The Universe as Machine Hypothesis

Progress on parsing the concepts,

9/10/2020 8:09 AM JSM

Overview of the Universe Machine Hypothesis:

The Universe as Machine hypothesis describes the series of interpretations and extrapolations that, as assembled mechanism, synthesize the 'boot-strapping' of an emergent 3 +1 reality centered on a singularity. The individual structural and functional mechanistic components are derived entirely from inert planar, random information arrays uncovered in the modular maths/geometries held in any point in 3 extant dimensions. The described derivation is entirely from simple geometries and modular maths concepts limited to D < 4 and all forces and motion are consistent as being derived from the Principle of Least Action. Fundamental thermodynamic considerations require any such system to be in steady state equilibrium: the model duplicates energy during inflation and recycles energy (high negative entropy) between universe iterations as specific residual, time-stable matter and dissipates degraded information/energy to the broader supporting host Uberverse. The mechanistic outline provides details into the relationship of time to momentum/rotational inertia, how gravity emerges from the mechanisms of time as well as how gravity fundamentally differs from other observed forces. Key concepts allowing emergence of 3 + 1 space are:

1) Quasicrystals: the unique role of quasicrystal arrangements as non-collapsible time and momentum structures 2) Folded matter waves: all wave-forms on the hosting maths are inherently unbiased as intercalated, mirrored wave and anti-wave; matter has resonant, folded wave structure allowing dominance of one form and thus emergence of properties such as charge 3) Random Information: availability of information as planar arrays of truly random information on cubic faces at Planck scale 4) Collapse, global and local: the centering of such a cubic planar array on an elliptic Point of Infinity underlies global collapse (big bang) and local matter wave collapse (particle behavior) 5) De-construction: planar information arrays centering on a collapse point can be de-constructed (for example, as photonic energy wave and electron folded matter-wave), sent to a distant point for re-overlay of the pattern resulting in reversible expansion of cubic space as local wave-form collapses create temporary, new patterns 6) Wave-form inversion: through a point of infinity upon collapse constitutes the largely irreversible events associated with the perception of time The hypothesis yields ready processes that could underlie a number of poorly understood observations including:

a) dominance of matter/antimatter b) resolution of any apparent paradox associated with EPR/Bell's Inequality c) dark energy and dark matter cosmological observations d) the structural origins and functional role of neutrino oscillation e) possible mechanisms underlying the Principle of Least Action f) relationship between deterministic and indeterministic processes

Properties of the hosting maths:

Modularity: self-reflection at all scalings - thus fractal and all devolve to a point at D = 0 Dimension: most of the action seems to occur at D < 4; no higher dimension consideration seems necessary and the mechanisms describe the process of expansion of space from D = 0 to D = 3 Direction: agnostic towards directions: back and forth, future/past as well as matter/antimatter. Symmetry: is pervasive with the elliptic maths functions forming chiral L/R intertwined arrangements in the cubic space at all scaling. Thus every action has an identical reverse reaction. Steps / Expansion of Space: this occurs in the modeling as result of energy dumping back into the center point of infinity, revealing information that adopts function. The information is revealed as 'universe machine' components which boot-strap expansion of space via replication of the core information pattern at a distant location. Expansion is not equivalent to increasing distance; rather refers to subdividing of the space cubically thus increasing the number of steps between two locations. The number of steps between two locations has the most relevance in terms of information exchange via processes such as photonic energy exchange and thus has relevance as the concept of distance. Wave / Universe Collapse: occurs around a point of infinity in the elliptic maths. Globally, this generates the observed big bang; locally the same point of infinity within the context of the cubic space it occupies is at the center of all observed wave collapses such as photonic or matter wave collapse. The imprinting of the information at a distant location results in the temporary expansion of space. A collapse event is a middle state in a reversible three state equilibrium that can either revert to the original state or transition to a new arrangement as third state. Superposition: is an observation of the universe: two adjacent spaces with identical information become as one, superimposed and non-differentiable. In the modular maths host, they are the same and collapse together. A mechanism for powering superposition is derived from considering the fate of depleted information/energy which bleeds to the larger hosting Uberverse as random vibration. All motion relies on a preferential re-establishment of wave form in a particular direction (as opposed to the inherently equal mirrored direction). Registration: The mirroring elliptic maths patterns can be considered to be either L or R (arbitrary designation) - with such registration continuous without break or disruption of the maths structures regardless of the scale of the universe. There is a continuous, fractal connectivity between all L or R points with the webs intersecting only at the points of infinity where wave inversion is possible. Re-imprinting / Particle Nature: the overlay of wave patterns creating symmetry allows superposition which is observed as wave collapse which is interpreted as 'particle' behavior for wave-forms. The collapse can be interpreted as a re-imprinting of the waveform as the collapsed state represents a stabilized, resonant form of an expanded pattern. The collapse is a transient intermediate between two other states that are in free and reversible equilibrium.

Asymmetries:

Direction: is derived from the action of momentum/inertia processes - this is established during inflation and survives until the end of the universe or the momentum machinery is shattered (high energy collisions, for example) Random Information: is available to tap in the inherent maths at D=3. This is simple outcome of the non-orthogonality of the more complex and chiral elliptic maths relative to the simple cubic symmetry architecture. The information becomes unveiled at the Planck scale as it must resolve at such scale - science indicates such scale is not further refinable within the universe's context. Presumably, the most primordial of information exposed generates the simplest machines such as neutrinos whereas the complex forging of quarks and nucleon components is a deeper reveal corresponding to the significantly higher energies available during the BBI period. Matter / Antimatter: the dominance of observed matter is a founder effect of the initial iteration of the universe (and presumably maintained in each big bang iteration since). Matter/antimatter are exactly equivalent when produced in our observed post-inflationary period with all difference traceable to the initial universe iterations. Motion: motion occurs for any wave-form (with, naturally, accompanying anti-wave) that can engineer to have a prefered direction of transition during the superposition events.

Machine concept:

Mechanisms, Processes: the hypothesis assumes any observation has an underlying mechanistic process: this implies structures that are hosted as representations on supporting maths patterns that have stochastically predictable behaviour as function. All processes are stochastic in that each inherently is completely reversible with direction favored through a mechanistic aspect derived from the Principle of Least Action. As such, the continuation of initial conditions (requiring the least action) is a primary mechanism favoring a direction in any equilibrium under consideration.

examples: a) Electrons have structural patterns that, when overlaid with a photon structural pattern results, through synthesis of symmetry at that particular location, the ability of the wave pattern to collapse - a process that can freely reverse or transition to a new arrangement and thus, a new future. b) Time as observation has an associated process and structural elements c) Matter/antimatter dominance is result of initial iteration of our primordial universe which has been matter dominant since d) Momentum as a preferred direction of travel that results from conditions created during the latest BBI inflationary period

Thermodynamic Equilibrium: the universe machine model is derived from assuming proper thermodynamic considerations - as such, the observed universe must be in equilibrium; hence the big-bang is part of a regular cycle. Energetic considerations require that the energy into such a system in equilibrium must be balanced with as much entering a cycle as exits. Energy creation (duplication) is hypothesized to occur at the extreme energy of inflation as by-product of momentum processes and energy loss result of degradation of energy to vibration that bleeds out to the larger, infinite hosting Uberverse. A fraction of the total energy is necessarily recycled: proposed are time-stable wave-forms of electrons and black holes (with other matter waves currently unclear given the state of knowledge - such as for neutrinos). Principle of Least Action (PLA): this underpins as assumed 'law zero' for many systems in maths and physics - objects/systems follow the path of fewest steps but it is a poorly understood assumption that has been kicked around now for hundreds of years. The machine hypothesis would allow interpretation the functional basis for this principle based on the machines hypothesized. For example, if you know how a system is constructed, you can count the various steps and thus predict which outcomes would be stochastically favored and as linked, presumed independent probability events, shortest paths become exponentially favored. All Observations are Functional: this could be considered as corollary to the PLA (or perhaps reinterpreted: Principle of Least Assumptions) - in essence, if a phenomenon is observed, then it is a necessary component of the universe machine. It can be considered as an economy or parsimony argument which is similar to arguments in evolution: nothing is generally tolerated if not necessary or a by-product of a necessary system. In such interpretations, most of the slew of particle observations (muon, pions, etc) are observed as broken fragments of a functional, necessary system. Others, such as photons or neutrinos, are given necessary and novel roles in the hypothesis (photons are part of the mechanism to expand the subdivisions of space). Planar Information Arrays: random information revealed at the Planck scale as the faces of cubic arrays. Such a cube centered on an elliptic PoI (point of infinity cusp) contains a collapse point and such information could potentially encode emergence of a universe (this could be called the Omphalos, in homage to ancient depictions). This two dimensional array of information is true random as a property of elliptic modular functions. The array is necessarily exposed as elliptic functions are not orthogonal to any orientation of space-filling cubic symmetry. Universe as Machine: the overarching concept that the universe itself emerges and functions as an entity - this could be considered as a machine with 'purpose', a function: - it can create and explore complexity, for example. The primary initial and required function, however, is to simply expand itself from the time-less planar information arrays. The Machine arises as the random, available information encodes not just structural components (such as neutrino and photons, matter, etc) but functional assembly: thus, for example, juxtaposition of structural components that assumes the property of momentum as a mechanism to pull matter waves into the future. The interaction of universe machine components enables emergence of a process we perceive as time. This is the boot-strapping that allows three symmetric dimensions to be stretched (as +1) towards 4 dimensions as space is subdivided and thus the universe inflates itself. Energy / High Negative Entropy: energy is created and is conserved from a universe to the next iteration via big bang. The concentration of energy at the big bang is a result of near simultaneous collapse of residual, stable matter waves. For example, if the primary stable folded wave surviving until re-cycle is the electron, then the energy results from the asymmetry (4:1) of the accumulated electrons as a stable, folded wave. Energy is 'created' by duplication mechanisms during inflation as the universe machine includes momentums which could, at high energy, result in natural duplication of folded-wave matter. The bulk of energy created during a universe cycle however is bled as degraded information/energy to the host environment. Uberverse Concept: would assume the observed universe is one of many that are in existence, thus somehow 'concurrent' and likely all will have some similar motifs in complexity and complex functionality. Such universes would necessarily cycle, evolve and take up some inflated space and, likely, experience some sort of periodic big bang. Information Degradation: an infinite Uberverse requires recycling of most materials: expansion of space is derived from events creating Churn above and below time. Without momentum/time events to reinforce the pattern, the churn patterns will degrade as they contain no inherent mechanism (such as local collapse) to reinforce the wave assembly. A universe cycle necessarily includes the bleeding of energies contained into the larger hosting Uberverse before the cold residue is contracted back to the universe origins. Churn that is not reinforced via re-imprinting of a pattern associated with a collapse equilibrium Metronome: in thermodynamic equilibrium, the steady state simmering Uberverse would contain the waste, degraded energy of all previous big-bangs as degraded energy. That is sufficient basis to assume the Uberverse and universes contained will vibrate at a fundamental frequency corresponding to the density (distance and timing) of big-bang energy duplication events. This metronomic property would imply expansion (the cubic subdivision) of the cubic, empty space is in free equilibrium; therefore no energetic difference between space condensed (via superposition of equivalent spaces) or expanded to the Planck scale. Expansion beyond this scale, however, requires processes such as momentum structures associated with folded-matter waves which, in turn, results in the non-equilibrium experience of gravity.

Components:

All Waves as Paired Wave / anti-Wave: (w / ~w) This is a direct outcome of considering the hosting elliptics which are fractal and must be chiral (as complex 3D structure) - hence mirroring at all scales. Such also implies that implicitly there is no preferred direction of travel which must be established by other mechanisms such as E/M orientation for photons and momentum structures laid at forging for matter waves. Photons as L/R Cubic, Adjacent Helical Units: photons can be represented as extensions of a cubic (as in, inscribed in a cube) helical motif that is necessarily adjacent L and R helices (in adjacent, intercalated cubes). Collapse of photonic waves tells us that, while they explore as expanded nose to tail expanded waves - each collapsible unit (spin = 1) must be superimposable with the linear adjacent unit allowing the observed zipping up into an electron. This zipping seems to be a process requiring specific, countable steps as light photon behaviour is dependent on the total photon energy. Tetrix Model of Matter / anti-Matter: this was a simple result of considering that on the hosting maths wave and antiwave must somehow co-exist yet there is observed asymmetry in matter: for example, positive and negative charge. That, however, also led to considering why quarks are as 1/3 charge and, presto, a very interesting fractal tetrahedron came to mind that has a 4:1 ratio of corners to center: thus an electron could be 4x 1/3 neg charge +1x 1/3 pos charge = -1 and exist as resonant, folded matter wave-form containing, as necessary for the hosting maths, intercalated wave and anti-wave (w & ~w). De-construction / Re-imprinting: this is an interpretation of the photon/electron interaction that creates a mechanism for otherwise static maths to host motion and change. The need is to transiently alter the local maths pattern thus allowing a preferred direction for any waves. Conceptually, it is as follows: during inflation, the three state equilibrium reaction essentially shakes photons loose allowing the electron wave to collapse to a preferred, stable, resonant tetrahedron. Thus, the high energy environment 'de-constructed' the core collapsible pattern which is recreated where-ever in expanded space a free-flowing photon interacts with a folded matter wave that is pulled by momentum. The interaction of the two re-imprints the core information in a distant location and in the process, subdividing the local space with a new pattern. The process also re-imprints the electron wave form which will continue to move via momentum processes which themselves are continuously re-imprinting their wave pattern. Three State Equilibrium of Change: relies on considering that photons interact with electrons as what must be a fully reversible reaction. Thus, electrons emit photons and absorb photons, repurposing the energy in the electron complex (molecule, etc) as momentums. Thus, free photon and electron transition from one state to another: this must occur through a middle, third state as required by information theory. This results in Change: the states are altered from before and after and thus, objectively, time has passed. It is proposed that the superposition of the photonic cubic helic on the tetrahedral electron folded wave results in resonance with an overall cubic architecture that is thus collapsible. See a description of the middle state below - Processes Above / Below Time: virtual photons are used to model E and M force mediations - also, photons are appreciably slowed by passing through otherwise transparent media. Both can be modeled as the photon completely interacting with an electron as a series of collapses, the number of which corresponding to the energy of the photon. It is known that transparent media is such as the energy of the photon cannot be accommodated: thus, any interaction of such photon and electron pair must simply reverse. The time delay is greater for higher energy photons and they are refracted greater than lower energy. Thus there are clearly photonic/electron interactions that are fully reversible and those that are more irreversible but both must involve collapse of the cubic photonic/electron architecture. Change as Wave / anti-Wave Inversion: collapse of a portion of a folded-wave matter structure and inversion through the point of infinity serves as non-reversible events that thus constitute the perception of time. Without wave-form inversion, processes are purely reversible and time as change cannot register. As such, the 'particle' nature of matter is necessary to create time QCs, for example, but all motion and interaction between wave-forms occurs as waves. Collapse also serves to re-imprint the wave-form in the machine component. Change / Time: time requires change; without processes that have a preferred direction of travel, for example, time simply doesn't pass. One change that can underlie time is the wave conversion that is associated, for example, with the three-state equilibrium associated with electron/photon interaction. Others changes may have role as well such as perhaps gluon interactions with other gluons or the dynamic processes that underlie momentum/rotational inertia. It seems also reasonable that free neutrinos may play a similar role as free photon with electrons but for the momentum/inertial processes that also need to prime space via some sort of collapse events under time. Time: Local and More Universal: Time clearly has a local aspect in that it derives from the changes that occur as assemblages of wave-forms (such as an atom with electrons and nucleon - protons and neutrons) exchange particles of energy and re-imprint their wave-forms at locations and thus experience motion. However, these local time events must meld with others occurring near and far: the QC requirements of each time event at any location is presumably part or fully responsible for maintaining registry of time events such that time here has a rigorous relationship to times elsewhere, no matter where. Electron Stability: the tetrix model for an electron would have unique time-stabilization via natural resonance of the fold. This would contrast, for example, to the quark/gluon situation where the components seem necessarily linked for stability (the bulk of energy in nucleon components, for example, is binding energy and neutrons are particularly unstable outside of the reinforcing nucleon environment). This inherent resonant stability to time of electrons is presumed a primary component of the high negative entropy that is transferred between universe iterations as the big bang and is extracted directly from coordinated collapses from the 4:1 w/~w ratio. Time/Momentum as 3D Array of Planar Quasicrystals (QC): time and inertial processes are modelled structurally as 3D arrangements of orthogonal planar information arrays that are laid out following the requirement of Penrose quasicrystals (QCs). This assumption confers a number of interesting properties as well as a requirement for mirrored events at opposite ends of a QC. Properties include 1) uniqueness of arrangement (thus immune to spatial collapse) 2) retainment of history in the pattern and 3) orthogonal independence of 3 planar information patterns. Momentum: is a property conferred during matter wave-form forging that occurs initially during BBI. A mechanism must exist to give a preferential direction of motion to the complex folded-wave structures that are derived from the planar information arrays. It is proposed that structural components, laid at forging, prime space in the direction corresponding to 'future' and are transferable between matter wave-forms. Given the parsimony consideration (as derivative of the PLA) as well as the apparent relationship between momentum and rotational inertia, oscillating neutrinos appear to have the necessary properties to encode and maintain inertial mass/energy. Momentum / Rotational Inertia: a quasicrystalline array interpretation for the process of time has further utility for modeling the relationships between linear and rotational momentums. Three orthogonal axes with a dynamic interplay occurring below the registration of time events are sufficient to encode the complex relationship between rotational and linear momentums. In such modeling, the PLA would imply motions associated with linear momentums have preference to those encoding rotational directions and such would re-set dynamically between time events. The QC pattern naturally results in equal yet opposite motion at each and every point symmetric on the quiescent center of rotation. Gravity: is result of matter's involvement and influence on the mechanisms of time. The metronome vibrations have wavelength corresponding to the Planck Scale; momentum and motion of matter require sub-dividing space beyond the Planck scale. Thus, any matter with associated energy as momentum will act as a net sink of the metronome vibration and time will be perceived as flowing into matter energy concentrations. Forces: a force is a preferred direction of motion on the symmetric modular maths host. Momentum corresponds to priming space with momentum structures ahead of motion; E and M, for example, are priming space between charges via virtual photonic churning. Motion is always stochastic with the preferred direction corresponding to a greater ability to Matter Motion: As a folded, complex pattern wave, matter would not spontaneously move to a neighboring math pattern. Thus the pattern must be primed and virtual collapses occuring to create the wave pattern allowing momentum to transition a pattern to adjacent space. In this sense, we collapse into the future not unlike a card-board cartoon cutout through a wall. Gravity / Other Forces Relationships: Gravity can only slow time, asymptotically to zero (as a black hole); other forces can effectively accelerate time through unidirectional collapses in the direction of motion. As such, with sufficient energy as force and momentum structures, they can effectively accelerate time as many fold as necessary to achieve the relative velocity in the preferred direction. Churn / Pattern Reinforcement: 'Churn' is a concept to describe the processes that must occur below the perception of time that allows the hosting maths pattern to be imprinted to allow preferred direction of travel for a folded-matter wave. The continual process of imprinting of the host pattern allows a wave to re-establish itself in a new location as it travels into the future. The resulting pattern would have memory of the passage similar to the churn observed in water with the passage of a ship and the pattern would eventually dissipate to the surrounding environment creating a choppy surface. Churn is a disruption to the inherent maths pattern that prevents collapse of adjacent space and thus keeps space inflated to the Planck scale. Churn would not be capable of generating the symmetry for collapse/re-inforcement and thus the patterns would eventually dissipate as structure. Fields: all observed fields correspond to churn patterns on the hosting maths patterns. Fields thus arise only with the presence of waves that create churn such as momentum structures, collapsing folded structures such as electrons or self-propagating waves such as E/M associated with photonic waves. E / M Fields: as self-propagating (one field builds the other), these are key in the self-inflation of space. The orthogonal structure is similar to radial inertia with E and M and direction of photonic wave motion all orthogonal to another thus corresponding to the Navel architecture surrounding the center PoI. Likely the E/M fields interact via collapse with the future resolving as per the PLA and thus the ying/yang of the self-propagation between the E and M. Photonic Waves: as self-propagating and thus self-reinforcing, these waves are necessary for expansion of space beyond the Omphalos region (the role of Neutrino waves tbd; gluon energy waves are limited to the nucleon environment). Presumably photons explore as extended wave with dimension corresponding to total energy and with collapse a serial, stepped, process that reverses in the case of virtual photons or if energy or time requirements are not met. The size of the extended wave is proportional to the energy with a 'short' wavelength of the higher energy reflecting more higher probability in location of the center of the extended wave.

Predictions:

Recycling: as essentially an infinite system and consistent with the Principle of Least Action and a Parsimony interpretation, all is necessarily recycled else the uberverse would become filled. Thus black holes must become dark matter (and breaching their time-locked status during inflation not a challenge given the gravity/time interpretation)

Neutrinos, Oscillating: the relatively recently identification of natural oscillation between three neutrino flavors, coupled with the corollary of parsimony suggests these folded-matter waves as likely first candidates to consider for encoding the information held as momentums and rotational inertia. Presumably neutrino folded-wave structures are primordial and would likely correspond to the three cubic faces centering on our Navel, our local point of infinity (POI) and would likely represent a degenerate (less information) form of the electron and photon structures. Free neutrinos may also have a role similar to free photons in the collapses that must occur associated with establishment of a prefered direction of travel that is momentum. Entanglement: is modelled as superposition of collapse of adjacent, mirrored wave-forms, thus creating a wave/~wave correlation between two wave-forms for future collapse events EPR / Bell's Inequality: a QC structural requirement for events as registering as time requires mirrored events at opposing ends of the structure. Entanglement sets a registration requirement that must be satisfied to register as a future time event - thus, mirroring of entangled wave-forms in future collapses. In this interpretation, the simple exigencies of registering as a non-reversible time event (as established by wave-form inversion) serves as ersatz 'hidden variable'. As such, events not consistent with a QC structure are subject to the reversible collapse of the non-QC structure. Partial Collapse of Matter Folded-Waves: The tetrix modelling and the requirements of EPR/Bell's /= observations leads to consideration that only a sub-unit of any matter wave/~wave collapses, for example at any given electron interaction with a photon. Thus, a photonic wave is free to collapse centering either on the L or R handed helix which would counter-align with the corresponding subunit of the electron to foster the cubic collapse. However, as the electron folded wave/~wave is spatial - filling an area, only a subunit of the total folded wave would collapse with any momentum structures and overall electron structure unaffected. The bulk of the folded matter structure would have an apparently seamless flow during the collapse Quarks / Gluons: a tetix interpretation for quarks, which have similar mass to electrons, does not seem as straight-forward as for the electron model which has inherent energetic (and thus time) stability. Quarks (as well as gluons) are only stable within a proton or nucleon context and thus must be part of a larger fractal motif, likely tetrix. Unlike photons, Gluons can interact with themselves (i.e. subject to wave collapse) and thus also register in time and re-imprint through such gluon/gluon interactions. Space Contraction / Dark Energy: interpreted as the basis for the cosmological observations of dark energy - essentially, light seems faster as it can travel faster in energy-dilute space which re-contracts. Each stride associated with the metronomic vibration is a larger step. Dark Matter: an infinitely re-cycling Uberverse would simply run out of room for BHs - and, they are only stable relative to metronomic time vibrations. Thus, they would be predicted to be swept back during space contraction and likely shredded in the big-bang/inflationary period with the surviving fragments depending on how such was modeled. But, presumably, sufficiently lumpy to account for any asymmetry in the exploding pastafarian mess tossed to the void. End of Time: as energy bleeds out as random vibration to the larger hosting Uberverse, the space expanded during BBI will start to re-condense as Churn energy is depleted. All time-stable matter will simply be swept back for re-cycling.

Abbreviations:

BBI: big-bang/inflationary period or energies associated with (apparent) EPR paradox: from wikipedia - The Einstein–Podolsky–Rosen paradox (EPR paradox) is a thought experiment proposed by physicists Albert Einstein, Boris Podolsky and Nathan Rosen (EPR), with which they argued that the description of physical reality provided by quantum mechanics was incomplete. In this hypothesis, the apparent paradox is resolved by considering the mechanism of time events with requirements for QC structures. PIA: planar information arrays - the cubic faces as revealed at Planck scale are a truly random pattern of elliptic cusps PIE: Planck (length) Interface Exemplar - information giving rise to a universe, the pattern necessarily revealed at the length associated with our observed universes minimum dimension POI: point of infinity - each collapsible universe within the Uberverse must be centered on such a cusp in the elliptics math QC: Quasicrystal - a penrose array that has certain properties including uniqueness (no collapsible architecture), preservation of history as mirrored duplicates and necessity for mirrored events at opposite ends of the structures. This latter is consistent with the requirements of EPR/Bell's Inequality observations. w: wave - a pattern of hosting maths that has a functional implication (e.g. photonic structure, matter folded structure) ~w: the mirrored wave: these must always co-exist as adjacent structures at any fractal resolution of a wave including matter folded-waves