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)
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)
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 establish formal mathematical isomorphisms between the coherence field C proposed in Radial Coherential Dynamics (RCD) and four established quantum protection mechanisms: continuous quantum Zeno effect, topological energy gaps, continuous dynamical decoupling (CDD), and thermodynamic frustration of decoherence. Our results demonstrate that unprotected quantum entanglement collapses faster than classical schemes under realistic noise, and that only architectures incorporating a dynamic rigidity mechanism — isomorphic to continuous Zeno, topological gaps, or decoherence frustration — can surpass the classical binding limit. Recent experimental validations, including Google Quantum AI's surface code achieving error suppression factor Λ = 2.14 and JILA's Zeno suppression in ultracold KRb molecules, provide empirical grounding for these theoretical correspondences. We demonstrate that the mathematical role played by the RCD C-field is isomorphic to that realized by several established coherence-protection mechanisms, suggesting a common functional role across diverse physical implementations. This is Paper XII in the RCD series, continuing the Quantum Binding track initiated in Paper XI. Keywords: coherence protection, quantum Zeno effect, topological protection, decoherence-free subspaces, quantum error correction, RCD theory, binding problem, isomorphism, Radial Coherential Dynamics
Decoherence stands as the fundamental bottleneck limiting the physical realization of large-scale fault-tolerant quantum computation. Conventional paradigms rely on passive strategies of environmental isolation and post-hoc quantum error correction, inherently bounded by Markovian approximation, weak-coupling assumptions and prohibitive physical qubit overhead. Breaking away from the dissipative preset of traditional open quantum systems, this work establishes a global system-environment closed dynamical framework with rigorous coherence conservation. Without Markovian coarse-graining or thermal bath approximation \cite{1,5}, we derive the exact non-Markovian reduced dynamic equation and present the necessary and sufficient coupling conditions for strictly conserved quantum coherence. We rigorously prove that decoherence is not an intrinsic fundamental law of quantum mechanics, but an emergent consequence of specific interaction structures and artificial approximation constraints. By constructing structured system-environment coupling Hamiltonians, coherent decay can be frozen at the dynamical root, achieving intrinsic decoherence suppression without error correction, topological quasiparticles or magic state distillation. Numerical simulations verify that coherence remains strictly constant under strong environmental coupling for the proposed coupling scheme, in sharp contrast to conventional decaying dynamics. This work reconstructs the underlying paradigm of open quantum systems, eliminates the decoherence bottleneck at the fundamental level, and provides a novel theoretical route toward large-scale, low-overhead, universal fault-tolerant quantum computation.
This paper introduces and formalizes the Principle of Structural Non-Neutrality: In a coherent system, no part can be structurally neutral. Beginning from the quantum limits of measurement—where informative observation necessarily disturbs the observed system—we argue that this apparent "strangeness" of quantum mechanics is not an anomaly but a minimal requirement for any system in which the observer is physically embedded. Classical physics, by contrast, implicitly assumes an external observer who can extract information without interaction—a privilege that no physical theory can consistently grant. From this insight, we derive a sharp distinction between systems and models: A system is that which cannot be known without being changed A model is that which can be known without being changed This distinction yields our central principle: in a genuinely coherent system, every part must contribute to the global structure. Structural neutrality—the presence of a part that makes no difference to the system's state space—is logically incompatible with coherence. Key Contributions Formal definition of structural relevance using mutual information: R(p, S) = I(p; S \ {p}), with exact neutrality defined as R = 0 Proof by contradiction demonstrating that coherent systems (as defined) cannot contain structurally neutral elements Unification of existing frameworks: reliability theory's "component relevance," quantum non-separability, and Integrated Information Theory's irreducibility are shown to be instances of a single structural requirement Resolution of apparent counterexamples: redundant components, silent genes, weakly coupled systems, and gauge degrees of freedom are analyzed and shown to be compatible with the principle Connection to quantum interpretations: the principle constrains (without adjudicating among) many-worlds, decoherence-based, QBist, and relational interpretations Applications: epistemology (coherentist justification), reliability engineering, biological networks, and ecological systems Theoretical Framework The paper traces a conceptual path: Quantum measurement limits → Observer embeddedness → Systems vs. models distinction → Structural non-neutrality principle → Applications across domains The principle is offered not as a revolutionary discovery but as a unifying formulation that makes explicit what several frameworks already imply, while grounding this shared requirement in the impossibility of genuinely external observation. Keywords quantum measurement; observer problem; coherent systems; structural non-neutrality; systems theory; integrated information; reliability theory; quantum foundations; philosophy of physics; mutual information; non-separability; decoherence Academic Context This work bridges quantum foundations, general systems theory, and philosophy of science. It is relevant to researchers in: Foundations of quantum mechanics Philosophy of physics Complex systems theory Integrated Information Theory Reliability engineering Theoretical biology Epistemology (coherentism) Note: This paper underwent multiple rounds of peer review and revision, addressing concerns about scope, mathematical formalization, relation to existing literature, and applicability limits. The final version includes a graded measure of structural relevance, explicit comparison with IIT and reliability theory, treatment of apparent counterexamples, and open questions for future research.
Papers I–III derived specific physical structures from three operational axioms: an action gap, finite accessibility, and intersubjective stability. This paper inverts the question: what structures are forbidden? Seven exclusion theorems are proved, showing that large classes of alternative physics are inadmissible under the operational axioms. Each theorem includes explicit assumptions and rigorous mathematical proof. The excluded structures are: 1. **Arbitrarily precise extended synchronisation** — no protocol can certify synchronisation across a domain exceeding the coherence radius R_coh 2. **Higher-than-second-order local dynamics** — via Ostrogradsky instability and certification cost arguments 3. **Non-Born probability assignments** — via the Cauchy functional equation; the Born rule is the unique continuous, non-contextual invariant measure 4. **Non-three-dimensional geometry** — via flux invariance; only d = 3 permits radius-independent total distinguishability 5. **Non-quartic high-frequency dispersion** — via complex analysis of the EFT derivative expansion 6. **Stable relativistic gravitationally-coupled matter** above the accessibility ceiling 7. **Protocol-dependent physical constants** — universality is forced by intersubjective stability The exclusions collectively define an admissibility corridor: the narrow set of physical structures compatible with bounded intersubjective certification. The paper shows that most logically possible alternatives violate the axioms, and that observed physics lies on structural boundaries of the corridor. **This paper is part of the Finite Accessibility series, which reconstructs gravitational geometry, quantum dynamics, gauge structure, cosmological perturbation theory, and the dark sector from a single operational primitive: a finite certification ceiling ω* governing the maximum rate at which physical relations can be maintained across extended domains.** **Introductory papers** - Geometric Limits to Coherent Timekeeping in Extended Reference Frames — https://doi.org/10.5281/zenodo.18824556 - Accessibility Selection Law (ASL) — https://doi.org/10.5281/zenodo.18824649 - Phase Boundary Gravity — https://doi.org/10.5281/zenodo.18824707 **Pillars (numbered I–IV)** - Paper I: Deriving Gravitational Geometry and Schrödinger Dynamics from Finite Accessibility — https://doi.org/10.5281/zenodo.18601600 - Paper II: Deriving Inertia, Motion, and Wave Propagation from Finite Accessibility — https://doi.org/10.5281/zenodo.18625174 - Paper III: Accessible State Spaces, Record Stability, and the Emergence of Quantum Statistics — https://doi.org/10.5281/zenodo.18625192 - Paper IV: Frame Dissolution, the Certification Ceiling, and Observable Deformations — https://doi.org/10.5281/zenodo.18654458 **Extension papers** - Dark Matter from Finite Accessibility — https://doi.org/10.5281/zenodo.18654433 - Dark Energy from Finite Accessibility — https://doi.org/10.5281/zenodo.18654523 - No-Go Theorems and the Admissibility Corridor — https://doi.org/10.5281/zenodo.18654493 - Gauge Structure from Finite Accessibility — https://doi.org/10.5281/zenodo.18928152 - Perturbation Theory from Finite Accessibility — https://doi.org/10.5281/zenodo.18928213 **Experimental paper** - Experimental Probes of Finite Accessibility: GW Dispersion and Vacuum Path Independence — https://doi.org/10.5281/zenodo.18931126 **Keywords:** no-go theorems, admissibility corridor, finite accessibility, exclusion theorems, Born rule uniqueness, spatial dimensionality, Ostrogradsky instability, higher-order dynamics, extended synchronisation, intersubjective stability, certification cost, dispersion constraints, protocol invariance, operational axioms, action gap, quantum gravity constraints
This paper introduces a constraint-first framework for physical law based on a single structural requirement: that distinctions and correlations be enforceable without contradiction under finite capacity. Rather than proposing new dynamics, entities, or microscopic mechanisms, the work reframes foundational questions in physics by asking a prior question—under what conditions is physical description itself possible? Central to the framework is the recognition that correlation enforcement cannot be unlimited. From this finiteness follows a notion of admissibility, separating correlation structures that can be jointly realized from those that are structurally incoherent, independent of probability or dynamics. Geometry, time, entropy, and global state descriptions are treated not as universal primitives, but as regime-dependent representations that emerge when enforcement constraints can be smoothly distributed—and fail when they cannot. Within this perspective, long-standing foundational puzzles—such as the arrow of time, entropy bounds, horizon paradoxes, and the breakdown of global descriptions—are reinterpreted as signals of regime mismatch rather than failures of physical law. Apparent paradoxes arise when descriptive tools are extrapolated beyond the regimes in which their enforcement is possible. The paper is deliberately pre-dynamical. It does not modify quantum mechanics or general relativity, nor does it derive specific equations or predictions. Its contribution is structural: to articulate the minimal conditions that any coherent physical description must satisfy, and to clarify why familiar physical structures appear where they do, persist where they can, and fail where they must. This work serves as the conceptual foundation for a companion technical paper that formalizes admissibility and finite correlation capacity as a calculus. Together, the papers aim to delineate the boundary between meaningful physical description and questions that cannot be consistently posed. About the series. Admissibility Physics derives the Standard Model gauge group, fermion content, quantum formalism, Lorentzian spacetime, the Einstein field equations, the cosmological constant, and the neutrino, strong-CP, and dark sectors from a single assumption — that enforcement is finite at every causally connected region — with zero free parameters. The core derivation runs Papers 0–11; the extension papers carry the individual sectors. Each paper's main text and Technical Supplement is deposited separately, and every quantitative claim traces to a named, executable check in the public theorem bank (over 3,800 bank-registered theorems across roughly 450 modules, 48 quantitative predictions). Website: admissibilityphysics.com. Engine and theorem bank: https://github.com/Ethan-Brooke/APF-Engine. Full series and latest deposits: Zenodo community admissibility_physics. The Engine — Admissibility Physics: An Executable Constraint Framework and Constants Map — DOI 10.5281/zenodo.18529115. Paper 0 — What Physics Permits: A Constraint-First Framework for Physics — DOI 10.5281/zenodo.18439523 Paper 1 — The Enforceability of Distinction — DOI 10.5281/zenodo.18439200 Paper 2 — Finite Admissibility and the Failure of Global Description — DOI 10.5281/zenodo.18439274 Paper 3 — Entropy, Time, and Accumulated Cost — DOI 10.5281/zenodo.18439363 Paper 4 — Admissibility Constraints and Structural Saturation — DOI 10.5281/zenodo.18439397 Paper 5 — Quantum Structure from Finite Enforceability — DOI 10.5281/zenodo.18439433 Paper 6 — Dynamics and Geometry as Optimal Admissible Reallocation — DOI 10.5281/zenodo.18439445 Paper 7 — A Minimal Quantum of Action from Finite Admissibility — DOI 10.5281/zenodo.18439513 Paper 8 — The Admissibility-Capacity Ledger — DOI 10.5281/zenodo.19721384 Paper 9 — The Geometric Substrate as Cost Structure of Comparison Continuations — DOI 10.5281/zenodo.20041675 Paper 10 — The Calculus of Finite Continuability — DOI 10.5281/zenodo.20041680 Paper 11 — Forced Universality from Capacity-Bounded Admissibility — DOI 10.5281/zenodo.20684198 Paper 13 — The Minimal Admissibility Core — DOI 10.5281/zenodo.18361446 Paper 16 — Markov Breakdown and the Hard Problems — DOI 10.5281/zenodo.20684207 Paper 18 — The Electroweak Sector as a Capacity Equilibrium — DOI 10.5281/zenodo.20684209 Paper 20 — The Enforcement Crystal — DOI 10.5281/zenodo.18531732 Paper 24 — The Recruitment-Radius Extension — Foundations — DOI 10.5281/zenodo.20684211 Paper 28 — Absolute Mass Scales from Electroweak Capacity Saturation — DOI 10.5281/zenodo.20684215 Paper 29 — Plaquette Representation Dominance and Confinement — DOI 10.5281/zenodo.20684218 Paper 30 — A Tube Mechanism for the Lattice Mass Gap — DOI 10.5281/zenodo.20684220 Paper 31 — Osterwalder–Schrader Structure of Lattice Yang–Mills — DOI 10.5281/zenodo.20684222 Paper 33 — Trace-to-Scheme Export Architecture — DOI 10.5281/zenodo.20684224 Paper 35 — The Dark Sector as a Two-Role Capacity Decomposition — DOI 10.5281/zenodo.20684228 Paper 40 — The Thermodynamics of Finite Distinction (Between Symmetry and the Void) — DOI 10.5281/zenodo.20684235 Paper 41 — The Horizon as a Continuation Ledger — DOI 10.5281/zenodo.20684241 Paper 42 — The Weak Mixing Angle Is Not Free — DOI 10.5281/zenodo.20684245 Paper 43 — The Neutrino Sector — DOI 10.5281/zenodo.21194191 Paper 44 — What a Finite Theory Owes the Continuum — DOI 10.5281/zenodo.21195874 Paper 45 — What the Vacuum Can Keep — DOI 10.5281/zenodo.21194195 Paper 46 — The Strong CP Angle Is Not Free — DOI 10.5281/zenodo.21194197 Paper 47 — The Confinement Antecedent Is Not Forced — DOI 10.5281/zenodo.21194199 Technical Supplements cross-link to their main paper via isSupplementTo and to the engine via isDocumentedBy. Concept DOIs above resolve to the latest version. Author. Ethan Brooke, Independent Researcher, San Anselmo, California, USA. ORCID: 0009-0001-2261-4682 LinkedIn: linkedin.com/in/ethanbrooke GitHub: github.com/Ethan-Brooke Contact: brooke.ethan@gmail.com