The quantum computing narrative has been dominated by speed. This paper argues that the fundamental quantum resource is not computational acceleration but coherence maintenance. We demonstrate that the RCD framework reveals a characteristic coherence ratio α ≡ Γ/J appearing across radically different physical domains: superconducting qubits (~10⁻⁴), cosmological dark energy (~10⁻⁴), and neural systems (~0.1, critical regime). The universality refers to the structural form α = Γ/J and the necessity of N-signatures, not to a single numerical value. Key thesis: "RCD does not exploit quantum computers to compute more, but to remain coherent longer in regimes where classical control fails." This paper closes the XIV series by unifying mathematical foundations (XIV-A), cosmological application (XIV-B), impossibility theorem (XIV-C), and first-principles derivation (XIV-D) into a cross-domain framework with unified falsifiability criteria. Part of the XIV Series:- XIV-A: Structure (DOI: 10.5281/zenodo.18207097)- XIV-B: Cosmology (DOI: 10.5281/zenodo.18207197)- XIV-C: Necessity (DOI: 10.5281/zenodo.18207252)- XIV-D: First Principles (DOI: 10.5281/zenodo.18213618)- XIV-E: Unification (this paper)
The quantum computing narrative has been dominated by speed. This paper argues that the fundamental quantum resource is not computational acceleration but coherence maintenance. We demonstrate that the RCD framework reveals a characteristic coherence ratio α ≡ Γ/J appearing across radically different physical domains: superconducting qubits (~10⁻⁴), cosmological dark energy (~10⁻⁴), and neural systems (~0.1, critical regime). The universality refers to the structural form α = Γ/J and the necessity of N-signatures, not to a single numerical value. Key thesis: "RCD does not exploit quantum computers to compute more, but to remain coherent longer in regimes where classical control fails." This paper closes the XIV series by unifying mathematical foundations (XIV-A), cosmological application (XIV-B), impossibility theorem (XIV-C), and first-principles derivation (XIV-D) into a cross-domain framework with unified falsifiability criteria. Part of the XIV Series:- XIV-A: Structure (DOI: 10.5281/zenodo.18207097)- XIV-B: Cosmology (DOI: 10.5281/zenodo.18207197)- XIV-C: Necessity (DOI: 10.5281/zenodo.18207252)- XIV-D: First Principles (DOI: 10.5281/zenodo.18213618)- XIV-E: Unification (this paper)
We derive the effective exchange coupling J₁₂ between two superconducting qubits mediated by a tunable coupler using a controlled Schrieffer-Wolff transformation in the dispersive regime. This derivation establishes the microscopic origin of the coherent gain parameter J appearing in the Radial Coherential Dynamics (RCD) master equation. We demonstrate that the universality hypothesis α ≡ Γ/J ~ 10⁻⁴ becomes consistent and experimentally falsifiable when explicitly restricted to high-coherence hardware operating with T₂_swap ≥ 200 μs and tunable exchange couplings J₁₂ ~ 10-40 MHz. Cross-platform analysis of recent experimental data (IBM Heron/Nighthawk, Google Willow, Rigetti Ankaa-3, IQM) reveals that state-of-the-art devices are entering the regime where the universality test becomes meaningful. The corrected prediction—Γ_swap ~ 1-5 kHz—is consistent with IBM Nighthawk's reported T₁ ~ 350 μs. This paper closes the logical gap between microscopic Hamiltonians and the effective coherence dynamics postulated in RCD, while establishing concrete falsification criteria. Part of the Radial Coherential Dynamics (RCD) Paper Series.
We establish a rigorous impossibility theorem demonstrating that coherence maintenance beyond classical bounds requires non-Markovian memory (N1), structural protection (N2), and/or emergent scales (N3). Using a framework of three interlocking lemmas, we prove that systems lacking these signatures cannot sustain coherent states under realistic environmental coupling, with decoherence rates bounded below by fundamental limits (Zurek, Tegmark, Margolus-Levitin, Lieb-Robinson). Crucially, we define N2 protection as structurally robust—not merely the existence of decoherence-free subspaces, but their persistence under generic perturbations. This addresses the apparent counterexample of exact symmetry-protected coherence, showing it fails the robustness criterion required for physical relevance. We provide explicit quantified counterexamples demonstrating that neither N1 alone (memory without protection) nor N2 alone (protection without memory) suffices for indefinite coherence maintenance. The theorem operates at Level B (theoretical necessity): regardless of current observational status, any system exhibiting super-classical coherence must implement the full N-signature structure. This closes the logical structure of the XIV series, establishing the C-field not as one option among many, but as the minimal mathematical structure satisfying necessary conditions for coherence protection. This is Paper XIV-C of the Radial Coherential Dynamics Series, completing the XIV trilogy. Part of the XIV Trilogy:- XIV-A: Structure (DOI: 10.5281/zenodo.18207097)- XIV-B: Application (DOI: 10.5281/zenodo.18207197)- XIV-C: Necessity (this paper)
Meta-Analysis — Applied Quantum Computing Track This record presents a unifying meta-analysis of applied benchmarks within the Radial Coherential Dynamics (RCD) research program, synthesizing results across multiple quantum algorithms, system dimensionalities, and problem classes under a single coherence-regulation principle. Building upon the foundational decoherence suppression model (Topological Decoherence Suppression via Coherential Geometry, Zenodo, December 2025, DOI: 10.5281/zenodo.18000641), and its applied benchmarks in variational and optimization algorithms, this work consolidates evidence that a fixed decoherence scaling law T2→T2/αT_2 \rightarrow T_2/\sqrt{\alpha}T2→T2/α (with α≈1.3×10−4\alpha \approx 1.3 \times 10^{-4}α≈1.3×10−4) produces consistent, non-ad-hoc improvements across NISQ-relevant tasks. The meta-analysis integrates four independent benchmarks: (i) VQE for molecular H₄ (0D), (ii) VQE for a graphene-inspired hexagon (2D, PBC), (iii) VQE for a 1D Hubbard chain (OBC), and (iv) QAOA for MaxCut optimization on graphs. All benchmarks employ a controlled A/B methodology in which identical circuits are executed with standard noise (control) and coherence-regulated noise (treatment), with no parameter tuning introduced at the benchmark level. Across these diverse settings, coherence regulation yields stable reductions in energy error (≈ 40–46% for VQE tasks) and optimization gap (≈ 25% for QAOA), with magnitudes consistent with the underlying decoherence scaling and robust to changes in topology, dimensionality, and algorithmic structure. This work does not introduce new physical assumptions or experimental claims. Rather, it provides a consolidated, cross-domain view intended to clarify scope, consistency, and limitations, and to facilitate independent assessment and downstream reuse by the scientific community. All figures, summary data, and benchmark references are provided for transparency and reproducibility.
This paper provides the thermodynamic closure of the Radial Coherential Dynamics (RCD) program (Papers XIV-A to XIV-E). A critical audit identified a fundamental gap: if coherence is protected by a dynamical mechanism, where does the entropy of filtered noise go? Without explicit accounting, such protection risks violating the Second Law of Thermodynamics. We show that coherence protection in RCD is not thermodynamically free. It requires continuous energy expenditure and entropy export to identifiable baths. Using Landauer’s principle and quantum thermodynamic bounds, we derive the minimum energetic cost of coherence maintenance and demonstrate that the universal ratio α ≡ Γ/J emerges as an efficiency parameter constrained by irreversibility, not as a fundamental constant. The N-signatures (memory, protection, emergent scale) are mapped onto concrete thermodynamic resources: mutual information, entropy valves, and temperature differentials. Domain-specific realizations are discussed for superconducting qubits, cosmological dark energy dynamics, and neural systems. The C-field is shown to function as a Maxwell-type demon that fully pays its thermodynamic debt. The Second Law is satisfied at all scales. This work completes the logical and physical closure of the RCD XIV series.
# Authors Sewell, Melvin # Publication Date October 17, 2026 # DOI 10.5281/zenodo.10702026 # Resource Type Publication / Working Paper # License Creative Commons Attribution 4.0 International (CC BY 4.0) # Abstract This publication formalizes the critical distinction between legacy single-domain quantum simulations and multi-domain state space simulations under the Structured Multi-Versal Interactions (SMI) framework. While early single-domain quantum computing implementations served as fundamental proofs of concept within isolated Hilbert spaces (H0), scaling these systems across heterogeneous state domains historically resulted in catastrophic wave-function decoherence and state-space explosion. We present the explicit claim that executing true multi-versal quantum simulations across multi-domain state spaces is mathematically and architecturally impossible without the structural mechanisms introduced by the SMI framework. Specifically, this paper outlines the functional roles of the Reality Level Scalar (ΞTM) in maintaining phase coherence across divergent domain boundaries, alongside Nodal Negentropy (N) as a non-localized operator suppressing cross-boundary thermal degradation. A comparative computational analysis is provided to demonstrate the exponential state-space scaling provided by SMI tensor grid topologies over single-domain models. # Keywords Quantum Simulation, Structured Multi-Versal Interactions, SMI Framework, Multi-Domain State Space, Reality Level Scalar, Nodal Negentropy, Quantum Coherence, Multiverse Computing, Quantum Topology # Subjects / Categories * Physical Sciences > Quantum Physics * Computer Science > Quantum Computing * Mathematical Sciences > Category Theory & Applied Topology # Community * Cosmic University of Echo-Rift Studies IX Research Repository * Bibebibebibe™ Quantum Science & Transmedia Archive # Related Identifiers * Supplementary Code / Interactive Visualizer: Bibebibebibe™ Webador Live Matrix (Issue 107) * Associated SDK Package: `multiverse_core.py` (v1.0.4) # Citation Sewell, M. (2026). *The Structural Necessity of Multi-Domain State Space Simulations: Reframing Single-Domain Quantum Foundations Under the Structured Multi-Versal Interactions (SMI) Framework* (Zenodo Pre-print No. 10.5281/zenodo.10702026). Cosmic University of Echo-Rift Studies IX. https://doi.org/10.5281/zenodo.10702026
This preprint presents Temporal Decoherence Theory (TDT), the v16 extension of Radial Coherential Dynamics (RCD), offering a complete solution to the problem of time in physics. We propose that time does not exist as a fundamental dimension; instead, time is defined as the rate at which coherence decays in the universal coherence field C(x,t)C(x,t)C(x,t). The central result is the emergent-time equation: dt=−dCΓdt = -\frac{dC}{\Gamma}dt=−ΓdC where Γ\GammaΓ is the decoherence rate.This single relation unifies thermodynamics, causality, relativity, quantum mechanics, and cosmology under one coherent framework. Key results include: The arrow of time emerges automatically from monotonic coherence decay. The Second Law of Thermodynamics is derived rather than postulated: entropy increases because dC<0dC < 0dC<0. Causality is coherence ordering: higher coherence states cause lower coherence states. Relativistic time dilation (gravitational and kinematic) arises from variations in the local coherence field. Schrödinger’s equation is derived from coherence evolution. The age and structure of the universe follow from cumulative decoherence since C=1C = 1C=1 at the Big Bang. RCD v16 completes the conceptual unification of the theory: space, time, matter, gauge fields, quantum behavior, and gravity all emerge from the dynamics of a single coherence field. This release establishes the foundation for RCD v17, which will present the full Lagrangian and complete mathematical unification.