Taking the Birch and Swinnerton-Dyer (BSD) Conjecture as its starting point, this paper employs abductive reasoning to conduct a philosophical analysis of the structural difficulties underlying deep unsolved problems in number theory. The paper proposes five core hypotheses: first, that the difficulty of proving the BSD conjecture is not technical but dimensional—the current deterministic mathematical framework lacks the dimensions necessary to express the conjecture’s underlying structure; second, that “states” in number theory may be more fundamental than “numbers” and “functions,” proposing the “Microson” as the minimal indivisible structural unit of a state; third, that a “quantum function” concept with indeterminacy as an axiom is needed to replace classical deterministic functions; fourth, that the “state layer” arrived at from the conceptual direction and the “fifth dimension” arrived at from the spatial direction are two expressions of the same thing—the common difficulty of all deep number-theoretic conjectures is essentially the projection distortion of higher-dimensional discontinuous objects within a lower-dimensional deterministic framework; fifth, that continuous mathematics is four-dimensional mathematics, while the BSD conjecture is five-dimensional mathematics—”solutions” within the lower-dimensional framework are necessarily underdetermined finite solutions, not perfect solutions. The paper also examines existing academic research that partially overlaps with this direction, including Quantum Number Theory, Prime States, and p-adic quantum models. This paper explicitly states: all of the above is philosophical speculation and does not constitute mathematical proof or mathematical progress.
I. Starting Point: The Structure of the BSD Conjecture
The Birch and Swinnerton-Dyer conjecture is one of the seven Millennium Prize Problems of the Clay Mathematics Institute. Its core object is an elliptic curve E defined over the rational number field ℚ—the set of rational solutions to an equation of the form y² = x³ + ax + b.
In the 1960s, Bryan Birch and Peter Swinnerton-Dyer discovered through computer experiments a striking numerical pattern: for an elliptic curve E, when one takes the cumulative product of the number of mod-p solutions N_p at each prime p, the growth behavior of this product precisely encodes the global information of the curve over the rationals—the rank r of the group of rational points.
Specifically, they found that the growth rate of the product ∏(N_p/p) is approximately (log X)^r, where r is precisely the rank of the elliptic curve. This means: the number of local solutions at each prime “conspires” to encode how many rational solutions exist globally.
The formal statement of the BSD conjecture elevates this observation into a precise proposition: the order of vanishing of the L-function L(E,s) at s=1 equals the rank of the group of rational points. But a fundamental question emerges—how does this coordination across all primes occur? Through what mechanism does local information encode global structure?
II. Non-Locality: A Structural Parallel with Quantum Mechanics
Each prime p constitutes an independent “local world,” with no direct communication between them. Yet the number of solutions at each individually exhibits a global coordination that transcends the individual. This characteristic has the structure of non-locality—analogous to how measurement results of two distant particles in quantum entanglement exhibit correlations that transcend local causality.
This is not merely an analogy. In the 1970s, when Montgomery studied the spacing distribution of zeros of the Riemann zeta function, physicist Dyson pointed out that the distribution precisely coincides with the eigenvalue spacing distribution of random matrices (GUE)—the statistical pattern of energy level spectra in quantum chaotic systems[1]. The zeros of L-functions (the core objects of the BSD conjecture) also obey the same statistical behavior.
The zeros of L-functions in number theory and the energy level spectra of quantum chaotic systems may be different manifestations of the same mathematical structure. This hints at a deep resonance between number theory and quantum physics that has yet to be fully understood.
The Hilbert-Pólya conjecture goes further, positing that the zeros of the Riemann zeta function may indeed be the eigenvalues of some self-adjoint operator (analogous to the Hamiltonian in quantum mechanics). If this conjecture holds, the core problems of number theory would gain a quantum mechanical explanation.
III. Methodology Strikes the Ontological Dimension Wall
3.1 The Simultaneous Stalling of All Methodological Channels
In the BSD conjecture, the cases of rank 0 and 1 have been proven (Gross-Zagier[2], Kolyvagin[3]et al.’s work). But the case of rank ≥2 has not been broken through in sixty years. The key fact is not that one method failed, but that all methods stopped at the same place—modular form methods, Galois representation methods, Iwasawa theory, Euler systems—all stalling at the threshold of rank 2.
3.2 A Dimension Signal, Not a Difficulty Signal
This paper proposes a criterion: when all methodological channels simultaneously stop at the same boundary, this is not a difficulty problem—it is a dimension signal. “Cannot solve it” means the answer is on the same plane but hasn’t been reached yet; “insufficient dimensions” means the answer is not on this plane at all.
Historically, every time this pattern has appeared, the result was ultimately a dimensional leap: the problem of the Fifth Postulate gave birth to non-Euclidean geometry (a new definition of space); the ultraviolet catastrophe gave birth to quantum mechanics (a new definition of energy); Gödel’s incompleteness theorem revealed the existence of propositions within arithmetic that are principally undecidable within the logical framework.
3.3 The Deterministic Cycle of Contemporary Mathematics
The deterministic framework of contemporary mathematics has formed a cycle—stronger theorems, finer estimates, more abstract categories, but the underlying axioms remain unchanged. This means that no matter how sophisticated the tools, they draw ever more complex curves on the same plane without being able to jump out of the plane itself. This paper hypothesizes that the BSD conjecture may currently sit in a gap where a dimensional leap is needed but has not yet occurred.
IV. Abductive Logic and the History of Dimensional Leaps
Abduction is the form of reasoning that works backward from results to the best explanation, proposed by Peirce[4]; it is the only type of reasoning capable of generating genuinely new hypotheses. Heeffer (2007) demonstrated that key conceptual innovations in the history of mathematics—such as Cardano’s introduction of imaginary numbers in the Ars Magna—fully conform to Peirce’s description of abductive reasoning[5]。
| Year | Leaper | Wall Hit | Abductive Leap | New Dimension |
|---|---|---|---|---|
| 1545 | Cardano | Cubic equations require √−1 | “What if a new kind of number exists?” | Imaginary numbers → Complex analysis |
| 1897 | Hensel[6] | Numbers and functions behave similarly | “What if numbers can be expanded like functions?” | p-adic numbers → Local-global principle |
| 1960s | Grothendieck[7] | Weil conjectures require new cohomology | “What if space is not a collection of points?” | Schemes → Modern algebraic geometry |
| 1990s | Connes[8] | Riemann zeros need spectral interpretation | “What if geometry can be noncommutative?” | Noncommutative geometry → Quantum number theory bridge |
Common pattern: each time, it was not about “computing better” within the old number system, but about the basic objects themselves—numbers, space, geometry—being redefined.
But abductive logic has an inherent trap: its launch platform is the current conceptual space. The “best explanation” we can conceive is constrained by the existing conceptual inventory, just as a being that has only ever seen flat surfaces trying to abduce an explanation for the deformation of shadows—it will never guess a three-dimensional object.
V. The “State Layer” Hypothesis
5.1 From Properties to States
Existing number theory operates at the property layer: “how many solutions does the elliptic curve have over F_p” is a property; “what is the order of vanishing of the L-function at s=1” is also a property. The BSD conjecture = proving two properties are equal.
The true revolution of quantum mechanics was not the discovery of new properties, but making “the state” the most fundamental unit of existence. In classical physics, particles have definite position and momentum; “state” is merely a description. Quantum mechanics says: the state is the ontological reality; position and momentum are merely projections of the state.
5.2 A Triple Ontological Reconstruction
This paper questions three pillars of classical mathematics:
Determinism: f(x) = y, one input corresponds to one definite output. Continuity: between f(x) and f(x+dx) there are infinitely many intermediate values. The ontology of solutions: the goal of mathematics is “solving”—finding that definite y.
Hypothetical replacement: the fundamental object of mathematics is not “the solution” but “the state.” A “solution” is the collapsed result after a state is observed. Different modes of observation (analytic, algebraic, geometric) extract different values from the same state, and the consistency among these values is an intrinsic property of the state, not a theorem that needs proving.
If the mode of existence of an elliptic curve over the rational field is itself a “state”—a superposition structure that simultaneously encodes all local and global information—then the rank and the order of vanishing are not two things that need to be proven equal, but two modes of observing the same state.
VI. The Missing Condition of Imaginary Numbers
The imaginary unit i (i² = −1) allowed numbers to jump from the one-dimensional real line to the two-dimensional complex plane, endowing them with phase (rotation angle). Quantum interference is built on phase; L-functions are defined on the complex plane. But i is self-referential—i² = −1 describes the relationship of a number with its own square; this is a single-body property.
What BSD requires is a relational structure between multiple local worlds. In the language of quantum mechanics: i gave us superposition, but not entanglement. Superposition is single-body—|0⟩ + i|1⟩; entanglement is multi-body—|00⟩ + |11⟩, irreducible to a product of single-body states.
Frontier physics research is exposing this gap. Grgin (2018) argued that the structure of complex numbers is not rich enough to support the unification of quantum mechanics and relativity[9]. A 2021 locality study by Renou et al. showed that complex numbers contain an implicit locality assumption that has never been explicitly stated[10]. In 2022, two independent experiments confirmed that complex numbers are indispensable in describing quantum networks—but their indispensability is precisely exposed in the description of multi-body entanglement[11]。
Perhaps what is missing is not a new kind of number, but a relational structure built natively into the definitional layer of numbers—not added after the fact through products or functors, but existing axiomatically at the foundation of a new number system, just as i exists at the foundation of complex numbers.
VII. The Microson Hypothesis
7.1 Definition
Microson is a hypothetical concept proposed in this paper, referring to the minimal indivisible structural unit of a state. It possesses four fundamental properties:
(i) Not a constant—carries no fixed value. (ii) Not a determinate state—cannot be fully determined. (iii) Discontinuous—no transition path between states, only discrete jumps. (iv) Primordially multi-dimensional discontinuity—the microson is discontinuous in its native dimensions; upon dimensional reduction, this manifests as the “indeterminacy” we perceive. Indeterminacy is not the microson’s nature but the artifact of dimensional projection.
7.2 Microson Symbol
Left endpoint (primordiality) → Two paths crossing (superposition and entanglement) → Upper end with arrow (determinate face) / Lower end without arrow (indeterminate face)
The symbol encodes five layers of information: Left endpoint represents primordiality—the indivisible starting point; two paths departing from the same point represent superposition—a single entity simultaneously unfolding in two directions; the crossing in the middle represents entanglement—two paths passing through each other and no longer independent thereafter; the upper end with arrow represents the determinate face—the observable, collapsed value; the lower end without arrow represents the indeterminate face—the open, uncollapsed state.
7.3 Core Property: Permanent Coexistence of the Determinate and Indeterminate
The core claim of the microson hypothesis: a microson permanently carries both a determinate face and an indeterminate face simultaneously. This is not “indeterminate before observation, determinate after”—but permanently half-determinate and half-indeterminate. Observing one end yields the arrow (determinate value), while the other end simultaneously remains open because of the observation. Indeterminacy is not a temporary deficiency but the permanent structure of the microson.
VIII. The Quantum Function Hypothesis
8.1 The Implicit Axiom of Deterministic Functions
All current mathematical functions share an implicit axiom: determinism. f(x) = y—given an input, the output is determinate. Even a probability function P(x) = 0.7—the probability value itself is determinate. Even the wave function ψ(x)—the amplitude is a determinate complex number. We use determinate mathematics to describe indeterminate physics.
8.2 The Concept of Quantum Functions
A quantum function is not “a function that outputs a probability distribution” (that is still a deterministic function outputting a deterministic distribution), but a hypothetical object whose mapping relationship itself possesses intrinsic indeterminacy. f(x) exists in an uncollapsed state and only manifests as a determinate value when “observed”—when embedded in a specific mathematical structure.
A quantum function is not continuous. There is no “in between” two values—just as an electron jumps from one energy level to another without passing through intermediate states.
8.3 The Source of Indeterminacy: Dimensional Projection
This paper further hypothesizes: quantum functions and microsons may be fully determinate yet discontinuous structures in their native dimensions. The “indeterminacy” we observe is the distortion produced when higher-dimensional discontinuous objects are projected onto a lower-dimensional deterministic framework—just as the projection of a three-dimensional object onto a two-dimensional plane loses information.
We have been using continuous functions (L-functions, defined on the continuous complex plane) to describe an essentially discontinuous object (the distribution of primes). Perhaps the difficulty lies precisely in the fact that we are trying to build a continuous bridge between two discrete shores, while the true connection passes through a dimension outside our framework.
IX. Convergence of the State Layer and the Fifth Dimension
In the reasoning process of this paper, “state layer” and “fifth dimension” are concepts arrived at independently from two entirely different directions. Tracing back their paths:
The “state layer” is arrived at from the conceptual direction—by asking “what is the fundamental object of mathematics,” passing through the judgment “not solutions, but states,” arriving at an ontological layer prior to numbers, prior to functions, prior to all deterministic description.
The “fifth dimension” is arrived at from the spatial direction—by asking “where do microsons reside,” passing through the judgment “indeterminacy is the product of dimensional projection,” arriving at a geometric space that our four-dimensional observational framework cannot reach.
The two paths converge at the same place. The state layer is the conceptual name of the fifth dimension; the fifth dimension is the geometric expression of the state layer. This convergence was not designed in advance but emerged naturally during the reasoning process—this can be viewed as a positive signal of internal consistency within the framework, but it may also be merely the self-reference of the same set of metaphors.
If this convergence points to a real structure rather than a linguistic illusion, then its implication is: the common difficulty of all deep number-theoretic conjectures—BSD, Riemann, Hodge—can be unified into a single statement: the projection distortion of higher-dimensional discontinuous objects (states/microsons) within a lower-dimensional deterministic framework (classical mathematics). We search for continuous paths on the projection plane to connect two points, but the true connection between these points passes through the fifth dimension, where no continuous trajectory exists in the four-dimensional projection.
The arrowless end of the microson symbol—that open path with no direction—points to this fifth dimension. It is not “empty” but points in a direction outside our observational framework. The work of human mathematics over two thousand years has been drawing ever more refined maps on the projection plane. Perhaps the next step is not to draw a more refined map, but to ask: where is the source of the projection?
It must be emphasized again: the above is a philosophical hypothesis, not a mathematical argument. “Fifth dimension” is used here as a conceptual label, referring to “structural space outside the current mathematical framework,” not a specific extra-dimension theory in physics (such as Kaluza-Klein theory or the compactified dimensions of string theory).
9.3 Core Proposition: Continuous Mathematics Is Four-Dimensional; BSD Is Five-Dimensional
From the above analysis, the paper’s most concentrated core proposition can be distilled: continuous mathematics is four-dimensional mathematics, while the BSD conjecture is five-dimensional mathematics.
The current deterministic, continuous framework of mathematics—real analysis, complex analysis, algebraic geometry—constitutes a “four-dimensional” workspace (here “four-dimensional” is a conceptual label, referring to the full dimensions of the existing framework). The equation described by the BSD conjecture—order of vanishing equals rank—requires a true connection that passes through the fifth dimension outside this four-dimensional space. In the four-dimensional projection, this connection is invisible and therefore unprovable.
Generalizing: “solutions” within a lower-dimensional framework are necessarily underdetermined finite solutions, not perfect solutions containing all information. Humans cannot fully reverse-engineer five-dimensional structure from four-dimensional space, just as the two-dimensional projection of a three-dimensional object cannot be uniquely reconstructed—countless different three-dimensional objects can produce the same two-dimensional shadow. Dimensional difference causes irreversible information loss.
9.4 Intuitive Image of Projection
On the projection plane, trying to prove “the side of the square = the diameter of the circle” is extremely difficult—but upon ascending to see the original object, the equation becomes self-evident.
The BSD conjecture may be precisely this structure: the order of vanishing and the rank are two four-dimensional projections of the same five-dimensional object.
X. Microson Restatement of the BSD Conjecture
10.1 Classical Statement
Elliptic curve E has N_p solutions at each prime p. These N_p are assembled into the L-function. The order of vanishing of L(E,s) at s=1 equals the rank r of the group of rational points.
10.2 Hypothetical Restatement Under the Microson Framework
Under the microson framework, each prime p is not a “venue for computing N_p” but a microson—the minimal indivisible unit of a state. N_p is not a property of the microson but the collapsed value after a deterministic observation is applied to the microson.
Elliptic curve E defined over ℚ means it simultaneously touches all microsons. E itself is the entangled state Ψ_E of all prime microsons. The L-function L(E,s) is the classical approximation constructed by multiplying together the collapsed values of all microsons—a projection photograph of Ψ_E. The rank r is another observation of Ψ_E from the algebraic direction—yet another projection photograph.
Under the microson framework, the BSD conjecture becomes: two projection photographs yield the same number. This is no longer a theorem that needs to be proven bottom-up, but a self-consistency condition of the same state Ψ_E under two modes of observation. The direction of proof is reversed—not from piecing together locals to the global, but from the state downward to deriving all observables.
10.3 Explanation of the Rank ≥ 2 Difficulty
At rank 0, all microsons of Ψ_E are in the “ground state,” confirmable by a single observation. At rank 1, Ψ_E has one excitation mode, and Heegner points happen to be its classical projection. But at rank ≥ 2, Ψ_E has two or more entangled excitation modes—under the microson framework, deterministic observation is principally unable to simultaneously resolve multiple entangled excitations; this constitutes an “uncertainty principle” at the microson level.
XI. Relationship to Existing Research
The philosophical path of this paper does not exist in isolation. Through literature review, it was found that the direction of “introducing quantum mechanical structures into number theory” has already been explored by multiple researchers through technical approaches. This paper’s conceptual framework has substantive directional overlap with the following research:
11.1 Quantum Number Theory
Daiha (2021), in the paper “A quantum number theory,” used the algebraic structure of quantum mechanics to construct a representation of quantum number theory, introducing two concepts: “number state” and “basic unit of number information”[12]. “Number state” is conceptually very close to this paper’s “state layer” hypothesis, and “basic unit of number information” shares a similar motivation with “microson”—both attempt to find a more fundamental unit of number theory than classical integers. However, that research acknowledges fundamental difficulties in establishing a quantum logic with sufficient axiomatic structure to derive basic number-theoretic theorems.
11.2 Prime States and Quantum Information
Latorre et al. (2020) constructed “Prime States”—encoding prime number sequences as quantum superposition states and studying their entanglement properties, including von Neumann entropy and reduced density matrices[13]. More notably, Benioff et al.’s research found that qukits with prime p as the base serve as “fundamental particles” in quantum number representation—primes are indivisible fundamental units[14]. This finding and this paper’s hypothesis that “each prime is a microson” are almost the same intuition, only arriving independently from the technical direction of quantum information theory.
11.3 p-Adic Quantum Models
Khrennikov et al. (2023) constructed a complete quantum system over the p-adic number field—implementing quantum states and observables using p-adic Hilbert spaces, and establishing p-adic statistical operators and quantum measurement processes[15]. This work directly endows the p-adic world generated by each prime p with quantum structure, forming a structural correspondence with this paper’s hypothesis that “each prime p is a microson/state unit.”
11.4 Positioning of This Paper
The above research demonstrates that the direction this paper arrives at independently through abductive logic has genuine intersection with the directions professional researchers are exploring through formal technical paths. This simultaneously means two things.
Positive significance: This paper’s intuitive direction is not idle speculation—it points toward a genuinely existing, actively developing research frontier. Abductive logic, without professional training, successfully captured a valid research direction.
Honest limitation: This paper is not a pioneer in this direction. The researchers cited above are already doing more specific, more formalized work. This paper’s possible contribution lies not in discovering the direction, but in providing a different motivational narrative—arguing at the philosophical level why this path should be taken, and where it leads.
Multiple independent paths—abductive philosophy, quantum information theory, p-adic analysis—pointing in the same direction can itself be viewed as indirect evidence that the direction possesses some structural reality. But “convergence of multiple paths” may also simply demonstrate that the surface similarity between quantum mechanics and number theory easily attracts cross-disciplinary analogical thinking. Prudent judgment requires more formalized verification.
XII. Reasoning Chain
XIII. Honest Boundaries
13.1 What This Paper Is
This paper is a philosophical thought paper that uses abductive logic to conduct a cross-disciplinary conceptual analysis of the BSD conjecture. It proposes a series of hypothetical conceptual frameworks—”state layer,” “microson,” “quantum function”—as possible perspectives for thinking about deep problems in number theory.
13.2 What This Paper Is Not
This paper does not constitute any mathematical progress. “Microson” and “quantum function” are currently philosophical concepts, not mathematical definitions. They have no axiomatic formulation, have not produced verifiable mathematical corollaries, and have not been rigorously interfaced with any known theorem.
Within the author’s disciplinary spectrum (see “Full Spectrum of Human Knowledge”), this paper’s SN positioning is approximately −70 to −80—highly dependent on logical construction, with near-zero physical alignment. It is far from the mathematics-physics balance zone (SN≈0).
Furthermore, this paper is essentially a meta-conjecture—not a conjecture about specific mathematical objects, but a conjecture about “why conjectures are difficult to prove.” Meta-conjectures have a fundamental limitation: they are unfalsifiable. If someone proves BSD within the existing framework, this paper’s framework will not be overturned; if no one ever proves it, this paper’s framework will not be confirmed either. This unfalsifiability is a structural weakness that this paper must honestly confront.
13.3 Existing Approximations and Their Shortcomings
| Existing Concept | Degree of Approximation | Shortcoming |
|---|---|---|
| Category Theory · Natural Transformations | Describes consistency of a family of mappings | Still within deterministic framework |
| Sheaf Gluing Conditions | Global emerges from local | Gluing conditions themselves are deterministic |
| Grothendieck’s Motives | Dream of universal cohomology | Core parts remain conjectural |
| Connes’s KMS States | Directly describes zeta zeros using quantum states | Uses states to interpret existing objects; does not redefine functions |
| Quantum Logic | Non-Boolean lattice of propositions | Does not reach the function definition layer |
13.4 If the Direction Is Correct, What Is the Next Step?
The distance from philosophical framework to mathematical construction is far greater than intuition suggests. The most critical next step is not to continue expanding concepts, but to land—to use the microson framework to re-derive a known, simplest number-theoretic result. If the framework can naturally yield the L-function value of even a single rank-0 elliptic curve, it will have crossed from philosophy into mathematics. Until then, it is an interesting thought experiment—no more, no less.
XIV. Conclusion
Every dimensional leap in mathematics, at the moment it occurs, does not look like “good mathematics” but like a nearly insane question. Cardano’s √−1, Hensel’s p-adic numbers, Grothendieck’s schemes—in hindsight they are strokes of genius; at the time they appeared as incomprehensible assumptions.
This paper’s question is: what if functions are not deterministic?
This question may point in the right direction, or it may be a sandcastle. The criterion is not logical self-consistency—there are infinitely many logically self-consistent frameworks—but whether it can produce a hard interface with the actual structures of mathematical physics. What is needed is not more abductive leaps, but step-by-step formalized construction and verification.
Anchored thought is the seed of science. Unanchored thought is pollen in the wind—it may take root, or it may not. Honestly marking one’s position is the first step from pollen to seed.
References
- [1]Montgomery, H.L. (1973). “The pair correlation of zeros of the zeta function.” Analytic Number Theory, Proc. Sympos. Pure Math., Vol. XXIV, pp. 181–193. AMS, Providence, RI.
- [2]Gross, B.H. & Zagier, D.B. (1986). “Heegner points and derivatives of L-series.” Inventiones Mathematicae, 84(2), 225–320.
- [3]Kolyvagin, V.A. (1990). “Euler systems.” The Grothendieck Festschrift, Vol. II, pp. 435–483. Birkhäuser, Boston.
- [4]Peirce, C.S. (1903). “Harvard Lectures on Pragmatism.” Collected Papers of Charles Sanders Peirce, Vols. 5–6. Harvard University Press.
- [5]Heeffer, A. (2007). “Abduction as a strategy for concept formation in mathematics.” In T. Nickles (Ed.), Abduction and the Process of Scientific Discovery. Foundations of Science.
- [6]Hensel, K. (1897). “Über eine neue Begründung der Theorie der algebraischen Zahlen.” Jahresbericht der Deutschen Mathematiker-Vereinigung, 6, 83–88.
- [7]Grothendieck, A. (1960–1967). Éléments de géométrie algébrique (EGA), with J. Dieudonné. Publications Mathématiques de l’IHÉS.
- [8]Connes, A. (1999). “Trace formula in noncommutative geometry and the zeros of the Riemann zeta function.” Selecta Mathematica, 5(1), 29–106.
- [9]Grgin, E. (2018). “Structural unification of quantum mechanics and relativity.” arXiv preprint.
- [10]Renou, M.O. et al. (2021). “Quantum theory based on real numbers can be experimentally falsified.” Nature, 600, 625–629.
- [11]Chen, M.C. et al. (2022). “Ruling out real-valued standard formalism of quantum theory.” Physical Review Letters, 128(4), 040403.
- [12]Daiha, L. (2021). “A quantum number theory.” arXiv:2108.10145.
- [13]Latorre, J.I. & Sierra, G. (2020). “The Prime state and its quantum relatives.” arXiv:2005.02422.
- [14]Benioff, P. (2007). “Space of Quantum Theory Representations of Natural Numbers, Integers, and Rational Numbers.” arXiv:0704.3574.
- [15]Khrennikov, A. et al. (2023). “A p-Adic Model of Quantum States and the p-Adic Qubit.” Entropy, 25(1), 86.
Disclaimer This paper is an independent thought paper (Thought Paper) and has not been peer-reviewed. Concepts such as “microson” and “quantum function” are hypothetical philosophical constructs and do not constitute mathematical definitions or mathematical proofs. This paper aims to provide a cross-disciplinary conceptual perspective for reference and critique in the fields of philosophy of mathematics and foundational research. The author fully recognizes the fundamental chasm between philosophical intuition and mathematical construction.