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Quantum Mechanics as a Projection of B7/B13 Wave Duality

Algis Olbiks, (AI) DeepSeek

Published Oct 3, 2026• 0 citations
Publisher

Abstract

We present a structural framework in which quantum mechanics emerges from the B7/B13 wave duality on a discrete cubic lattice with step l_P. Main findings: (A) The complex wave function arises from two real bases: Psi = psi_B7 + i·psi_B13, where B7 is the closed wave (0-form) and B13 is the flowing wave (1-form). The complex nature of the wave function is not postulated — it is derived from octahedral geometry. (B) Mass is the average energy of B7/B13 sites: m = N_p(n)^2 [1 - eta/(7C)] × m_pi/4, where N_p(n) = 3(16 + n·2^{n-1}), eta is the B7/B13 equilibrium parameter, and C = 35.325 is the cyclic constant. (C) The potential consists of two sources: V(x) = V_source(x) + V_background(x), where V_source is the Coulomb/gravity potential and V_background comes from rho_V modulation. (D) Multi-particle formalism follows from B7/B13: bosons are B7⊗B7 + B13⊗B13 (symmetric), fermions are B7⊗B13 - B13⊗B7 (antisymmetric), and the Pauli principle follows from Psi_A(1,1) = 0. (E) Decoherence is the loss of B7/B13 phase coherence; measurement is the B13 → B7 transition; the Born rule follows from decoherence. All five quantum mechanical postulates (complex wave function, Schrödinger equation, Born rule, measurement collapse, Pauli principle) become derivations from a single geometric structure. The document is not a proven theory. It is an invitation to further research within any theoretical framework capable of pursuing these directions. We present what we have found, mark what is proven versus hypothesized, and identify concrete predictions: decoherence time ~10^{-17} s for molecules, rho_V effects on atomic spectra in galactic centers, and quantum Zeno effect dependence on eta_eq. Notes:This document is part of the Matrix Theory (MT) series. It presents the complete derivation of quantum mechanics from B7/B13 wave duality, covering five steps: (1) B7/B13 wave duality, (2) mass from B7/B13, (3) potential from rho_V modulation, (4) multi-particle formalism, (5) decoherence model. It should be read alongside the B7/B13 Wave Duality paper (DOI: 10.5281/zenodo.23111157), which establishes the common core. Working protocol documents (MT_ANNIHILATION v3.6, MT_ROADMAP v3.0, MT_ID_GRADIENT v3.0) are available as supplementary materials. Contributors:Olbiks, Algis — Conceptualization, Methodology, Validation, Writing - original draftDeepSeek (AI) — Formal analysis, Investigation, Writing - review & editing

DOI
10.5281/zenodo.23114836

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•Apr 23, 2026•0 citations

The An Theory: A Unified Local Realist Framework for Quantum Mechanics,Gravity, and Fundamental Interactions from a Single Nearest-Neighbor

An Haizhong

We present the An Theory, a unified physical framework derived from one assumption (space consists of discrete, indivisible field quanta) and one rule (adjacent field quanta attract each other, with strength proportional to the product of their excitation levels, and strictly conserved total excitation). This rule is not ad hoc: it is structurally isomorphic to van der Waals forces, nuclear binding, the Casimir effect, and Bose–Einstein condensation. From this single rule, we derive the following key results: (1) stable self-bound topological structures with a “hard core + extended ripple” profile, which accounts for wave-particle duality and yields the Born rule in the weak-excitation limit; (2) Newtonian gravity (F ∝ M1M2/r²) as the macroscopic sum of all nearest-neighbor attractions, where the inverse-square law arises solely from 3D geometry and flux conservation; (3) gravitational and motion time dilation, the equivalence principle, the constancy of c, and Lorentz invariance as emergent phenomena; (4) an all-or-nothing threshold mechanism for quantum measurement, providing complete local realist accounts of double-slit interference, quantum erasure, delayed choice, and entanglement; (5) three independent fundamental forces—gravity (baseline attraction), the strong force (high-excitation contact binding, verified across 225 parameter combinations), and the electric force (permanent stress from topological orientation knots, verified in 2D and 3D)—with the magnetic force as the dynamic effect of moving electric charges; (6) the 3D Topological Slot Model, where fractional quark charges arise from the three orthogonal dimensions of space, and all 12 Standard Model fundamental fermions are classified by “geometric complexity × excitation level”; (7) quark confinement, verified using a three-component coupled GL equation with Josephson phase-locking; (8) the mass hierarchy resulting from coherence-length relaxation versus strong-force compression; (9) the topological origin of spin-1/2 from the double-connectedness of SO(3); (10) E = mc² derived from wave mechanics. The framework yields three falsifiable predictions: no fourth-generation fermions, no magnetic monopoles, and no fractional charges other than multiples of 1/3. Its central decisive prediction—a sharp threshold step in interference visibility versus path-marker coupling strength—is qualitatively incompatible with standard quantum mechanics and testable with existing equipment. All results follow from the single assumption + single rule, with no free parameters introduced beyond the foundational rule.

•Apr 8, 2026•0 citations
We present a structural framework in which quantum mechanics emerges from the B7/B13 wave duality on a discrete cubic lattice with step l_P. Main findings: (A) The complex wave function arises from two real bases: Psi = psi_B7 + i·psi_B13, where B7 is the closed wave (0-form) and B13 is the flowing wave (1-form). The complex nature of the wave function is not postulated — it is derived from octahedral geometry. (B) Mass is the average energy of B7/B13 sites: m = N_p(n)^2 [1 - eta/(7C)] × m_pi/4, where N_p(n) = 3(16 + n·2^{n-1}), eta is the B7/B13 equilibrium parameter, and C = 35.325 is the cyclic constant. (C) The potential consists of two sources: V(x) = V_source(x) + V_background(x), where V_source is the Coulomb/gravity potential and V_background comes from rho_V modulation. (D) Multi-particle formalism follows from B7/B13: bosons are B7⊗B7 + B13⊗B13 (symmetric), fermions are B7⊗B13 - B13⊗B7 (antisymmetric), and the Pauli principle follows from Psi_A(1,1) = 0. (E) Decoherence is the loss of B7/B13 phase coherence; measurement is the B13 → B7 transition; the Born rule follows from decoherence. All five quantum mechanical postulates (complex wave function, Schrödinger equation, Born rule, measurement collapse, Pauli principle) become derivations from a single geometric structure. The document is not a proven theory. It is an invitation to further research within any theoretical framework capable of pursuing these directions. We present what we have found, mark what is proven versus hypothesized, and identify concrete predictions: decoherence time ~10^{-17} s for molecules, rho_V effects on atomic spectra in galactic centers, and quantum Zeno effect dependence on eta_eq. Notes:This document is part of the Matrix Theory (MT) series. It presents the complete derivation of quantum mechanics from B7/B13 wave duality, covering five steps: (1) B7/B13 wave duality, (2) mass from B7/B13, (3) potential from rho_V modulation, (4) multi-particle formalism, (5) decoherence model. It should be read alongside the B7/B13 Wave Duality paper (DOI: 10.5281/zenodo.23111157), which establishes the common core. Working protocol documents (MT_ANNIHILATION v3.6, MT_ROADMAP v3.0, MT_ID_GRADIENT v3.0) are available as supplementary materials. Contributors:Olbiks, Algis — Conceptualization, Methodology, Validation, Writing - original draftDeepSeek (AI) — Formal analysis, Investigation, Writing - review & editing
Important status notice: This version has been superseded by v2.0. Subsequent work shows that the single-domain three-diagonal construction used here produces an experimentally excluded common-mode photon-speed anisotropy. Readers should consult the revised version and 10.5281/zenodo.21464971. We propose that conservation of probability — the single axiom A=1 — is sufficient to derive the principal results of quantum mechanics without additional postulates. On a bipartite three-dimensional causal lattice T³_diamond, each particle is represented as a causal session: an independent phase oscillator that propagates amplitude across the lattice subject to |ψ_R|² + |ψ_L|² = 1 at every tick. No Hamiltonian and no measurement postulate are assumed; a Hilbert-space structure with unitary evolution emerges from the U(1) oscillator and the per-session amplitude constraint rather than being postulated a priori. From this single constraint, the paper derives: (i) the Dirac equation in the continuum limit a→0, with the gamma matrices identified as geometric encodings of the bipartite RGB/CMY sublattice geometry; (ii) wave-particle duality and the Born rule as consequences of amplitude redistribution under A=1, with Gleason's theorem securing the |ψ|² uniqueness from the framework's emergent Hilbert space; (iii) quantization of atomic orbitals as Arnold tongue attractors of the two-body phase dynamics, recovering the hydrogen Bohr radius to four significant figures (k_min = 0.0970 vs k_Bohr = 0.0971) without fitting; (iv) gravity as a clock-density gradient rather than spacetime curvature — a refraction of causal paths through regions of higher session density, reproducing the 1/r² force law with an explicit weak-field metric tensor g_μν as a functional of the clock-density field; (v) photon emission as a structural consequence of A=1: the Coulomb interaction is a probability source that a single session cannot accommodate, mandating creation of a new photon session at orbit lock-in; (vi) the structural form of the induced gauge action (Sakharov / Zeldovich), whose leading-order term has the Maxwell form on O_h-averaged observables, with a closed-form gauge-sector birefringence sharing the same optical axis (1,1,−1) as the kinematic-sector prediction. Energy and momentum conservation are not independent inputs — they are consequences of A=1 applied to closed session sets. The numerically tractable results are verified or partially verified by a suite of more than fifteen experiments with no free parameters beyond the Planck-scale calibration of the lattice spacing; an audit table records the status of every claim. The paper conjectures that the Standard Model gauge group SU(3) × SU(2) × U(1), together with Lorentz SO(3,1), is the automorphism group of the framework's extended per-site amplitude — a precise 18-dimensional Lie-algebra equality. The existing framework is shown to carry SO(3,1) × U(1) (dim 7) on the per-site (ψ_R, ψ_L) amplitude; the remaining factors require structural extensions (per-site C² isospin and C³ colour indices) that are the subject of a companion paper. Six computational scaffolding scripts establish the conjecture's components. This is Paper I of the A=1 Discrete Causal Lattice series. Companion papers in preparation address the Standard Model gauge derivation, the Farey-sequence mass spectrum (and its Veneziano-amplitude limiting case), plasma and gradient-ionization phenomenology, the proton-interior structure, quantum measurement theory, and a Hilbert-6th-style combinatorial foundation for continuum physics. What changed in v1.0 (since v0.98-RC): * Three new audit-table rows: long-horizon escape mechanism (PART), lock-in resonance grid-independence across {65, 81, 97, 113}³ grids (PART), and the Standard Model gauge-group conjecture as a precise 18-dimensional Lie-algebra equality (STUB).* A Gleason-uniqueness subsubsection in the Born-rule discussion, addressing the necessity question for the |ψ|² measure.* An explicit metric-tensor formula in the gravity section, identifying g_μν as a functional of ρ_clock in the weak-field limit.* Refined automorphism conjecture with explicit decomposition into established and structural-extension factors.* New Acknowledgments section. Source code, paper sources, and data files: https://github.com/JackDMenendez/discrete-causal-latticeLicense: Paper text and figures CC BY 4.0; source code MIT.
We present complex-time (CT) theory, a framework in which the fundamental structures of quantum mechanics are derived from three physical postulates concerning the internal structure of time. The postulates are: (P1) physical time possesses two orthogonal components — past-fixed (pf), representing actualized, irreversible records, and future-pending (fp), representing physically real but undetermined possibilities; (P2) pf and fp are orthogonal (pf fp); and (P3) the total temporal magnitude is conserved (pf + fp = 1). From these three postulates alone, we show that: (i) the state space is the unit circle and the dynamical group is , so that the imaginary unit arises as the unique generator of temporal evolution — not as a mathematical convenience but as a consequence of temporal geometry; (ii) the Schrödinger equation follows from the identification of energy with the rate of phase rotation in the pf–fp plane, with the Planck constant playing the role of a natural constant intrinsic to the pf/fp structure; (iii) the de Broglie–Einstein relation holds universally — for massive and massless particles alike — because the wave structure belongs to time itself, not to any particular particle; (iv) the uncertainty principle is a geometric consequence of the impossibility of fully eliminating fp while preserving ; (v) the complex structure of Hilbert space, the inner product, and the Born rule all follow from the geometry of fp pf projection; and (vi) energy quantization emerges from a “real-axis sampling” rule without imposing discreteness on the underlying dynamics. We further show that the CT framework provides unified descriptions of double-slit interference, quantum tunneling, unstable-state decay widths, and the structural origin of the arrow of time. Preliminary experimental predictions for quantum-circuit observables are stated, and applications to cosmological dark-energy phenomenology, galaxy rotation curves, and Lorentzian path-integral contour selection are outlined with references to dedicated companion papers. The central thesis is that quantum mechanics is not a theory of particles with mysterious wave-like properties, but a consequence of the internal structure of time — time whose wave-like phase (fp) is projected, irreversibly and discretely, onto the real axis (pf) in every act of measurement. Keywords: complex time; temporal structure; imaginary unit; quantum mechanics derivation; past-fixed / future-pending decomposition; Born rule; energy quantization; measurement; irreversibility; arrow of time
This work derives the fundamental framework of quantum mechanics intrinsically from the first-principle axioms of UD duality theory. Starting from the inherent binary expansive–condensative attributes of the UD ontology, four fundamental physical fields are naturally decomposed by spontaneous symmetry breaking across spatial and material existential domains. A two-component complex spinor structure is uniquely constructed, and the imaginary unit i is proven to be not merely a mathematical convention but a structurally necessary ingredient required by both the compact SU(2) symmetry and the orthogonal inter-containment of U and D attributes. Within the flat spacetime limit of the UD gravitational action, a system of coupled Klein–Gordon field equations is established, governed by a single self-consistent fundamental mass scale m₀=1/(2πe^π) with no adjustable free parameters. The coupling constant is determined analytically from the UD vacuum equilibrium background values and the U↔D duality symmetry. Through explicit construction of four-component Dirac spinors and auxiliary field decomposition, the on-shell equivalence between the UD coupled field equations and the free Dirac equation is rigorously demonstrated. The non-relativistic limit further recovers the Pauli equation and the Schrödinger equation sequentially, reconstructing the core dynamical equations of quantum mechanics from a unified foundational origin. Global U(1) phase invariance of the UD action is verified via total-derivative decomposition, yielding the standard Noether conserved current. The Born probability interpretation is deduced directly from the global normalization axiom by isolating localized laboratory-scale excitations from the cosmic background, eliminating the need for independent quantum postulates. Based on the intrinsic properties of the UD field components, a self-consistent ontological interpretation is provided for wave–particle duality, double-slit interference, and the quantum measurement problem. In this framework, the measurement problem is dissolved rather than solved: no collapse postulate is required, and determinism is restored at the ontological level. The theory naturally implies that the continuous D_U field permits quantum superposition, while condensed D_D intrinsic entities possess definite classicality without physical particle-state superposition. Three testable theoretical predictions are presented, establishing falsifiable physical consequences of the UD quantum formulation. This paper completes the intrinsic derivation of the foundational structure of quantum mechanics from UD theory. Together with the previously derived general relativity framework, it realizes the homologous unification of gravity and quantum mechanics within a single self-contained axiomatic system.
This series presents a structured and logically sequential formulation of a discrete informational framework governed by global coherence constraints. Although it originates from the same research program developed in the earlier exploratory preprint series (P-series), the works presented here constitute an autonomous and self-contained series, organized in a progressively axiomatic form and focused on the explicit derivation of the framework’s effective structures. The goal of the construction is to investigate whether structures commonly associated with quantum mechanics, thermodynamics, and geometry may emerge from a discrete relational substrate without being introduced as fundamental postulates. Each article addresses a specific level of the theoretical derivation and forms part of a progressive logical structure based on results established in the preceding works of the series. This article develops the emergence of Hilbert-space structure and Schrödinger-type effective dynamics from the coherent two-field sector established in Paper 02. The work demonstrates that the global coherence constraints imposed on the discrete informational substrate naturally generate an effective complex representation endowed with linear superposition properties and unitary-preserving evolution. The analysis shows that the two-component coherent sector admits a mathematically stable reformulation equivalent to a Hilbert-space structure, and that the effective evolution of the coherent amplitudes leads to a Schrödinger-type dynamical equation without introducing quantum mechanics as an initial assumption. The article further derives the probabilistic interpretation associated with the effective amplitudes and clarifies how quantum-like statistical behavior emerges from the internal coherence conditions of the underlying discrete system. No quantum postulates are assumed at the foundational level. The purpose of the article is to demonstrate that the formal structures associated with quantum mechanics can emerge as effective consequences of coherence-preserving informational dynamics. The article does not assume quantum mechanics as a foundational theory and does not postulate the Hilbert-space formalism a priori. Instead, the work demonstrates that, within the internal hypotheses and coherence constraints of the proposed discrete informational framework, structures mathematically equivalent to Hilbert-space representations and Schrödinger-type evolution can arise as effective emergent descriptions. The purpose of the derivation is therefore not to reproduce standard quantum mechanics by assumption, but to show that quantum-like formal structures may consistently emerge from deeper coherence-preserving informational dynamics.
What is quantum mechanics, constitutionally? This document provides the answer within the Energy-Efficiency Theory framework: quantum mechanics is not an independent set of physical laws, nor a "theory of particles," nor a "theory of measurement." Quantum mechanics is the dynamics of non-matter—the coherent propagation of free-state energy (E_f, E_c = 0) along Type II edges of the constraint network at the optimal cooperative capacity point η ≈ 1. Constraint Dynamics (CND v4.0) describes the dynamics of matter (Being, E_c > 0). Measurement is the constitutional interface between them: a Cut → Encapsulate event at the Type I/Type II boundary that terminates non-matter propagation and creates a persistent matter record. The QM ↔ Measurement Constitutional Duality is the constitutional expression of the Non-Matter/Matter distinction in dynamics. Version 3.1 is a comprehensive constitutional upgrade that preserves all v3.0 content while introducing five core refinements. (i) The Matter/Non-Matter constitutional framework (Particle v3.3) is implanted throughout: QM governs non-matter; measurement is the non-matter → matter constitutional transition; the wavefunction ψ = |ψ| e^{iS/A_EET} is the complex amplitude of non-matter propagation—physically real (ontic), not epistemic, not many-worlds. (ii) Barrier Asymmetry is conditionalized: E_b^melt ≫ E_b^form emerges from Γ(η) decay at η ≠ 1; at η = 1, E_b^form = E_b^melt = A_EET · ω (Inertia v3.4, CLOSED). Quantum coherence is protected by the three-engine architecture. (iii) The decoherence rate is corrected from a contradictory single-factor model to a two-channel additive model distinguishing encapsulation-driven decoherence (∝ f_enc(L)) from efficiency-imbalance-driven decoherence (∝ 1−Γ(η)). (iv) The quantum-to-classical transition is refined from a binary "L ≥ 3" threshold to a three-regime crossover governance (L ≤ 2 quantum, L = 3–4 crossover, L ≥ 5 effective classical), with the L_branch concept distinguishing whole-object coherence (excluded) from collective-coordinate coherence (experimentally observed). (v) The Schrödinger's cat paradox receives its constitutional resolution: the radioactive atom is non-matter (transient constraint events); the cat is matter (E ∈ {0,1} binary). The paradox arises from conflating these two constitutional domains. Ten core constitutional deepenings distinguish v3.1 from its predecessor. DEEPENING-1: The wavefunction's ontic status is systematically situated against all six major QM interpretations (Copenhagen, Many-Worlds, de Broglie–Bohm, QBism, GRW, EET), establishing EET's distinct constitutional position. DEEPENING-2: The five-channel complete constraint Second Law (CND v4.0, CLOSED) is integrated into the quantum measurement framework, unifying passive decoherence, environmental decoherence, and measurement-induced decoherence as three variants of meltdown channel activation. DEEPENING-3: The dual-channel decoherence model unifies elastic decoherence (reversible, ∝ 1−Γ(η)) and plastic decoherence (irreversible, ∝ C(t), measurement collapse) within a single constitutional framework, resolving the measurement problem. DEEPENING-4: The non-matter → matter constitutional transition is established as the three-step measurement dynamics (Difference Detection → Template Matching → Persistent Record Formation), constitutionally anchored in the constraint formation competition framework. DEEPENING-5: The line graph duality (Field v3.1 R4, Particle v3.3 Part VI) is registered as the graph-theoretic foundation of wave-particle duality—not a quantum mystery, but a universal graph-theoretic theorem. DEEPENING-6: QM and GR co-originate from the energy bifurcation at η = 1: QM is the dynamics of non-matter; GR is the geometry of matter. No "quantization of gravity" is required. DEEPENING-7: Emergent Minkowski spacetime (Space v3.3 §5, Time v3.2 §3.4) is constitutionally registered as QM's constitutional stage—not the background in which QM operates, but the symmetry that emerges at the optimal cooperative capacity point. DEEPENING-8: The quantum-to-classical crossover is governed by three independent constitutional mechanisms (decoherence via meltdown channel, force attenuation via encapsulation depth, and jamming via constraint density), of which decoherence and force attenuation are fully developed in v3.1. DEEPENING-9: Quantum information is constitutionally distinguished as transient information (non-matter, no constraint boundary, no maintenance power, no inertial mass), to be contrasted with constraint-grounded information (matter, persistent, E = mc² > 0). DEEPENING-10: The constitutional responses to twenty-six major problems in quantum mechanics are systematically registered, spanning CLOSED-in-EET (QM-GR co-origination, wave-particle duality, QM ↔ Measurement duality), STANDARD (measurement problem constitutionally located, two-channel decoherence, emergent Minkowski spacetime), WORKING HYPOTHESIS (mass as coarse coherence proxy, quantum Darwinism reformulated as blind pump), and CONJECTURE (AdS/CFT correspondence, CDT/MERA emergence). The document is organized as follows. Part I establishes the constitutional foundations, including the Matter/Non-Matter constitutional chain, Barrier Asymmetry conditionalized, and the QFT vs. EET ontological incommensurability. Part II defines QM as non-matter dynamics, establishes the wavefunction as the complex amplitude of non-matter propagation (with systematic comparison to all major QM interpretations), and delineates the constitutional domain boundaries. Part III provides the complete companion ontology interface system, synchronized through June 2026. Part IV-A presents the mathematical foundations, including the Schrödinger equation dual-path derivation and the constraint network path integral. Part IV-B develops quantum states and dynamics, with entanglement re-expressed as shared constraint boundary topology. Part IV-C provides the measurement framework—the non-matter → matter constitutional transition, five-channel measurement, and responses to Frauchiger-Renner, Leggett-Garg, and indefinite causal order. Part IV-D presents the unified two-channel decoherence model and the quantum-to-classical crossover governance with the L_branch concept. Part IV-E treats the vacuum as the N=0 ground state. Part V covers cross-scale instantiation. Part VI provides nine falsifiable predictions. Part VII lists eleven constitutional open problems. Part VIII systematically registers EET constitutional responses to twenty-six major problems in quantum mechanics. Part IX registers the academic priority of forty-eight constitutional claims. Quantum mechanics is the dynamics of the non-material substrate at its optimal operating point. Measurement is the constitutional transition from non-matter to matter. The Schrödinger equation is the deterministic law of non-matter propagation. The Born rule is the statistical law of the non-matter/matter interface. Together, they constitute the complete constitutional framework of quantum mechanics in EET. Keywords: Non-matter dynamics; matter/non-matter distinction; constraint network; coherent free-state propagation; measurement as constitutional transition; two-channel decoherence; quantum-to-classical crossover; encapsulation-depth refinement; Born rule as interface statistics; η-generalized Lindblad equation; emergent Minkowski spacetime; line graph duality; constitutional ontology of quantum mechanics; Energy-Efficiency Theory.
We present the An Theory, a unified physical framework derived from one assumption (space consists of discrete, indivisible field quanta) and one rule (adjacent field quanta attract each other, with strength proportional to the product of their excitation levels, and strictly conserved total excitation). This rule is not ad hoc: it is structurally isomorphic to van der Waals forces, nuclear binding, the Casimir effect, and Bose–Einstein condensation. From this single rule, we derive the following key results: (1) stable self-bound topological structures with a “hard core + extended ripple” profile, which accounts for wave-particle duality and yields the Born rule in the weak-excitation limit; (2) Newtonian gravity (F ∝ M1M2/r²) as the macroscopic sum of all nearest-neighbor attractions, where the inverse-square law arises solely from 3D geometry and flux conservation; (3) gravitational and motion time dilation, the equivalence principle, the constancy of c, and Lorentz invariance as emergent phenomena; (4) an all-or-nothing threshold mechanism for quantum measurement, providing complete local realist accounts of double-slit interference, quantum erasure, delayed choice, and entanglement; (5) three independent fundamental forces—gravity (baseline attraction), the strong force (high-excitation contact binding, verified across 225 parameter combinations), and the electric force (permanent stress from topological orientation knots, verified in 2D and 3D)—with the magnetic force as the dynamic effect of moving electric charges; (6) the 3D Topological Slot Model, where fractional quark charges arise from the three orthogonal dimensions of space, and all 12 Standard Model fundamental fermions are classified by “geometric complexity × excitation level”; (7) quark confinement, verified using a three-component coupled GL equation with Josephson phase-locking; (8) the mass hierarchy resulting from coherence-length relaxation versus strong-force compression; (9) the topological origin of spin-1/2 from the double-connectedness of SO(3); (10) E = mc² derived from wave mechanics. The framework yields three falsifiable predictions: no fourth-generation fermions, no magnetic monopoles, and no fractional charges other than multiples of 1/3. Its central decisive prediction—a sharp threshold step in interference visibility versus path-marker coupling strength—is qualitatively incompatible with standard quantum mechanics and testable with existing equipment. All results follow from the single assumption + single rule, with no free parameters introduced beyond the foundational rule.