Can the Dyscoherence-Decoherence Transition Be Reduced to a Single Constant? The Tipping Constant ζ ≈ 0.2607 and the Structural Phase Transition From Relational Discord to Structural Collapse V4.A22 — Article 22 of the series Derived from the M2FA Edifice
Can the dyscoherence-decoherence transition be reduced to a single constant? Two systems in relational discord (dyscoherence Dy) can tip toward a loss of internal coherence (decoherence H) if the discord is not resolved. This article deepens the framework introduced in NCTV.X and synthesised in SS.V. It formalises dyscoherence and decoherence as distinct quantities: dyscoherence is relational (phase disagreement between systems), decoherence is structural (loss of internal coherence). The transition Dy → H is governed by a single constant, the tipping constant ζ ≈ 0.2607. The article provides the internally observed relation: ζ = H/ϕ + λ/π − λ/ϕ 3.The transition occurs in 95.80% of cases (100,000,000 runs). A transversal protocol (physics, biology, sociology, economics) with stratified split and statistical sizing is provided. The claimed level is 3σ (strong candidate), with 4σ (discovery) as an extension. All numericalvalues presented are internal to the M2FA framework; external empirical confrontation remains open. The notation Dy is used in continuity with the notation Dy of V3.A15. Keywords: dyscoherence; decoherence; tipping constant; structural phase transition; relationaldiscord; existential rupture; critical transition; irreversibility; M2FA.
Can the dyscoherence-decoherence transition be reduced to a single constant? Two systems in relational discord (dyscoherence Dy) can tip toward a loss of internal coherence (decoherence H) if the discord is not resolved. This article deepens the framework introduced in NCTV.X and synthesised in SS.V. It formalises dyscoherence and decoherence as distinct quantities: dyscoherence is relational (phase disagreement between systems), decoherence is structural (loss of internal coherence). The transition Dy → H is governed by a single constant, the tipping constant ζ ≈ 0.2607. The article provides the internally observed relation: ζ = H/ϕ + λ/π − λ/ϕ 3.The transition occurs in 95.80% of cases (100,000,000 runs). A transversal protocol (physics, biology, sociology, economics) with stratified split and statistical sizing is provided. The claimed level is 3σ (strong candidate), with 4σ (discovery) as an extension. All numericalvalues presented are internal to the M2FA framework; external empirical confrontation remains open. The notation Dy is used in continuity with the notation Dy of V3.A15. Keywords: dyscoherence; decoherence; tipping constant; structural phase transition; relationaldiscord; existential rupture; critical transition; irreversibility; M2FA.
NCT V.IX introduced the Shared Existence Theory and formalized theconcepts of shared space Eshared, resemblance coefficient R, phase cohesion Cϕ,dyscoherence Dy, energy confluence F, Mafetic Inconnector ⊕E , Shared ShieldBshared, maféisation, and hatching.The present NCT V.X pursues three objectives:1. Practical dimension: clarify the transition Dy → H and its threshold.2. Conceptual clarification: establish correspondences between sharedexistence concepts and observed physical phenomena.3. Establishment of the tipping constant ζ: demonstrate itstwo discoveries (phenomenological and fundamental) and retain itsfundamental value.A specific simulation (100,000,000 runs) was conducted to measure theDy → H transition. The results show that:• The transition occurs in 95.80% of cases.• The phenomenological critical threshold is. ζ1 ≈ 0.260271.• The fundamental value is ζ = 0.26074 ≈ 0.26.• The gap between the two values is ι = 0.00047, the sensitivity constant.NCT V.X closes Seal V by unifying relational dynamics (shared existence)and structural dynamics (held existence).Keywords:M²FA, NCT V.X, shared existence, dyscoherence,decoherence, phase transition, physical observations, tipping constant ζ.Related publications:• NCT V.IX: 10.5281/zenodo.21528719• NCT V.VIII: 10.5281/zenodo.21509124• NCT V.VII: 10.5281/zenodo.21497247
This document contains the Python simulation code for the M²FA model asdescribed in NCT V.IV (The Alert Constant λ = 0.3 — Part II: A Hybrid Constantof Order, Wave, and Practical Utility). The code implements:• Validation of the fundamental relation λ=4H/πφ• Exploration of ontological porosity ε = 0.2%• Demonstration of the two safety margins (21.3% and 21.5%)• Statistical analysis over 1,000,000 runs• Visualization of the hybrid nature of λThe simulation is fully reproducible. The code demonstrates that λ = 0.3 is ahybrid constant, emerging from the relation between Order (H, φ, 4) and Wave (π).Keywords: M²FA, NCT V.IV, Alert Constant λ, hybrid constant, golden ratio,decoherence, order and wave, ontological porosity.Related publications:• NCT II: 10.5281/zenodo.19950456• NCT II.3: 10.5281/zenodo.20037122• NCT V: 10.5281/zenodo.21188867• NCT V.II: 10.5281/zenodo.21351682• NCT V.III: 10.5281/zenodo.21398367• NCT V.IV: 10.5281/zenodo.21429945
We investigate the disappearance of discord in 2- and multi-qubit systems subject to decohering influences. We formulate the computation of quantum discord and quantum geometric discord in terms of the generalized Bloch vector, which gives useful insights on the time evolution of quantum coherence for the open system, particularly the comparison of entanglement and discord. We show that the analytical calculation of the global geometric discord is NP-hard in the number of qubits, but a similar statement for global entropic discord is more difficult to prove. We present an efficient numerical method to calculating the quantum discord for a certain important class of multipartite states. In agreement with previous work for 2-qubit cases (Mazzola et al 2010 Phys. Rev. Lett. 104 200401), we find situations in which there is a sudden transition from classical to quantum decoherence characterized by the discord remaining relatively robust (classical decoherence) until a certain point from where it begins to decay quickly whereas the classical correlation decays more slowly (quantum decoherence). However, we find that as the number of qubits increases, the chance of this kind of transition occurring becomes small.
The Universal Theory of Resilience — Master Edition v3.2 presents the first complete formalisation of Axiom VIII: The Corruption Principle of Multiversal Branching.This edition unifies mathematical physics, information theory, evolutionary biology, and cosmology under a single foundational principle: antagonistic physics corrupts primordial distinctions, and this corruption generates multiplicity. Building on the UTR framework of duality, antagonism, resonance, and coherence, v3.2 introduces: Formal operators for Distinction (𝔻), Antagonistic Dynamics (Ĥ), and Corruption (Ĉ) A stochastic Hilbert-space formulation of impurity growth A general branching criterion based on purity loss and interference collapse A unified model showing that: quantum decoherence, biological diversification, cosmological inflation, and phase transitionsare all expressions of the same underlying corruption mechanism Predictive parameters (λ, ζ, γ) with measurable consequences in quantum systems, evolutionary stress experiments, and CMB data Explicit falsification tests, making the theory scientifically confrontable This Master Edition consolidates Axioms 0–VIII, integrates the full formal derivation of Axiom VIII, and includes the visual A3 diagram illustrating the corruption-driven emergence of multiple universes.It is the most complete and rigorous statement of the Universal Theory of Resilience to date.
Quantum decoherence—the loss of coherence in a quantum system due to environmental coupling—has been described since the 1980s as a continuous exponential decay of the off-diagonal elements of the density matrix. This mathematical description captures the statistical average of many events, not the underlying mechanism of decoherence itself. Based on the Structural Axiom System (Lin Xiaohei, 2026), this paper proposes: **decoherence is not a continuous, smooth decay, but a discrete process composed of indivisible micro-coupling events.** Each micro-coupling event corresponds to a structural unit—a binary asymmetric relation, the smallest configurational unit—taking shape between system and environment. Each step of decoherence removes one integer share of quantum coherence; macroscopic "gradual decoherence" is the statistical smoothing of many discrete steps. This paper provides: 1. A quantitative formula for the step height: κ = g × d, where g is the micro-coupling strength and d is the structural unit directionality, both independently calibratable. 2. A decomposable verification prediction: changing photon frequency → g changes, but d remains unchanged → the normalized step shape remains invariant. 3. A complete experimental design: single-photon path superposition state + precision environmental coupling + quantum state tomography. If this experiment succeeds, the structural unit will become the first directly observed "configurational quantum"—the empirical confirmation of the smallest unit of existence. This would be the ultimate resolution of the quantum-classical transition problem, comparable in significance to Brownian motion confirming the existence of atoms.
We study the dynamics of quantum and classical correlations in the presence of nondissipative decoherence. We discover a class of initial states for which the quantum correlations, quantified by the quantum discord, are not destroyed by decoherence for times t<[symbol: see text]. In this initial time interval classical correlations decay. For t>[symbol: see text], on the other hand, classical correlations do not change in time and only quantum correlations are lost due to the interaction with the environment. Therefore, at the transition time [symbol: see text] the open system dynamics exhibits a sudden transition from classical to quantum decoherence regime.