The principle difference between the toroidal behavior of the Cat’s Eye Nebula (or the universe itself^12.5) and that of quanta is one of scale, not only in space but (of course) in time as well, the magnitude of which we contrast with one noteworthy example. Here we refer to our description of the torus (2.1) as “a sphere that expands and contracts along a rotating spiral vector in space-time.” On a macrocosmic scale, as in this image, the rotational development of the toroidal surface and the vortices is relatively static from one observation to the next, but on a microcosmic scale, the expansion and contraction cycle of the toroidal surface (a tip of the hat to the prodigious powers of the strong force, or the balance between nonlinearity and dispersion) and the rotational cycle of the vortices are also beyond our observable capability, but for the opposite reason, that is, they are within one interval of an expansion and contraction phase of quanta, in other words, within the fundamental unit of space-time. Our inference that the vortices rotate along the entire toroidal surface supports both the spherical (or single point) and doughnut moments of quanta (see 5).

2.7. Tangential Dimensions. Just as the normal states of matter break down at the limits of vibrational activity—e.g., the manifestation of the Einstein-Bose precipitate near zero degrees Kelvin (Absolute Zero) and the manifestation of the Plasma Ball near maximum degrees Kelvin (i.e., the singularity in the nanoseconds preceding the Big Bang)—so coincidentally and simultaneously at these limits do the restrictions of four-dimensional space-time dissolve into other states of space-time, as accounted for in the calculations of String Theory and other related formulations of multi-dimensional activity. These unitary states of matter that manifest at the extremes of vibration, in which infinity and zero are the same (just as “1” and “-1”, as representative of particle and wave, exist at the same time), are why String Theory derives additional dimensions (11 in total). As so described, these additional dimensions and states are tangential to the Great Anomaly/Singularity (First Cause or G-d principle), otherwise perceived as the fully-contracted moment of quanta, which is a pass-through phase in which a phenomenon known as Geometric Phase (or Berry Phase) takes place. Here, per our Quantum-Torus model, where the wave collapses inward, flips spin, and expands back out, provides a perfect visual representation of this 720-degree quantum symmetry. (For a reference in nature, Narwhal tusks provide an example of two opposing spins, one within the other.https://www.popsci.com/environment/narwhal-tusk-twist/)

The implications of this anomalistic state are misunderstood by contemporary science, leading many to the conclusion that Horava’s reconciliation of gravity with quantum mechanics (via exotic phase transitions mathematics) is inconsistent with Einstein’s theory of gravity (general relativity) and somehow resurrects Newton’s notion that time is separate from space. However, at this immeasurable singularity (see 6.4), time does not separate from space; it disappears (as does space and everything else) into unity. This anomalous state remains omnipresent in all matter, which is why Horava’s gravity formulations work at every point on the toroidal continuum.

Thus, Horava’s formulations actually verify Einstein’s theory of gravity. Horava is to be commended for recognizing the application of exotic phase transitions mathematics to gravity. The change captured by these formulae occurs within the fundamental unit of space-time, at the pass-through phase; that is, during an immeasurable interval or “in no time.”

(It should be noted that since our original formulation of this proof, advances in technology have enabled a mapping of quantum activity across trillionths of a second, showing the wave and point phases (or phase transition or pass through phase) of quanta within a single unit of space-time [story here and video here (at 1:47 and following), the video appearing along the X-axis, with our animation showing the Z-axis here].)

We also note that in 2021, a study published in New Atlas “with the help of another, different state of matter, known as a Bose-Einstein condensate (BEC),” that occurs at temperatures close to absolute zero, where all the atoms become one entity, it is claimed that this is a new state of matter, like plasma, which occurs at the other end of the vibrational scale, for example, a white hole, as noted above. We take issue with this claim regarding “new states of matter”, because the BEC and plasma are just the anomalies of the vibrational spectrum, and these anomalies are predictable events, because the building blocks of matter—quanta—each contain an anomaly, so everything that they comprise would, logically speaking, also contain anomalies. The reason for this misperception of matter is that the conventionally accepted model of quanta is missing some nuances, beginning with the embedded anomalistic property and its behavior as the quanta are built out into ever-more complex phenomena; in other words, the quantum-torus model is not on mainstream science’s radar screen.

Another example of how the absence of this nuance leads to inadequacies in other models is exhibited by the toroidal model (very close to our own) posited by the CIA in a paper declassified in 2000, wherein the authors declare that “remote viewing” is a viable practice, but that they cannot explain it. This is because their model of quanta does not include the anomalistic point (the “pass-through” point), which behaves as a singularity, thus connecting the past, present, and future in the same space (i.e., in the absence of time), as is obvious in our quantum-torus model.

An additional example of how the lack of a complete quantum-torus model leads to speculative and overly complex explanations is the ER=EPR equation being floated in some circles. As we have noted, entanglement involves the interaction of strings that become one unit of spacetime, sometimes over long distances, thus one candidate for a wormhole. Another candidate for wormholes is the availability of everything that ever was, is, and will be in the state of Singularity, which is, ultimately a pass-through state; however, “the other side” is, technically, forward in space-time, not backwards.

3. BINARY CORRESPONDENCE

3.1. Quanta represented as Solid and Broken Lines. As previously noted in 2.3, the binary behavior of quanta may be represented by a variety of symbols, including light and dark, on and off, line and broken line, 1 and 0, sphere and doughnut, particle and wave, mass and energy, etc. Just as we employed the wave-particle duality of quanta to build our Quantum-Torus Model, now let us employ lines and broken lines to represent its behaviors, as we carry forward through analogous/congruent reasoning the Great Anomaly (First Cause) from the microcosm to the macrocosm and in-between, in this case from quanta to the human genome (3.4).

3.2. The I Ching. The oldest extant exploration of the implications of binary replication in space-time belongs to the I Ching, or Book of Changes, ascribed to Confucius and other scholars of his era. The premise of this work is to extrapolate forward six-fold (2⁶)—from the anomalistic division of the First Cause (Great Anomaly) into binary phenomena (quanta)—to describe the subtleties of the variations or “changes” resulting from this progression. The fact that this mapping of the 64 basic phases of change against human behavior using poetic and philosophic symbolism was also used as a divinatory reference accessed through acausal selection (a methodology which we will not explore in this paper [notes are included in our book]) in no way prejudices our application of the 64 symbols (hexagrams or kua) and their linguistic representations to our analogous argument.

3.3. The Form of the Structural Check for Congruency in Scientific, Philosophic, and Spiritual Principles. As described at the end of 1.5, we are now prepared to present a check for the proof of congruency in scientific, philosophic, and spiritual principles that we presented in 1.3. We define such a check as an analogous/congruent sequence taking an alternate, non-mirrored, route to the same conclusion as the theorem that it proves, i.e., science, philosophy, and spirituality are, in their most refined states, different methodologies and languages for describing the same universal phenomena.

3.4. Structural Correspondence: The 64 Codons and the Human Genome. If the structural equivalence between Heisenberg’s Uncertainty Principle, Plato’s Allegory of the Cave, and the Taoist and Hebrew prohibitions against representing the Deity is the first proportional step (a : b), then Martin Schönberger’s discovery — demonstrating the structural correspondence between the binary patterns of the 64 hexagrams of the I Ching and the 64 codons of human DNA — constitutes the second step (:: c : d). This correspondence is not claimed as causal, but as a further instance of the same relational architecture recurring across domains — the signature, we argue, of a single underlying generative principle.

3.5. The Anomalistic Hexagram and Genetic Anomalies. The Great Anomaly as described in 1.3 — a state that does not conform to the logic of all that precedes or follows it — finds its structural equivalent in Hexagram 52 of the I Ching, the anomalistic moment of rest within a continuum of change. Given that the anomaly is present in the quantum-torus model, and given that everything is derived from quanta (5.1, 5.2), the model predicts the presence of analogous anomalies at every level of complexity derived from quanta — including the human genome.

4. INTERPRETIVE EXTENSION: ANOMALISTIC EXPRESSION IN THE HUMAN GENOME AND HUMAN EVOLUTION

Our model does not yield a falsifiable prediction of when a supreme anomalistic expression will appear in human history, nor does it identify any particular individual. What it does yield is a structural expectation: that anomalistic expressions of extraordinary magnitude — of the order represented historically by figures such as Abraham, Buddha, Jesus, Krishna, Mozart, or Einstein — are not random accidents but predictable features of a universe built from toroidal quanta, each carrying the signature of the Great Anomaly. The periodicity and scale of such expressions vary, as Vedantic philosophy long recognized, but their occurrence is structurally entailed by the model.

This structural expectation is, we note, proportionally correspondent with the prophetic traditions of every major spiritual lineage — not as proof of those traditions’ specific claims, but as a point of deep convergence between scientific modeling and the intuitions of spiritual inquiry across cultures. On this specific point, science and spiritual tradition arrive at the same structural conclusion by different paths — which is itself a further instance of the proportional correspondence that animates this proof.

4.2. The Separation of Dogma and Principles: A Note on Method. One could expound on the nature of this manifestation of the human spiritual anomaly, the world teacher, who is predicted by our proof and various prophetic traditions, including Judaism, Christianity, Islam, Hinduism, Buddhism, et al., and we have done so at length in our book, but for the sake of brevity and consistency within the strictures of this form, we have distilled these descriptions in 7 and 8. The purpose of using this genre and this forum to present our proof is to parlay its empirical discipline and consequent lack of dogma into a universal discussion wherein the equivalencies between scientific, philosophic, and spiritual language are recognized. For example, where Adonai, G-d, and Allah, or Messiah, Christ, and Prophet have been used by particular religions to describe the G-d principle and its periodic anomalistic incarnations, we have substituted the terms Great Anomaly, First Cause, and singularity or the spiritual anomaly, avatar, and world teacher. In this manner, we hope to encourage a general cessation of hostilities between religious systems leveraging exclusive claims on the G-d principle and particular anomalistic incarnations to further the instinctive and egoistic objectives of their practitioners.

5. STRUCTURAL VERIFICATION: POINCARE‘S CONJECTURE AND THE QUANTUM TORUS MODEL

5.1. Perelman’s Proof of Poincaré’s Conjecture as a Structural Check. Grigory Perelman’s solution to Poincaré’s Conjecture establishes that every simply-connected, closed three-dimensional manifold is topologically equivalent to a 3-sphere — reducible, that is, to a combination of spheres and doughnuts. We note that the four-dimensional generalization of this result remains one of the most significant open questions in contemporary mathematics. Rather than claiming that generalization as settled, we propose that our Quantum-Torus Model offers a candidate framework precisely for that open territory: if Perelman’s result holds structurally in three dimensions, and if the torus is the natural four-dimensional extension of the sphere-doughnut pair as described in 2.1, then our model is at minimum consistent with and suggested by Perelman’s result, and invites formal mathematical investigation of that 4D extension. And, please, let us ditch the Klein bottle as a viable model, as it illustrates the futility of relying on pure mathematics to generate plausible geometric shapes in nature, particularly at the quantum level.

5.2. Structural Correspondence Between the Quantum-Torus Model and the Big Bang Theory. As described in 2.1, the torus stands in the same dimensional relationship to three-dimensional space as the sphere and doughnut stand to two-dimensional space. This proportional correspondence — not a derived proof but a structural alignment — supports the coherence of our model with the current cosmological framework. Specifically, a universe derived from a singularity and differentiated first as quanta is structurally correspondent with a universe whose fundamental unit of space-time is toroidal. The Big Bang (duality, or “m” [matter]) is, then, the release of the potential energy (E=mc²) of the singularity (“E” [Energy]) at the acceleration of light (“c²”) — a formulation our model accommodates naturally.

6. APPLICATION OF THE FRAMEWORK

6.1. String Theory. Having checked our proof, we offer an application of key principles contained therein to solve another vexing scientific puzzle, that of strings and String Theory. As it stands today, String Theory has provided us with an elegant mathematical framework for solving the quest begun by Einstein, for a unified field theory, by mathematically expressing the equivalencies for the four fundamental forces—the strong force, the weak force, the electromagnetic force, and the gravitational force. But much like Einstein’s Special Theory of Relativity awaited an empirical proof that came with Royal Society’s and the Royal Astronomical Society’s observations at Sobral (Brazil) and the island of Principe (West Africa) on May 29th, 1919, so String Theory awaits empirical proof for the existence of strings. Astonishingly, the experimental evidence has already been gathered, though it has not been recognized as such. As we shall see, this is in part due to the general lack of awareness that, like Poincaré’s Conjecture, Strings are a subset of toroids.

6.2. White Holes, Black Holes, and the Great Anomaly. Before we debrief the experimental evidence for strings, it is necessary to revisit the implications we discussed in 2.7 concerning the breakdown of the general laws of the mass-energy-space-time continuum that occur at the limits of vibrational activity (near absolute zero and near singularity [there’s that zero and one again!]). For the purposes of this discussion we shall not delve into the progression of events that transpire during the final moments of a black hole leading to singularity, but rather on the initial moments after singularity, since the fingerprints that we seek from our current universal cycle begin there.

6.3. Artifacts of the Big Bang as Contrapositive Reflections of the Einstein-Bose Precipitate. Specifically, we describe the properties of the Plasma Ball as contrapositively related to the Einstein-Bose Precipitate; that is, the Plasma and the Precipitate arise under opposite conditions (maximum vibration v. minimum vibration) and exhibit congruent mirrored reflections of anomalistic behavior, i.e., abnormal states of matter in which the individuation of particles has ceased. In other words, much like the convergence of science and spirituality over a particular principle (4.1), the properties of the Plasma and the Precipitate converge over a specific quality—a unique form of unity in which the general laws of four-dimensions have been suspended, with space-time taking on new qualities (much as the tangential dimensions discussed in 2.7). The fractal progression of the Quantum-Torus is defined by these two states, which together contain a holograph of the entire universe of possibilities.

6.4. The Fundamental Unit of Space-Time at the Limits of Vibrational Activity. In addition, both these unique forms of matter (the Plasma and the Precipitate) exist entirely within “one interval of a wave-“pass through” phase of quanta” (2.6), that is, they represent a fundamental unit of space-time at the limits of vibrational activity (2.7). As noted in 6.2, for the purposes of this discussion we are concentrating on events following the singularity, focusing on the remnants of the Big Bang as they proceed in space-time. And again, for the purposes of this discussion, we shall not concern ourselves with the general transformation of Plasma into a variety of quantum particles, but rather we shall focus on a particular class of artifacts of the Plasma that represent “one interval of a wave-“pass through” phase of quanta.” Regardless, as we have said, we shall see that, like Poincaré’s Conjecture, String Theory, too, explores a subset of toroids.

6.5. Action at a Distance. As we noted in 6.1, String Theory awaits an empirical proof of the existence of the strings themselves and we propose that such experimental evidence has already been gathered, though it has not been recognized. We are referring to the “Action at a Distance” (so-called “Spooky Action”) observations, in which two objects, apparently separated in space with no known connection, interact with each other as if they “know” the mass (in the case of gravity) or charge (in the case of electromagnetism) of the other distant object.

6.6. Empirical Evidence for Strings: A Structural Identification. Again, we go back (in the nanoseconds before the Big Bang) to the Plasma Ball (singularity), when all of space-time was the very same substance—not atoms or particles of a homogeneous substance, but one indivisible entity, unmanifest within and of itself (represented by the Hebrew letter Aleph, which means, in this case, before the beginning).

The fact that space-time expanded and differentiated itself infinitely from this singularity doesn’t mean that the original connection between everything that comprised the beginnings of this iteration of the universe was lost (which is why Horava’s reconciliation of gravity and quantum mechanics works for all states of matter). Rather, this original “plasma” stretched, twisted, snapped, and evolved into other manifestations. Action at a distance, then, is simply the response of an artifact of creation, that is, different segments of a single string of quanta reacting to the same stimuli. The same phenomenon can be created by entanglement, joining quanta into a single unit (https://www.quantamagazine.org/new-entanglement-results-hint-at-better-quantum-codes-20221024/). The observation that the response is transmitted faster than the speed of light (which would violate Einstein’s Special Theory of Relativity) is an illusion, because the stretched string is a remnant of the Plasma Ball, that is, a fundamental unit of space-time at the limits of vibrational activity (2.7), or entangled strings that respond in the same manner. As per the Uncertainty Principle, our instruments and calculations are simply not now, nor will they ever be, capable of detecting an interval between the stimulus and the response, because the interval is less than the wave-“pass through” periodicity of one quantum (the fundamental unit of space-time)—thus it seemingly occurs instantaneously, in no space-time, that is, faster than would be possible if the two “ends” of this string were in fact separate quanta. So, as in the game of Jeopardy, the observations of spooky action are the answers to the question, “What are the indications that strings are not only present now, but have been present since the creation of this universe?” In other words, everything is connected in the 1^st dimension. Note: Any variation between the “strings” described here and the strings in String Theory would be attributable to a variance in String Theory mathematics from the mathematics of toroids as manifested in the Quantum-Torus Model.

If we apply this principle to current experiments, what we are actually looking at is one unit of spacetime that has been stretched over increasingly large distances (an experiment in 2020 succeeded at 27 miles). Since anything that occurs to one unit of spacetime occurs at the same time throughout the unit, then it appears that the information is passed faster than the speed of light across distances, but this is not the case, since the spacetime is the same throughout; i.e., one unit. Thus, in the case of entanglement of 2,000 atoms (2020), what we are seeing is the same unit of spacetime, even if the strings are not evident to the observer.

6.7. QED. From a metaphysical point of view, then, the infinite differentiation of the universe is the flip side of the unitary integration of the universe: the total connectedness present in the Plasma Ball (at the singularity) is still present, only masked by the countless permutations and combinations of the fractal progressions of the Quantum-Torus. Matter is neither created nor destroyed and the laws of science (including logic and its subsets, physics, mathematics, etc.) and spirituality (“the mind of G-d”) need only account for the Great Anomaly (“the G-d principle”) and its infinite reflections to recognize their mutual consistency and convergence.

Hereafter, as Professor Igor Gamow (his father George being one of the principle theorists of the Big Bang) explained to me, the Quantum-Torus Model serves as the working model until it cannot explain key empirical evidence—allowing a generous amount of time to develop an explanation for such, while remaining consistent with its basic principles. For example, in June, 2026, our description of a particle was modified to a “pass-through phase” or “phase transition,” to align it with Horava’s application of exotic phase transitions and the Geometric Phase (or Berry Phase) phenomenon; in other words, when observed (stopped by a plate), it registers as a particle, because all the energy of the quantum is concentrated at a point, but if it were not being observed, this concentration of energy is simply undergoing a Geometric Phase transition.

7. IMPLICATIONS OF THE FRAMEWORK

7.1. The Nature of the Spiritual Anomaly. Having thus presented our proof, its checks, and a few of its applications, let us now turn to its implications for human beings living in such a universe. As shown in 4.1 and 4.2, our proof concludes that a spiritual anomaly (like Abraham, Jesus, Buddha, Krishna, et al.) shall incarnate periodically, but that the time and place (and, for that matter, the details of such a manifestation) are unpredictable. Since the argument developed in this paper relies upon scientific protocol (unlike our book, which uses Socratic and Talmudic dialogue and journalistic observations) to expand upon the details of such a manifestation, let us continue in this empirical vein, albeit with a certain allowance for intuition and vision as notably employed by Newton and Einstein in deducing their famous formulations, and with a nod to Joseph Campbell in the use of mythological examples to inform our scientific quest.

Like the Gospel of Thomas and (Thomas) Jefferson’s Bible, we seek to strip away the mythological and fictional qualities attributed to a master teacher and lay bare the basic parameters that define a spiritual anomaly. Given, then, the perceived lack of Divine Revelation (in its narrowest sense) casting a spotlight on such a being, and given the lack of an inspired selection system such as that employed to identify each incarnation of the Dalai Lama, we are thrust into circumstances much like the times of King David and King Arthur, both of whom were identified by the merits of their work and not by a genetic or spiritual pedigree.

7.2. The Philosopher’s Stone. Synchronistically, it is worth noting that a stone plays a key role in both David’s and Arthur’s ascensions—for David as a projectile in slaying Goliath and for Arthur as a forge from which he alone extracts the sword, Excalibur—that is, the stone is a manifestation of the periodic Chosen One’s power. Analogously, a stone is also the symbol we use to represent our predicted spiritual, philosophic, and scientific breakthrough—the so-called Philosopher’s Stone, sometimes referred to as the Perennial Philosophy. Given the technology, information, and leisure afforded by our historical circumstances, the characteristics of this philosophy would be nothing less than “the outline for the cross-disciplinary synthesis and integration of human knowledge into one indivisible multi-dimensional database reflective of the universe that it describes, including the prescription for sustainable human evolution” as we refer to in 1.1 (and explore in detail in our book).

7.3. The Philosopher’s Stone and the Spiritual Anomaly: Interpretive Correspondence with the Avatar and World Teacher Traditions. The relationship between the Spiritual Anomaly and the Philosopher’s Stone is reflexive, that is, the proof of the Spiritual Anomaly’s manifestation and the details thereof are derived from the Quantum-Torus Model (2.1 and 2.2) and the Proof of the Congruency of Science and Spirituality (1.4 and 4.1), key elements in the Philosopher’s Stone itself. Contrapositively, if the time, place, and nature of the Spiritual Anomaly’s manifestation are not predictable (as we have shown in 4.1 and as is prophesized, “no man knoweth the Son, but the Father; neither knoweth any man the Father, save the Son …” [Matthew 11:27]), it is only the Spiritual Anomaly that could derive and debrief such a proof (i.e., to the degree that the Great Anomaly [or G-d Principle] can be symbolized or made manifest in the flesh, the Spiritual Anomaly would be this event). Indeed, it is the Spiritual Anomaly’s mission to present this proof as part of a larger effort at revealing the parameters necessary for the evolutionary progression and sustainable survival of the human race (detailed in our book). To this end, the Spiritual Anomaly serves humanity periodically as the Avatar or World Teacher. However, it is important to note that just as idols misrepresent the anomalistic G-d principle, so do such singular-event notions as Christ or Messiah misrepresent the periodic nature of the Spiritual Anomaly, turning the recurring appearances of a once-in-an-age teacher into a divine form separate from its human (and thus dualistic) basis. In actuality, the appearance of the Spiritual Anomaly, the proof that he offers for his appearance, the availability of information, technology, and leisure that afforded him the opportunity to produce such a proof, and the space-time where and at which such events occur are inseparable and indivisible phenomena rooted in the singular origins of the universe in which they manifest.

7.4. Structural Correspondence Extended to the Socio-Historical Paradigm. In addition to our proof of the convergence of scientific and spiritual disciplines and its check and application, we also observe that noted practitioners of both science and spirituality are issuing similarly dire warnings concerning the current and future state of humanity. Without going into a long list of evidence (as we do in our book), let us briefly note some of the key details that give rise to these warnings:

• Global warming/climate change
• Pollution of the biosphere
• Geometric population growth
• Entrenched power of the war industry
• Private control over public utilities (currency, water, energy, etc.)

Ironically, these threatening factors are a result of our success as a species when measured against the parameters of the Theory of Evolution and the Protestant Ethic as they are generally understood today. To a large degree, this so-called success has been economic, what we described in 7.2 as, “the technology, information, and leisure afforded by our historical circumstances.”

Mapping the aforementioned positive and negative examples of contemporary human achievement to our Quantum-Torus Model, we can only deduce our current position is on the cusp of a “phase shift” in organizational structure: We must evolve in order to survive, for the nature of space-time itself is evolutionary, regardless of whether the universe is expanding or contracting—i.e., the succession of quantum-torus intervals and the behaviors therein follow certain principles (except at the limits of vibrational activity). Going back to the various binary metaphors we have assigned to our model, e.g., “light and dark, on and off, line and broken line, 1 and 0, sphere and doughnut, particle and wave, mass and energy …” (2.3), we observe that the self-conscious choice, or change, we face is one that resembles the transformation from darkness to light. Again, science and spirituality agree!

Indeed, this characterization matches the conclusion we reach by alternate analysis—mapping human consciousness to its consequence in human behavior, that is, deconstructing the two key evolutionary steps in human development and extrapolating their primary factors to describe our present circumstances. To wit,

The two key evolutionary steps in human development to which we refer are:

• Overcoming gravity and mastering physical tools (standing erect and prehensile thumbs)
• Overcoming communication barriers and mastering symbolic forms (developing language, music, mathematics, etc.)

Deconstructing these steps, we derive the following:

• Overcoming gravity and mastering physical tools = unconscious physical evolution
• Overcoming communication barriers and mastering symbolic forms = subconscious mental evolution

Extrapolating these characterizations leads to the following dialectical progression of Homo sapiens:

• Unconscious physical evolution (Homo erectus)
• Subconscious mental evolution (Homo symbolicus)
• Conscious spiritual evolution (Homo spiritus)

Our scientific deduction and check proves to be the same as the spiritual teachings since time immemorial: we must overcome the tyranny of the instincts and the ego by employing our spiritual tools to evolve in a sustainable manner.

Another argument that we provide to support the choice of conscious spiritual evolution is derived from the nature of life itself, that is, light manifesting as DNA. Here, we find that just as the Great Anomaly (First Cause) animates creation with constant change (the Greek letter Delta), so the life-force (prana) exhibits the “will to live.” Consider the tree that splits the stone of a mountain or the blade of grass that cracks the sidewalk, both to grow and evolve.

As we have noted, in human history, we have manifested the “will to live” at the instinctive physical level (standing erect) and at the egoistic mental level (mastering symbolic forms). Now we are at the crossroads of another major evolutionary choice, much like Hamlet as he ponders, “To be, or not to be.”

Have we lost the will to live, or do we have what it takes as a species to survive? “That is the question.” Our collective answers will determine whether we choose to survive (evolve) or not. As we discuss in 7.5, free will and determinism will mutually influence the outcome.

We now have shown four alternative arguments in 7 that point to the same conclusion concerning the present moment in human development: the appearance and role of the Spiritual Anomaly, overcoming the tyranny of the instincts and ego (conscious spiritual evolution), the mapping of our historical circumstances to the Quantum-Torus Model, and the self-conscious choice that the universe presently requires for evolution.

7.5 Chaos Theory as Further Impetus for Conscious Spiritual Evolution. Chaos Theory equations show that even in a deterministic universe, outcomes remain unpredictable (quantifiable inputs produce unpredictable results). This means that Free Will and Determinism necessarily co-exist. The mathematics may be complex, but the meaning is simple: we must act as if we have free will, because as far as we can ever know, we have it. Before the mathematics of Chaos Theory were developed, the only way to prove the interdependence of free will and determinism was through the logic of letters (words and propositions). Now the letters and numbers agree: As the progression of the Quantum-Torus Model shows, “conscious spiritual evolution” is to be humanity’s next step and it is to be accomplished one person at a time, through self-conscious action, arrived at through our own free will.

While it is not the focus of this paper to describe the specifics of this species-defining transformation (we do so at length in our book), we do believe it important to briefly note the range of individual actions with which the next stage of our evolution begins.

7.6. Individual Spiritual Practice as the Next Evolutionary Step. Essentially, what we have identified here is individual spiritual practice as the basis for progressive human development. The simplest form of such spiritual practice and the starting point for our work is nothing more than taking a deep breath and counting to ten. The purpose of this exercise—which, despite its apparent simplicity, is difficult to consistently employ—is to counter instinctive and egoistic reactions as they occur, for example, when we get cut off in traffic or are criticized by a significant other. By consciously and consistently choosing alternative behaviors to the instinctive reaction of responding in kind to such perceived offenses, we strengthen that part of ourselves which spiritual teachers identify as “the higher self” or Self. This is the same Self that Jung refers to in his essay, “Christ, the Symbol of Self,”¹⁶ that is, an archetype within each of us (alternate descriptions of which, such as Messiah or Buddha or Krishna consciousness, are discussed at length in our book); in other words, a tangential point within each of us that reflects the Great Anomaly (What Brahmans refer to as Atman, the individual soul; in essence, the same as the universal soul, Brahman). These psycho-spiritual dynamics are the same for the Spiritual Anomaly (the Avatar or World Teacher), except for his/her periodic singular expressions synthesizing seemingly disparate elements and integrating them into a convergent framework for the current stage of the evolutionary process.

Of course, in addition to the fundamental breathing exercise, there are other established practices that accomplish the same spiritual goal, a variety of which we describe in our book, in particular that of Yoga, through which we describe the non-denominational science of spiritual rebirthing. However, we include within our scope here a mapping of the human body to our Quantum-Torus Model to explain the inside-out process by which Yoga catalyzes the coincidence of consciousness and the Great Anomaly and our experience of the Quantum-Torus through the heart (Love):

The Quantum Torus and Human Form
(Light Manifesting as DNA)
Original text and illustration:

Just as our physical bodies heal themselves through unconscious and subconscious processes (e.g., bleeding, coagulating, scabbing, etc.) in healing a physical wound, so our spiritual bodies heal spiritual wounds without the intervention of our egos. Yoga is simply a catalyst for accessing this life-force that, like the singularity from which it is brought forth, embodies certain indefinable anomalistic properties.

Through this scientific spiritual rebirthing process we rediscover our own connection with the Great Anomaly, and in so doing alter our consciousness and behavior—the primary result of which is in our willingness to share with others, a central objective of conscious spiritual evolution.

We fully expect to hear from cynics who posit that such a result is utopian, that is, beyond the capability of human beings and human nature to attain or sustain. We counter:

Spiritual evolution may have been utopian at one time; it is now necessary.
There is no such thing as fixed human nature; human beings are evolutionary, just as the light from which they are made.

Further, we have “the technology, information, and leisure afforded by our historical circumstances” (7.2) to make this work (for example, Buckminster Fuller’s “World Game”), as well as any number of examples (take your pick—Abraham, Jesus, Buddha, Krishna, Mother Theresa, Gandhi, the Dalai Lama, et al.) from which to draw inspiration that such behavior is attainable. The parameters and outcomes for individual development certainly vary according to unique hereditary, environmental, and self-conscious factors, but, nevertheless, we each have a connection to the Great Anomaly—what Jung describes as the Christ (Messiah, Buddha, Krishna, et al.) archetype—that we are compelled to express.

8. THE BOOK (https://www.amazon.com/dp/0615185371/)

8.1. Publication. The means by which the Spiritual Anomaly (Avatar or World Teacher) presents the details of this mission takes the form of a book, the first volume of which is complete. This paper in its original form, including additional commentary, is included in the book; however, we suggest referring to this online edition, which is updated as relevant experiments and papers are published..

8.2. Public Reaction and Obstacles. The success of this mission will be determined by conscious individual choices. The primary obstacle to individual and group success is, as we have noted in 7.4, the tyranny of the instincts and the ego. On a global scale such behavior is currently exhibited in the priority to which we assign Capital over human evolution. Whether we interpret such behavior scientifically, by mathematically expressing it as and attributing it to the expansionary nature of Capital, both in terms of demand for resources and markets and thus the eventual commoditization of all things, or whether we interpret such behavior spiritually, as the worship of the Golden Calf and Mammon, the deduction is the same: Capital is an abstraction that rules our lives—that is, we now worship a false G-d.

The scope of this paper does not include a detailed analysis of the political, economic, and psychological dynamics that follow from this involuted behavior (such analysis is provided in detail in our book, noted at the top, and in our latest works, here and here), but it is necessary to note that those ascribing to such, by their own admission, worship at the altar of Capital and private gain at the expense of the spiritual evolution of the human race. However, it is also worth noting that those who exercise the greatest control over these now regressive forces individually profess in significant numbers to follow the tenets of the major religions, including Christianity, Judaism, Islam, Hinduism, et al. In presenting our proof of the congruency of science and spirituality and its applications, we sincerely hope that these individuals take heed that they “cannot serve G-d and Mammon,”¹⁷ and stop professing to do both. We await their response, “for by thy works shall ye be judged.”¹⁸

Secondary obstacles to the spiritual evolution of the human race include dogmatic religious bureaucracies and their subscribers, particularly those variants that claim to be privy to the truth to the exclusion of all other approaches. To counter the fallacy of such thinking, in addition to having heretofore proven the unifying principle of all religions (see “G-d principle” in 1.3, 2.5, 4.2, and 6.7), we employ the following cybernetic metaphor: We all have unique passwords to the same server; The Great Anomaly grants similar access rights to all users; There is no specific group that holds administrative rights to the exclusion of others. We call upon religious leaders to respond to our proof and to separate themselves and their followers from the temporal elements of their faith and those who seek to use spiritual trappings for material ends.

8.3. The Ongoing Work. Finally, we urge everyone to “think globally and act locally.” Identify and develop the unique gift that you have been given and share it with the world. In this way, we shall evolve one person at a time and together create a sustainable and enlightened world.

SUPPORTING LITERATURE REVIEW

Overview

The following peer-reviewed and formally published literature provides external grounding for the key sections of Solomon’s Proof and the Quantum-Torus Model. Sources are grouped by the section of the proof they most directly support. Where literature is emerging or preliminary rather than fully peer-reviewed, this is noted. Each entry includes the citation, a plain summary of what it establishes, and how it maps to the proof.

I. Toroidal Universe — Cosmological Physics

Supports Sections 2.1, 5.1–5.2

1. COMPACT Collaboration (2022–2024)

COMPACT Collaboration. “Promise of Future Searches for Cosmic Topology.” arXiv:2210.11426v4 (March 2024). Also: “Cosmic Topology. Part I. Limits on orientable Euclidean manifolds from circle searches.” arXiv:2211.02603.

What it establishes:

The COMPACT collaboration — an international partnership of cosmologists — has demonstrated that a 3-torus topology for the universe remains entirely consistent with all existing observational data, including the Planck CMB maps. Previous analyses that appeared to rule out toroidal geometry are shown to have been overstated. The 3-torus (a finite, bounded, edgeless universe in which opposite faces connect) remains one of 18 mathematically possible flat-space topologies that current evidence cannot eliminate.

Relevance to Solomon’s Proof:

Directly supports the claim that the torus is the fundamental geometric structure of the universe. The 3-torus is the macrocosmic expression of what the Quantum-Torus Model describes at the quantum level — the same geometry operating at different scales, which is precisely the proportional correspondence the proof argues.

“We haven’t ruled out as many interesting topologies as some previously thought… many weird cosmic topologies are still entirely consistent with the observed data.” — COMPACT team member, The Guardian, June 2024

2. APS Physics: “The Universe’s Topology May Not Be Simple” (2024)

Physics 17, 74 (2024). American Physical Society.

What it establishes:

A 2024 APS summary confirms that the topology of the universe remains an open and active question. Correlated patterns in the CMB could indicate closed loops in the topology, consistent with toroidal geometry, reflecting growing mainstream acceptance that toroidal universe models deserve serious investigation.

Relevance to Solomon’s Proof:

Establishes that the Quantum-Torus Model’s core geometric assumption — that the universe has toroidal structure — is not fringe speculation but an active area of mainstream cosmological research.

3. Hyper-Torus Universe Model (HTUM, 2024)

McCammon, C.R. “The Hyper-Torus Universe Model — A New Paradigm for Understanding Reality.” Preprints.org (2024). DOI: 10.20944/preprints202406.0674.v3.

What it establishes:

An independently developed model proposes that the universe is a quantum system structured as a hyper-torus, using this framework to unify quantum mechanics, cosmology, and consciousness. HTUM explicitly treats the torus as the fundamental unit of universal structure at both quantum and cosmological scales — arriving at remarkably similar conclusions to Solomon’s Proof independently.

Relevance to Solomon’s Proof:

The independent convergence of HTUM on the same core geometric framework constitutes a form of corroboration — two investigators, working independently, arriving at the same structural conclusion.

Note: HTUM is a preprint, not yet peer-reviewed in a journal. Cite as a corroborating independent framework.

4. Quantum Field Theory on Toroidal Topology

Khanna, F.C., et al. “Quantum field theory on toroidal topology: Algebraic structure and applications.” Physics Reports 539 (2014): 135–224. arXiv:1409.1245.

What it establishes:

A comprehensive peer-reviewed treatment of compactified quantum field theory on toroidal topologies, showing that the torus is a natural and mathematically rigorous structure for describing quantum fields in bounded spacetime.

Relevance to Solomon’s Proof:

Provides formal mathematical grounding for the Quantum-Torus Model’s mapping of wave/particle duality onto toroidal expansion/contraction/rest phases.

II. Wave-Particle Duality and Toroidal Light Behavior

Supports Sections 2.2–2.3

5. Experimental Separation of Wave and Particle Attributes (Nature Photonics, 2022)

Chen, Y., et al. “Experimental demonstration of separating the wave and particle attributes of a single photon.” Nature Photonics 16 (2022): 869–874. DOI: 10.1038/s41566-022-01063-5.

What it establishes:

Using the quantum Cheshire cat concept, researchers experimentally separated wave and particle attributes of a single photon for the first time — demonstrating that these properties are not simultaneously present in the same location, but represent genuinely distinct states.

Relevance to Solomon’s Proof:

Directly supports the Quantum-Torus Model’s core claim that wave and particle behaviors represent distinct phases of the same underlying structure — the experimental separation of these attributes is consistent with the model’s phase-based interpretation.

6. Wave-Particle Duality as Distinct, Exploitable Properties (Stevens Institute, 2023)

Stevens Institute of Technology. “Groundbreaking Quantum Study Puts Wave-Particle Duality to Work.” (2023).

What it establishes:

Wave and particle aspects of quantum objects can be treated as distinct, separately deployable properties — not merely as complementary descriptions of the same event.

Relevance to Solomon’s Proof:

Operationally validates the model’s assignment of wave and particle behaviors to different phases of toroidal expansion — these are genuinely different phases, not just different descriptions.

III. Quantum Biology and DNA

Supports Sections 3.4–3.5

7. Quantum Tunneling in DNA (Communications Physics, 2022)

Brovarets, O.O. and Hovorun, D.M. “An open quantum systems approach to proton tunnelling in DNA.” Communications Physics 5 (2022): 128. DOI: 10.1038/s42005-022-00881-8.

What it establishes:

Peer-reviewed experimental evidence that quantum mechanical effects — specifically proton tunneling — play a direct role in DNA replication and mutation. The quantum tunneling contribution is shown to be several orders of magnitude larger than the classical mechanism alone would predict.

Relevance to Solomon’s Proof:

Directly supports the claim that quantum-level phenomena propagate upward into the structure and behavior of DNA. If quantum effects determine mutation rates, the Great Anomaly’s presence at the quantum level is structurally connected to genetic expression — as the proof argues.

8. DNA as a Quantum System (Scientific Reports, 2024)

Gonzalez, J., et al. “DNA as a perfect quantum computer based on the quantum properties of the molecule.” Scientific Reports 14 (2024). DOI: 10.1038/s41598-024-62539-5.

What it establishes:

Recent research characterizes DNA as a multi-resolution quantum system whose behavior cannot be fully explained by classical chemistry — structurally exhibiting quantum computational behavior.

Relevance to Solomon’s Proof:

Strengthens the bridge between the Quantum-Torus Model and the human genome. If DNA is itself a quantum system, the proportional correspondence between quantum-torus structure and genetic structure reflects a real physical continuity, not merely analogy.

9. Quantum Biology — Field Review (PMC, 2024)

“Quantum Biology Using Ultrafast Integrative and Molecular Approaches.” PMC13055015 (2024). Foundational text: Al-Khalili, J. and McFadden, J. Life on the Edge. Crown, 2014.

What it establishes:

Quantum biology has emerged as a legitimate scientific discipline demonstrating that quantum effects — tunneling, coherence, entanglement — play functional roles in photosynthesis, enzyme catalysis, bird navigation, and DNA mutation.

Relevance to Solomon’s Proof:

Establishes the broader scientific legitimacy of the claim that quantum mechanics is causally active in biological systems. The Schönberger I Ching / DNA structural correspondence can be situated within this literature as a structural observation consistent with quantum biology’s findings.

IV. Category Theory and Cross-Domain Structural Equivalence

Supports Section 1.4

10. Category Theory in Cognitive Science (PMC, 2022)

Goguen, J., et al. “What is category theory to cognitive science? Compositional representation and comparison.” PMC9716143 (2022).

What it establishes:

Category theory — the branch of mathematics that formalizes structural equivalence across domains via morphisms and functors — is explicitly applied as a tool for understanding structural analogies between different cognitive and scientific domains. Structural (analogical) relations between domains are a legitimate and rigorous object of mathematical study.

Relevance to Solomon’s Proof:

Provides formal academic grounding for the method used in section 1.4. Renaming analogous reasoning as structural equivalence and proportional correspondence situates the proof within an active area of formal mathematics.

11. Tonal Isomorphism as Cross-Domain Methodology (MDPI, 2021)

“Tonal Isomorphism: A Methodology for Cross-Domain Analysis.” MDPI Humanities 10(6):122 (2021).

What it establishes:

Isomorphism — the formal mathematical equivalence of structure between domains — is applied as a rigorous analytical methodology across the sciences and humanities, citing category theory as its formal basis.

Relevance to Solomon’s Proof:

Directly supports the approach of Section 1.4. The proportional correspondences (a:b::c:d) between Taoism, Platonism, Heisenberg, and DNA are a form of cross-domain isomorphism with formal mathematical precedent.

12. Stanford Encyclopedia of Philosophy: Category Theory

Marquis, J-P. “Category Theory.” Stanford Encyclopedia of Philosophy (Fall 2019). plato.stanford.edu/entries/category-theory/

What it establishes:

The authoritative philosophical reference establishing that category theory unifies mathematical structures via equivalence classes and isomorphism types — structural relationship rather than identity of substance.

Relevance to Solomon’s Proof:

Provides the philosophical foundation for the claim that structural equivalence is a rigorous form of proof — one that establishes unity at the level of relational architecture rather than material identity.

V. Horava-Lifshitz Gravity

Supports Section 7

13. Horava-Lifshitz Gravity: Progress Report

Blas, D., and Sanctuary, H. “Horava gravity at a Lifshitz point: A progress report.” International Journal of Modern Physics D 26 (2017). World Scientific.

What it establishes:

Horava’s quantum gravity theory is a published, peer-reviewed attempt to reconcile quantum mechanics and general relativity using exotic phase transition mathematics. It remains an active area of theoretical physics.

Relevance to Solomon’s Proof:

The proof’s claim that Horava’s formulations verify Einstein’s gravity (rather than contradicting it), explained by the Quantum-Torus Model’s behavior at singularity, can be positioned as offering a resolution to an acknowledged open problem in the literature.

VI. Bose-Einstein Condensate / Plasma Extremes

Supports Sections 6.3–6.4

14. Continuous Bose-Einstein Condensation (Nature, 2022)

Bennetts, S., et al. “Continuous Bose-Einstein condensation.” Nature 606 (2022): 694–699. PMC9217748.

What it establishes:

Experimental confirmation of continuous-wave BEC — a Bose-Einstein condensate that persists indefinitely. Deepens the understanding of BEC as an extreme state of matter in which individual atoms lose discrete identity, directly analogous (at the opposite extreme of vibration) to plasma.

Relevance to Solomon’s Proof:

Supports the proof’s description of BEC and plasma as contrapositive limit states — anomalistic forms of matter at opposite extremes of vibrational activity in which normal four-dimensional space-time laws are suspended. The 2022 experimental confirmation significantly strengthens the empirical basis of this claim.

FOOTNOTES:

¹ Argüelles, José A., Earth Ascending: An Illustrated Treatise on the Law Governing Whole Systems, Shambhala, Boulder & London, 1984.

² Dalai Lama, The Universe in a Single Atom: The Convergence of Science and Spirituality, Morgan Road Books, New York, 2005.

³ Tao Tê Ching (The Way of Life), written by Lao Tsu in the 6th Century B.C., is the foundation of Taoism.

⁴ This is perfectly consistent with Einstein’s famous equation (E=mc²). Light is energy (E) and mass (m), wave and particle, at the same time, each quanta representing the fundamental unit of space-time. If you look for waves, you see waves; if you look for particles, you see particles. We have no means of measuring a smaller interval than the periodicity of quanta from wave to particle to wave, or from particle to wave to particle.

⁵ Heisenberg, Werner, Philosophic Problems of Nuclear Science, Fawcett Premier Books, New York, 1952, p. 28.

⁶ Ibid., p. 27.

⁷

⁸ This is much like Einstein’s point that if you could travel faster than light you would come back to the same place that you started. Any slower speed would return you to a different place-time, i.e., the “inside” or “outside” of the point-of-origin, rather than the point-of-origin itself. In the drawing, Time is on the Z-axis that comes out of the page or goes through the page. The spiraled path (as noted by the broken line) experiences both the outside surface and inside surface of the Torus at the tangential “x” points (see drawing below) a 90-degree shift (rotated in and out of the page).

⁹

¹⁰ As reflected in the esoteric maxim, “As above, so below,” and the Star of David in its construction using an upright and an inverted equilateral triangle. Data from a recent experiment indicates that the universe is a toroidal loop, although “science” is loath to admit this: https://sputniknews.com/science/201911051077225867-our-idea-of-cosmos-may-be-all-wrong-as-universe-may-be-infinite-loop

¹¹ For an in depth discussion of the parallels and compatibility of Genesis and the Big Bang (and evolution), see the works of Gerald L. Schroeder, particularly Genesis and the Big Bang and The Science of God.

¹² From Dr. Edwin D. Babbitt’s Principles of Light and Color, 1878, as reprinted in Hall, Manly P., The Secret Teachings of All Ages: An Encyclopedic Outline of Masonic, Hermetic, Qabbalistic and Rosicrucian Symbolical Philosophy, The Philosophical Research Society, Inc., Los Angeles, 1968, XIII.

^12.5 Despite the evidence for the universe as a torus, physicists are reluctant to break out of their two- and three-dimensional models: https://www.scientificamerican.com/article/is-the-universe-a-giant-loop/

¹³ Dr. Martin Schönberger, The I Ching & the Genetic Code: The Hidden Key to Life, Aurora Press, Santa Fe, 1992 (originally published in German as Verborgener Schlüssel zum Leben, Scherz Verlag, Bern and Munich, 1973).

¹⁴ Ginestra Bianconi and Christoph Rahmede, “Quantum mechanical formalism for biological evolution,” @ http://arxiv.org/PS_cache/arxiv/pdf/1011/1011.1523v1.pdf

¹⁵ Matthew 24:44

¹⁶ This also means that we could calculate, using Einstein’s famous equation (E = mc²), the original energy released by the Big Bang if we knew the mass of the universe, or, vice versa, we could calculate the mass of the universe if we knew the original energy released. The solution for this calculation, used in conjunction with the mathematics of toroids as an infinite fractal loop, would explain the illusion of our universe expanding faster than the speed of light and could be applied to the questions of inflation, the red shift, whether our universe will continue to expand or eventually collapse, or whether it is a continuous creation toroid (https://blog.sci-nature.com/2022/09/what-shape-is-universe-new-study.html).

¹⁷ Jung, Carl, Aion: Researches into the Phenomenology of the Self, Volume 9, Part II, The Collected Works of C.G. Jung, Bollingen Series XX, Princeton University Press, 1959.

¹⁸ Matthew 6:24 and Luke 16:13

¹⁹ I Peter 1:17 and Revelations 20:12

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