other universes. This reading already meets experimental measurements at two points. First, the ratio of dark to ordinary matter is read as 3√3 = 5.196; when left free in the fits, Planck and DESI DR2 data give 5.21–5.22 (as registered in record 2.44, https://doi.org/10.5281/zenodo.23329080). Second, the acceleration scale of galaxies is read as a₀ = cH₀/6, the same scale that appears in Verlinde's emergent gravity: the computed value is 1.09–1.18 × 10⁻¹⁰ m/s² against the measured value of 1.20 (record 2.46.1, https://doi.org/10.5281/zenodo.23506655). Both readings were formulated with the measurements already known; the tests to check them against future data are registered in the same records. In the first logical nexus between space and time — which became homogeneous with Einstein — there is a non-local phase, made only of a pure logical distinction: space is not time. Between the two there is no relation of quantitative calculation, only the logical entity they have in common, which is needed to make them exist with respect to each other. This level is not distant: it is present in every phase of reality, in every place and at every instant. It shows in entanglement, where two distant systems remain correlated more strongly than any explanation based on separate properties and free of faster-than-light influences allows, without anything physically travelling between them. In this non-local phase the two distinct terms, space and time, share only one logical element, which we shall call their greatest common divisor (GCD), just as the numbers 3 and 5 have only 1 in common. The local world arises when a relation is counted through this GCD: its multiples and its fractions form a matrix. Seen by an observer inside the system like us, the multiples appear as time and the fractions as space. When that same multiple is directly contained in the matrix of the point of observation, it turns into mass — that is, into concrete matter as we usually understand it. There is therefore a close link between time and mass, in full agreement with Einstein's relativity, which ties mass to spacetime. The observed objects, while being logically autonomous entities in their local relations, enter into relation with the observer through a logical diffraction — that is, a decomposition into fractions — of the observer's matrix. This reading also gives a reason for the limit of the speed of light, which in Einstein's relativity is instead taken as a starting principle. The speed of light is the fixed exchange rate between the multiples and the fractions of the same GCD, meaning how much space a single step of time is worth: exceeding it would mean, for some observer, covering space without counting time, and thus leaving the local world. Logic always starts from a logical relative, and this exchange rate has nothing absolute in itself either: it is a necessary relative which, inside the system, becomes an absolute hypothesis, the same for everyone and impossible to exceed. Outside the system, by contrast, it has no justification at all, because outside there is only non-existence: justifying something requires another term to relate it to, and out there there is none. Asking for a reason from outside is like asking what lies north of the North Pole. The same theoretical framework that reads space, time, mass and the observed objects also admits quantum mechanics. The non-local phase and the mirror-like logical reciprocity between the two ends of the nexus give a reason for the probabilistic behaviour of matter. When the observed object is large enough, its mass fixes it in the matrix of the point of observation: for this reason we see it in one precise place and at one precise instant. When instead the object falls below a certain mass threshold, the principal GCD (that of the point of observation) and the GCD of the diffraction that generates the object are forced to become equal, reflecting each other as in a mirror. At that point the object no longer occupies a single point of the spacetime generated by the observer, but spreads over several possible positions, and we observe it as probability. It is like having to describe the number 10 using only the number 1: the only way is to distribute the 1 over ten positions, one for each unit of the 10. Today we know that even objects made of thousands of atoms behave in this way, and no experiment has yet found the boundary. The idea that the passage from quantum to classical behaviour depends on mass is close to that of Penrose and Diósi; in MM the threshold is the point where the two GCDs, the principal one and that of the local diffraction, become equal. For all these reasons the universe behaves like a simulation without really being one. It follows exact rules, made of counts, everywhere and at every instant, but no machine runs them and no programmer wrote them: a structure of mathematical relations does not need to be computed in order to exist. Tegmark (2008) had already noted that such a simulation need not be run, while Vazza (2025) estimated that running it physically on a machine would require resources that the very laws of the universe do not allow. The work is shared openly so that it can be judged by as many readers as possible: anyone who knows someone interested can pass on this single link, valid for the whole framework (with an overview in English and Italian): https://doi.org/10.5281/zenodo.23535916. The entry page, with the complete list of all records, is https://doi.org/10.5281/zenodo.22667516. To cite the framework: Lanciano, U. (2026). The number 1 in front of the mirror: Mathematical Materiality from the nexus to the cosmos. Zenodo. https://doi.org/10.5281/zenodo.23535916. The records have been deposited since 5 August 2026, each with its own date, and are released under CC BY 4.0: anyone may use them by citing the source. Objections and errors found are welcome at riverantares@gmail.com, since Zenodo has no space for comments. This record contains the four-page summary of the framework, in English and in Italian: the question of why physical laws hold everywhere with nothing to enforce them; the Great Reversal; the non-local phase and its empirical trace in Bell-type experiments; the five postulates with the example of 3 and 5; the matrix; the equals sign as a mirror; a clock made of 3 and 5, whose two means give Einstein's slowing of moving clocks (a known identity: Bondi 1964; Knuth and Bahreyni 2014); and the comparison with two measured numbers. The full overview, with the list of all records, is at DOI 10.5281/zenodo.22667516. The author is not a professional physicist; the framework and its premises are the author's own. The texts were written with the help of AI assistants. There has been no review by human referees.
In modern physics the common relational approach should be extended to the concepts of element and set. The relationalization of the concepts of element and set means that in the final analysis the World exists as an indivisible whole, not as a set (of one or another kind of elements). Therefore, we have to describe quantum systems in terms of potentialities and probabilities: since quantum systems cannot be analyzed completely into sets of elements, we can speak only of the potentialities of isolating elements and sets within their structure. On the other hand this quantum property of the world as an indivisible whole accounts for the astonishing logical properties of the structure of the potentialities of quantum systems which it brings forth. This has been confirmed by quantum-correlation experiments (A.Aspect and oth.). These effects have a relational nature, not a physical-causal or material one, and they are brought forth by the changes (resulting from measurement or physical interaction) in the structure of the relations of the mutually complementary sides of reality. One of these sides expresses an actually existing structure of the system as a real (and physically verifiable) but only relatively separable set, and the other expresses the sets of potentialities in it which arise from the astonishing property of finite non-analyzability of the system into elements and sets (i.e. by the quantum property of the world as an indivisible unit).
This record. Whether a mass exists above which quantum superposition stops: registered readings confronted with the 2026 interference record, and a prediction dated to 2035. Reading path: Quantum mechanics, 2 of 2 · before: Born geometry, the Tsirelson bound and the singlet · all themes. Common introduction to all the records of this series. The content of this record follows below. Mathematical Materiality (MM) in brief. Why are the laws of physics the same everywhere and at every instant, even though nothing forces matter to obey them? MM proposes an answer: the laws are not rules imposed on matter from the outside; rather, matter itself is made of mathematical relations. And mathematics cannot change: a relation binds two distinct terms everywhere and always. In logic, nothing exists on its own: to exist means to be in relation to another logical entity, and outside this web of relations nothing can exist, not even other universes. This reading already meets experimental measurements at two points. First, the ratio of dark to ordinary matter is read as 3√3 = 5.196; when left free in the fits, Planck and DESI DR2 data give 5.21–5.22 (as registered in record 2.44, https://doi.org/10.5281/zenodo.23329080). Second, the acceleration scale of galaxies is read as a₀ = cH₀/6, the same scale that appears in Verlinde's emergent gravity: the computed value is 1.09–1.18 × 10⁻¹⁰ m/s² against the measured value of 1.20 (record 2.46.1, https://doi.org/10.5281/zenodo.23506655). Both readings were formulated with the measurements already known; the tests to check them against future data are registered in the same records. In the first logical nexus between space and time — which became homogeneous with Einstein — there is a non-local phase, made only of a pure logical distinction: space is not time. Between the two there is no relation of quantitative calculation, only the logical entity they have in common, which is needed to make them exist with respect to each other. This level is not distant: it is present in every phase of reality, in every place and at every instant. It shows in entanglement, where two distant systems remain correlated more strongly than any explanation based on separate properties and free of faster-than-light influences allows, without anything physically travelling between them. In this non-local phase the two distinct terms, space and time, share only one logical element, which we shall call their greatest common divisor (GCD), just as the numbers 3 and 5 have only 1 in common. The local world arises when a relation is counted through this GCD: its multiples and its fractions form a matrix. Seen by an observer inside the system like us, the multiples appear as time and the fractions as space. When that same multiple is directly contained in the matrix of the point of observation, it turns into mass — that is, into concrete matter as we usually understand it. There is therefore a close link between time and mass, in full agreement with Einstein's relativity, which ties mass to spacetime. The observed objects, while being logically autonomous entities in their local relations, enter into relation with the observer through a logical diffraction — that is, a decomposition into fractions — of the observer's matrix. This reading also gives a reason for the limit of the speed of light, which in Einstein's relativity is instead taken as a starting principle. The speed of light is the fixed exchange rate between the multiples and the fractions of the same GCD, meaning how much space a single step of time is worth: exceeding it would mean, for some observer, covering space without counting time, and thus leaving the local world. Logic always starts from a logical relative, and this exchange rate has nothing absolute in itself either: it is a necessary relative which, inside the system, becomes an absolute hypothesis, the same for everyone and impossible to exceed. Outside the system, by contrast, it has no justification at all, because outside there is only non-existence: justifying something requires another term to relate it to, and out there there is none. Asking for a reason from outside is like asking what lies north of the North Pole. The same theoretical framework that reads space, time, mass and the observed objects also admits quantum mechanics. The non-local phase and the mirror-like logical reciprocity between the two ends of the nexus give a reason for the probabilistic behaviour of matter. When the observed object is large enough, its mass fixes it in the matrix of the point of observation: for this reason we see it in one precise place and at one precise instant. When instead the object falls below a certain mass threshold, the principal GCD (that of the point of observation) and the GCD of the diffraction that generates the object are forced to become equal, reflecting each other as in a mirror. At that point the object no longer occupies a single point of the spacetime generated by the observer, but spreads over several possible positions, and we observe it as probability. It is like having to describe the number 10 using only the number 1: the only way is to distribute the 1 over ten positions, one for each unit of the 10. Today we know that even objects made of thousands of atoms behave in this way, and no experiment has yet found the boundary. The idea that the passage from quantum to classical behaviour depends on mass is close to that of Penrose and Diósi; in MM the threshold is the point where the two GCDs, the principal one and that of the local diffraction, become equal. For all these reasons the universe behaves like a simulation without really being one. It follows exact rules, made of counts, everywhere and at every instant, but no machine runs them and no programmer wrote them: a structure of mathematical relations does not need to be computed in order to exist. Tegmark (2008) had already noted that such a simulation need not be run, while Vazza (2025) estimated that running it physically on a machine would require resources that the very laws of the universe do not allow. This record develops one aspect of the theoretical framework. The work is shared openly so that it can be judged by as many readers as possible: anyone who knows someone interested can pass on this single link, valid for the whole framework (with an overview in English and Italian): https://doi.org/10.5281/zenodo.23535916. The entry page, with the complete list of all records, is https://doi.org/10.5281/zenodo.22667516. To cite the framework: Lanciano, U. (2026). The number 1 in front of the mirror: Mathematical Materiality from the nexus to the cosmos. Zenodo. https://doi.org/10.5281/zenodo.23535916. The records have been deposited since 5 August 2026, each with its own date, and are released under CC BY 4.0: anyone may use them by citing the source. Objections and errors found are welcome at riverantares@gmail.com, since Zenodo has no space for comments. This record. Standard quantum mechanics has no mass at which a superposition stops: large objects look classical because of decoherence, the environment that keeps recording where they are. Collapse models (Ghirardi–Rimini–Weber, CSL, Diósi–Penrose) add such a limit by hand. The framework says that a threshold exists: below a certain mass level the principal GCD of the point of observation and the GCD of the diffraction that generates the object become equal, and the object spreads over several positions (see the box above). The box gives no number. This deposit tries to give the threshold a number, or to say clearly why it cannot. A second part tests two later remarks of the author: the limit cannot be fixed as a mass, because a calculation of the «fractional distance» is missing; and large distant bodies stay fixed because their size makes up for the distance. It was announced in deposit 2.64 (DOI 10.5281/zenodo.23610071). The main result: for distance, the limit is not a mass alone. In the two readings of the fractional distance that hold, it is a ratio between the size that has to be told apart and the cell of the copies that do the telling, together with the number of copies; the readings of part one with a mass threshold at the Planck scale remain possible, untested, and that the two readings are one rule of the framework is a proposal. For the state of an object the copies are the photons and molecules the environment carries away, and one copy cannot tell apart two positions closer than about half a wavelength: a 16-microgram crystal stays quantum over 2 × 10⁻¹⁸ m because about 10³⁴ thermal copies would be needed to fix it. For the way a distant observer reads an object, the cell is the diffraction cell of the observer's aperture at the object's distance: two stars of almost the same mass fall on opposite sides (the disc of Sirius B, 1.02 solar masses at 2.64 pc, inferred from its radius, is 20–60 times smaller than the finest cell of today's interferometers; τ Ceti, 0.78 at 3.65 pc, and 61 Cyg A, 0.67–0.74 at 3.49 pc, are resolved): with this instrumental classification the sample does not support a mass-only limit growing with distance. Both rules coincide with known physics (decoherence and wave optics): the framework admits them; experiments put them to the test but cannot tell them apart from standard physics. Prior work, first. Decoherence: Joos and Zeh (1985), Zurek (2003), Schlosshauer (2019); measured against separation and number of photons: Chapman et al. (1995), Kokorowski et al. (2001), Hornberger et al. (2003), Hackermüller et al. (2004). Collapse models: Károlyházy (1966), Ghirardi, Rimini and Weber (1986), Diósi (1987, 1989), Pearle (1989), Ghirardi, Pearle and Rimini (1990), Penrose (1996), the review of Bassi et al. (2013), Howl, Penrose and Fuentes (2019). Tests and limits: Nimmrichter and Hornberger (2013), Romero-Isart (2011), Donadi et al. (2021), the Majorana Demonstrator (2022), Carlesso et al. (2022), Gasbarri et
Abstract Ever since its foundations were laid nearly a century ago, quantum theory has provoked questions about the very nature of reality. We address these questions by considering the universe—and the multiverse—fundamentally as complex patterns, or mathematical structures. Basic mathematical structures can be expressed more simply in terms of emergent parameters. Even simple mathematical structures can interact within their own structural environment, in a rudimentary form of self-awareness, which suggests a definition of reality in a mathematical structure as simply the complete structure. The absolute randomness of quantum outcomes is most satisfactorily explained by a multiverse of discrete, parallel universes. Some of these have to be identical to each other, but that introduces a dilemma, because each mathematical structure must be unique. The resolution is that the parallel universes must be embedded within a mathematical structure—the multiverse—which allows universes to be identical within themselves, but nevertheless distinct, as determined by their position in the structure. The multiverse needs more emergent parameters than our universe and so it can be considered to be a superstructure. Correspondingly, its reality can be called a super-reality. While every universe in the multiverse is part of the super-reality, the complete super-reality is forever beyond the horizon of any of its component universes.