# Graviton-Mediated Qubit Coherence in the Transition from Hydrogen-2 to Hydrogen-3: A DLSFH and SGCV Framework

Antonios Valamontes, Emmanouil Markoulakis

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Antonios Valamontes, Emmanouil Markoulakis. Graviton-Mediated Qubit Coherence in the Transition from Hydrogen-2 to Hydrogen-3: A DLSFH and SGCV Framework. 2025. hal-05060915

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# Graviton-Mediated Qubit Coherence in the Transition from Hydrogen-2 to Hydrogen-3: A DLSFH and SGCV Framework

Antonios Valamontes a,a,b,c, Emmanouil N. Markoulakis b,d,e

<sup>a</sup>Kapodistrian Academy of Science, Tampa, Florida, USA

<sup>b</sup>Address correspondence to: avalamontes@Kapodistrian.edu.gr

<sup>c</sup>Kapodistrian.edu.gr

<sup>d</sup>Hellenic Mediterranean University, Romanou 3, Chania, 73133, Crete, Greece

<sup>e</sup>markoul@hmu.gr

## Abstract

This paper presents a geometric-coherence model for the nuclear transition from Hydrogen-2 (Deuterium) to Hydrogen-3 (Tritium), based on the Dodecahedron Linear String Field Hypothesis (DLSFH) and the Superluminal Graviton Condensate Vacuum (SGCV). Within this combined framework—termed the Dodecahedral String-Graviton Coherence Framework (DSGCF)—nucleons are treated as qubit-configured lattices embedded in curvature-regulated dodecahedral geometries. We show that graviton phase fields, though external to the qubit lattice, act as coherence-corrective agents that redistribute entropy and curvature tension during isotopic transformation. These off-lattice graviton fields enable phase realignment following neutron-induced asymmetry, preserving metastable nuclear coherence.

The DSGCF approach offers an alternative to purely force-based models by interpreting binding energy differentials and decay instabilities as geometric coherence responses to curvature imbalances. The coherence collapse in Tritium is modeled through entropy-threshold feedback defined by the Valamontes–Markoulakis Coherence Collapse Mechanism (VM–CCM) and the associated differential identity (VMI). Additionally, observational parallels from GRB 221009A suggest that graviton-mediated coherence delays in astrophysical photon propagation may reflect the same curvature-regulated dynamics observed in nuclear structure. Overall, the DSGCF provides a unified quantum-geometric framework for understanding light isotope behavior through gravitational phase encoding.

**Keywords:** Graviton phase fields, DLSFH, SGCV, nuclear coherence, isotopic transition, quantum geometry

## 1. Introduction

Hydrogen isotopes provide an elegant yet foundational system for probing how nuclear transitions may be influenced not only by the well-established principles of quantum chromodynamics (QCD), but also by extended coherence dynamics that operate beyond the Standard Model. In conventional nuclear theory, the strong force—mediated by gluon exchange—governs the binding of quarks within nucleons and of nucleons within nuclei. However, QCD offers no intrinsic explanation for certain anomalous coherence instabilities observed in light isotopes, nor for entropy-aligned decay patterns that appear in select nuclear systems [3].

Recent theoretical proposals suggest that these limitations may be addressed by a geometric extension of quantum field theory known as the *Dodecahedron Linear String Field Hypothesis* (DLSFH), in which nucleons are modeled as structured qubit lattices distributed over a dodecahedral network [6]. Each vertex in this geometry hosts a qubit whose phase and spin are coherently aligned across curvature-preserving connections. The full system forms a twelve-qubit
entangled configuration governed by local coherence tensors and curvature-symmetry constraints. This approach blends elements of quantum topology, supersymmetry, and string-field interaction to recast nucleon structure as a geometry-dependent coherence system.

Transitions between light isotopes such as Deuterium (Hydrogen-2) and Tritium (Hydrogen-3), however, pose a unique challenge. The addition of a second neutron in Hydrogen-3 disrupts the previously balanced curvature in the DLSFH lattice, introducing geometric asymmetry and coherence stress. Within such a model, minor geometric shifts can lead to decoherence events unless externally regulated. Conventional strong-interaction frameworks do not account for such phase instabilities or their suppression.

To resolve this, Valamontes [4] introduced the concept of *off-lattice graviton fields*—superluminal phase-correction agents that emerge from a nonlocal background structure known as the *Superluminal Graviton Condensate Vacuum* (SGCV). These graviton fields do not manifest as traditional spin-2 particles within the Standard Model but function as coherence-regulating operators that actively redistribute entropy and tension across the nucleon's geometric network. Their action realigns misphased qubit interactions, restoring partial coherence under curvature strain.

Markoulakis [3] extended this concept by formalizing the entropy-responsive nature of SGCV graviton fields. In his formulation, coherence preservation is governed by local entropy gradients that dynamically adjust the curvature-induced deformation of the coherence tensor $C^{\mu\nu}(x, t)$. This formulation supports phase diffusion balancing during nucleon reconfiguration, especially under sudden geometric asymmetry.

Together, these developments constitute the foundation of the *Dodecahedral String-Graviton Coherence Framework* (DSGCF), wherein the evolution and collapse of quantum coherence is mediated by geometric curvature and graviton phase fields. This theory has been formalized through the Valamontes-Markoulakis Coherence Collapse Mechanism (VM-CCM) and the associated Valamontes-Markoulakis Identity (VMI), which provides a differential law for entropy-driven coherence decay. These constructs serve not only as theoretical insights but also offer testable models of nuclear transitions.

Moreover, coherence-driven graviton mediation receives indirect astrophysical validation from observations of Gamma-Ray Burst GRB 221009A [5]. The measured energy-dependent time delays in TeV photon arrival are consistent with DLSFH-SGCV predictions, suggesting that the same coherence-tension mechanisms responsible for isotopic transitions may also manifest at cosmological distances in photon transport phenomena.

In this paper, we investigate the nuclear transition from Hydrogen-2 to Hydrogen-3 through the lens of the DS-GCF. We demonstrate that graviton-mediated phase realignment plays a critical role in preserving coherence as qubit curvature is distorted by neutron addition. This approach provides a new geometrical path for understanding metastability, isotopic mass differentials, and coherence decay thresholds in light nuclei—extending gravitational coherence theory into nuclear structure.

## 2. DLSFH Representation of Nucleons

In the Dodecahedron Linear String Field Hypothesis (DLSFH), each nucleon is topologically encoded as a 12-qubit quantum configuration distributed over a discretized dodecahedral lattice structure composed of 20 vertices and 30 edges. This arrangement is not arbitrary—it encodes local curvature constraints, quantum number symmetries, and coherence preservation through string-qubit tensor couplings [5].

Each vertex $v_i$ ($i = 1, ..., 20$) corresponds to a qubit $q_i \in \mathbb{C}^2$ with an associated spin-coherent state $|\psi_i\rangle = \alpha_i|0\rangle + \beta_i|1\rangle$ constrained by $|\alpha_i|^2 + |\beta_i|^2 = 1$. The global nucleon state $|\Psi_N\rangle$ is a symmetry-weighted entangled tensor product:
$$|\Psi_N\rangle = \bigotimes_{i=1}^{12} |\psi_i\rangle, \qquad (1)$$

with inter-qubit coupling dynamics described by a local curvature-induced coherence Hamiltonian $\mathcal{H}_{\text{DLSFH}}$ defined as:

$$\mathcal{H}_{\text{DLSFH}} = \sum_{\langle i,j \rangle} J_{ij} (\vec{\sigma}_i \cdot \vec{\sigma}_j) + \sum_i \kappa_i R(v_i) \sigma_i^z, \qquad (2)$$

where:

* $J_{ij}$ are dodecahedral adjacency-dependent coupling constants between qubit $i$ and $j$,

* $\vec{\sigma}_i$ is the Pauli vector for qubit $i$,

* $\kappa_i$ is the local curvature-sensitivity factor,

* $R(v_i)$ is the discrete Ricci curvature at vertex $v_i$ [4].

For the deuteron (Hydrogen-2), the proton (uud) and neutron (udd) are encoded on separate but entangled dodecahedra, stabilized through an internal coherence tensor $C^{\mu\nu}(x, t)$, which satisfies:

$$\partial_t C^{\mu\nu}(x, t) = -\eta(x, t) \cdot \partial_t S(x, t), \qquad (3)$$

where $\eta(x, t)$ is the local coherence susceptibility and $S(x, t)$ is the entropy density [4]. This ensures thermodynamic compatibility while preserving quantum phase alignment.

## 2.1. Hydrogen-3 Extension and Coherence Imbalance

In Hydrogen-3 (Tritium), the addition of a second neutron introduces a geometric asymmetry within the coupled dodecahedral structure. The curvature imbalance manifests as a distortion in the internal tensor network:

$$\delta R(v_k) \propto -\nabla_A C_{\mu\nu}^A(x, t), \qquad (4)$$

where the emergent curvature correction $\delta R$ generates quantum mechanical strain between the added neutron and existing qubit vertices. This strain would lead to decoherence if not regulated.

## 2.2. Role of Graviton Fields from SGCV

To maintain coherence, graviton fields from the Superluminal Graviton Condensate Vacuum (SGCV) intervene nonlocally. These fields $G^\mu(x)$ do not couple to energy-momentum directly but modulate the coherence tensor via:

$$\delta C^{\mu\nu}(x, t) = \int G^\mu(x') G^\nu(x, x') dx', \qquad (5)$$

where $G^\nu(x, x')$ is a graviton-coherence propagator derived from SGCV's superluminal metric [6]. This mechanism aligns with findings from GRB 221009A, where photon phase delays matched predictions of curvature-tension realignment via coherence-regulating fields.
## 2.3. DLSFH Constraints and Stability Criteria

The qubit-qubit coherence is maintained under the following inequality:

$$ |\Delta\phi_{ij}| < \frac{\pi}{5}, \quad \forall \langle i, j \rangle, \qquad (6) $$

where $\Delta\phi_{ij}$ is the relative phase angle between neighboring qubits. Violation of this bound triggers local decoherence, initiating beta decay in H-3 as entropy-driven collapse of qubit curvature memory [4].

The combined geometric and algebraic architecture of the DLSFH model thus encodes both nucleonic stability and gravitational phase correction, governed by dynamic interplay between qubit curvature, entropy gradients, and SGCV graviton interactions.

## 3. Graviton Fields as Coherence Regulators

Gravitons in this context are not embedded within the dodecahedral qubit lattice itself, but instead propagate as off-lattice corrective phase fields within the Superluminal Graviton Condensate Vacuum (SGCV). These fields exhibit superluminal characteristics and operate in response to spatially-varying entropy gradients, $\nabla S(x, t)$.

As proposed by Markoulakis [3], the graviton field $G^\mu(x)$ dynamically senses coherence instabilities and injects corrective curvature to maintain quantum geometric balance. The coupling between entropy gradient and coherence loss can be modeled through the decay of the coherence tensor $C^{\mu\nu}$:

$$ \partial_t C^{\mu\nu}(x, t) = -\eta(x, t) \cdot \partial_t S(x, t), \qquad (7) $$

while the SGCV's corrective field response follows a saturation curve:

$$ \mathcal{F}_{\text{SGCV}}(x, t) = 1 - \exp\left(-\frac{\nabla S(x, t)}{\sigma_c}\right), \qquad (8) $$

where $\sigma_c$ is the critical entropy scale beyond which spontaneous decoherence triggers. Figure 1 illustrates the opposing dynamics between coherence degradation and graviton-mediated stabilization.
<figure><img src="image_2.png" /><figcaption>Figure 1: Interaction of entropy gradients with coherence decay and graviton stabilization. As entropy gradients increase, the coherence tensor $|C^{\mu\nu}|$ diminishes, while the SGCV field $\mathcal{F}_{\text{SGCV}}$ rises to compensate.</figcaption></figure>

This dual dynamic provides a mechanism for preserving isotopic stability under otherwise destabilizing curvature asymmetries and entropy flows, forming the basis of phase realignment across nucleonic transformations.

## 4. Phase-Induced Transition: H-2 to H-3

The nuclear transformation from Deuterium (H-2) to Tritium (H-3) introduces an additional neutron into a pre-coherent two-body system. The geometric consequence is an increase in local curvature strain, which disrupts the qubit phase symmetry and challenges the balance enforced by the dodecahedral structure. The addition of the neutron modifies the entropy landscape, inducing a coherence crisis if not corrected.

The transition requires:

* **Gravitation-induced rebalancing of qubit interactions:** The internal edge-to-edge phase relationships must be re-aligned by SGCV fields to preserve constructive superposition.

* **Curvature diffusion across dodecahedral edges:** Ricci curvature corrections diffuse nonlocally across the lattice, modulating coupling coefficients $J_{ij}$ in Eq. (2).

* **SGCV tension redirection to restore partial coherence:** Graviton fields redistribute coherence pressure and entropy sink regions, effectively steering $\psi_s^*$ back into a metastable symmetry basin.

This process results in a metastable Hydrogen-3 configuration. While momentarily coherent, the system is primed for beta decay due to the increasing curvature tension and entropy imbalance. This decay can be interpreted not merely as a nuclear instability, but as a gravitationally-driven coherence collapse [4]. The graviton field acts here as both an informational regulator and a thermodynamic buffer, enabling transient stability in a high-curvature nucleonic landscape.
## 5. Decay and Coherence Collapse

In the DLSFH-SGCV framework, decay is not viewed solely as a particle transformation, but as a phase-space instability triggered by the accumulation of entropy across a coherence-regulated quantum geometry. Specifically, when the entropy gradient $\nabla S(x, t)$ in the surrounding graviton-coherence field surpasses a critical threshold $\sigma_c$, a discontinuity in the coherence tensor $C^{\mu\nu}(x, t)$ emerges. This discontinuity marks the onset of decoherence propagation throughout the qubit lattice.

The formal condition for coherence collapse is given by:

$$|\nabla S(x, t)| > \sigma_c \quad \Rightarrow \quad C^{\mu\nu}(x, t) \to 0, \qquad (9)$$

where $\sigma_c$ is the entropy criticality constant associated with the coherence resilience of the qubit system, as introduced in Valamontes [4] and extended thermodynamically by Markoulakis [3].

Once this threshold is exceeded, the coherence tensor undergoes exponential decay:

$$\frac{dC^{\mu\nu}}{dt} = -\gamma(x, t)C^{\mu\nu}, \quad \text{with} \quad \gamma(x, t) \propto \frac{|\nabla S| - \sigma_c}{\sigma_c}, \qquad (10)$$

This entropy-responsive evolution law is formally defined as the Valamontes-Markoulakis Identity (VMI), which underpins the collapse dynamics governed by the Valamontes-Markoulakis Coherence Collapse Mechanism (VM-CCM) [4, 3].
## THEOREM: COHERENCE COLLAPSE TRIGGERED BY ENTROPY THRESHOLD (CCTET)

Let $C^{\mu\nu}(x, t)$ represent the coherence tensor of a quantum qubit-lattice system and $\nabla S(x, t)$ be the spatial entropy gradient. Then the system undergoes irreversible coherence collapse if:

$$ \int_{t_0}^{t_1} \left( \frac{|\nabla S(x, t)| - \sigma_c}{\sigma_c} \right) dt > \tau_c, $$

where $\tau_c$ is the coherence buffer threshold. Under this condition, the system transitions from metastability to decoherence, and the Valamontes–Markoulakis Coherence Collapse Mechanism (Valamontes–Markoulakis Coherence Collapse Mechanism (VM–CCM)) is triggered. This collapse dynamically aligns with the behavior encoded in the Valamontes–Markoulakis Identity (Valamontes–Markoulakis Identity (VMI)) and is geometrically regulated by the curvature flow described in the Dodecahedral String–Graviton Coherence Framework (DSGCF) framework.

### Valamontes–Markoulakis Coherence Collapse Mechanism (VM–CCM)

The entropy-sensitive rate of coherence decay formalized by the Valamontes–Markoulakis Coherence Collapse Mechanism (VM–CCM) is governed by the *Valamontes–Markoulakis Identity (VMI)*, which describes the dynamic evolution of $C^{\mu\nu}$ as a function of $\nabla S$ and establishes the threshold-based disintegration law central to the Dodecahedral String–Graviton Coherence Framework (DSGCF) framework.

Let $C^{\mu\nu}(x, t)$ be the coherence tensor describing qubit field alignment, and $\nabla S(x, t)$ the local entropy gradient within the SGCV. Then the **Valamontes–Markoulakis Coherence Collapse Mechanism (VM–CCM)** asserts:

$$ \nabla S(x, t) > \sigma_c \implies C^{\mu\nu}(x, t) \to 0, $$

This coherence collapse triggers:

* Disintegration of qubit phase alignment,

* Redistribution of $\psi_s^*$ energy into:

- Ghost curvature fields ($\psi_s^{\text{ghost}}$),

- Vacuum fluctuations ($\delta\psi_{\text{vac}}$),

- Ricci curvature memory ($\Delta R_{\mu\nu}$).

VM–CCM describes a topological phase collapse of quantum geometry triggered by entropy instability, governing processes such as beta decay in Hydrogen-3 [4, 3].

### 5.1. Decay as Coherence Phase Collapse

In Tritium (Hydrogen-3), the curvature strain induced by neutron addition accumulates entropy in a localized region of the SGCV. If this curvature is not counterbalanced effectively by graviton-mediated phase correction, decoherence propagates radially across the lattice network. This initiates beta decay, transitioning the system from a metastable to a restructured state—namely, Helium-3 and an emitted beta particle and antineutrino.
The field $\psi_s^*(x, t)$, which encodes observable coherence in DLSFH, collapses via a phase-symmetric reduction:

$$ \psi_s^*(x, t) \rightarrow \psi_s^{\text{ghost}} + \delta\psi_{\text{vac}} + \Delta R_{\mu\nu}, \qquad (11) $$

where:

* $\psi_s^{\text{ghost}}$ is a non-observable residual coherence field retained within SGCV curvature structure,

* $\delta\psi_{\text{vac}}$ is redistributed vacuum fluctuation energy contributing to zero-point field noise,

* $\Delta R_{\mu\nu}$ is the gravitational curvature memory encoded into spacetime geometry [4].

## 5.2. Geometric Memory and SGCV Embedding

Following the collapse, the SGCV retains a persistent curvature imprint—a “geometric memory” analogous to an entropy-weighted holographic trace. This imprint is stored in the Ricci response field $\Delta R_{\mu\nu}$ and remains phase-accessible by future coherence fluctuations. This phenomenon aligns with both the multiscale coherence conservation hypothesis in MC-SGCV geometry [4] and with recent interpretations of graviton-vacuum modularity [5].

Thus, beta decay is recast not merely as a nuclear disintegration but as a graviton-mediated coherence phase collapse that conserves total informational curvature by encoding it across non-observable sectors of SGCV spacetime. This gives rise to a new class of decay categorization: Valamontes-Markoulakis Coherence Collapse Mechanism (VM-CCM), potentially generalizable to early-universe baryogenesis and mesonic transformations.

# 6. Quantum Coherence at 37°C

In conventional quantum mechanics, coherence is fragile under thermal noise, and systems operating at biologically relevant temperatures such as 37°C are expected to rapidly decohere. Thermal vibrations and environmental entanglement typically reduce phase alignment on time scales $\tau \ll 10^{-12}$ s, governed by the decoherence rate [8]. This creates a long-standing incompatibility between sustained quantum coherence and macroscopic or biological systems.

However, the Dodecahedron Linear String Field Hypothesis (DLSFH) coupled with the Superluminal Graviton Condensate Vacuum (SGCV) introduces a non-traditional correction mechanism. In this framework, off-lattice graviton fields act as dynamic coherence regulators that stabilize qubit string states against entropy flux. These fields are not thermalized in the usual sense but reside in a superluminal phase space, enabling them to operate outside the constraints of local temperature noise [4, 3].

## 6.1. Entropy-Corrected Decoherence Rate

We extend the traditional decoherence model to include graviton-induced phase stabilization. The modified decoherence rate $\Gamma_{\text{eff}}$ in the presence of SGCV background fields becomes:

$$ \Gamma_{\text{eff}}(x, T) = \Gamma_0(T) - \xi(x, T) \cdot \mathcal{F}_{\text{SGCV}}(x), \qquad (12) $$

where:

* $\Gamma_0(T)$ is the standard thermal decoherence rate,
* $\xi(x, T)$ is the local coherence susceptibility in the qubit lattice,

* $\mathcal{F}_{\text{SGCV}}(x)$ is the graviton field's corrective response function, defined as:

$$ \mathcal{F}_{\text{SGCV}}(x) = \exp\left(-\frac{\nabla S(x)}{\sigma_c}\right). \qquad (13) $$

This shows that as entropy gradients $\nabla S(x)$ rise, $\mathcal{F}_{\text{SGCV}}$ is activated to buffer the system's coherence decay, preventing $\Gamma_{\text{eff}}$ from diverging. In this way, the SGCV field actively preserves string-qubit phase structure even in warm, noisy conditions.

<figure><img src="image_3.png" /><figcaption>Figure 2: SGCV coherence-correction field $\mathcal{F}_{\text{SGCV}}$ as a function of entropy gradient $\nabla S$. The field activates non-linearly to suppress decoherence in high-entropy regimes.</figcaption></figure>

## 6.2. Temperature-Threshold Tolerance in DLSFH

Under this correction, the critical temperature $T_c$ above which coherence normally collapses is shifted upward:

$$ T_{c,\text{eff}} = T_c + \Delta T_{\text{SGCV}}, \qquad (14) $$

where $\Delta T_{\text{SGCV}} \propto |G^\mu(x)|$, the local strength of the SGCV field. This implies that systems embedded in SGCV-regulated environments—such as a graviton-enhanced quantum lattice—can maintain coherent states above 300K.
<figure><img src="image_4.png" /><figcaption>Figure 3: Increase in effective coherence critical temperature $T_{c,eff}$ as a function of SGCV graviton field strength $|G^μ|$Graviton coherence modulators raise the decoherence threshold, permitting phase stability above ambient thermal levels.</figcaption></figure>

Thus, coherence at 37°C becomes thermodynamically viable within the DLSFH formalism. Biophysical systems such as microtubules, DNA solitons, and quantum photosynthetic complexes may be modeled using embedded graviton-field corrections [2, 1, 6].

<figure><img src="image_5.png" /><figcaption>Figure 4: Temperature dependence of coherence lifetimes $\tau_0 = 1/\Gamma_0$ (classical) and $\tau_{eff} = 1/\Gamma_{eff}$ under SGCV correction. SGCV-enhanced systems maintain extended coherence duration at biologically relevant temperatures.</figcaption></figure>
## 6.3. Implications for Quantum Biology

The possibility of graviton-mediated coherence stabilization at physiological temperatures opens the door to a reconciliation between quantum mechanics and biology. In this paradigm:

* Qubit configurations may form temporary coherence islands within thermally active tissue,

* Information may be preserved in a phase-protected format, even during enzymatic reactions or synaptic transmission,

* Curvature and entropy geometry become active participants in biological information dynamics.

<figure><img src="image_6.png" /><figcaption>Figure 5: Comparison of quantum phase fidelity degradation with and without SGCV graviton correction. At 310 K (37°C), SGCV modulation preserves entanglement integrity.</figcaption></figure>

The DLSFH–SGCV mechanism thus provides a framework for understanding warm-environment quantum persistence not as a paradox, but as a natural extension of curvature-mediated coherence stabilization. This model may also provide testable signatures in systems exhibiting long-lived biological entanglement, offering a geometric route toward quantum-biophysical unification [5].

### Valamontes–Markoulakis Identity (VMI)

Let $C^{\mu\nu}(x, t)$ be the coherence tensor, and $\nabla S(x, t)$ the entropy gradient. The VMI states:

$$ \frac{dC^{\mu\nu}}{dt} = -\left(\frac{|\nabla S| - \sigma_c}{\sigma_c}\right) C^{\mu\nu} $$

for $\nabla S > \sigma_c$. This identity governs entropy-induced coherence decay within the Dodecahedral String–Graviton Coherence Framework (DSGCF) framework [4, 3].
## 7. Graviton Mediation of the H-2 to H-3 Interface

The nuclear interface between Hydrogen-2 (Deuterium) and Hydrogen-3 (Tritium) introduces a localized coherence stress within the qubit-curvature geometry of the Dodecahedron Linear String Field Hypothesis (DLSFH). This stress arises from the geometric imbalance created by the addition of a second neutron to a previously curvature-stabilized qubit system. The coherence tensor $C^{\mu\nu}(x, t)$, which governs internal qubit alignment, becomes deformed due to asymmetric coupling along several dodecahedral edges [6].

This deformation is mediated by a graviton-corrective mechanism sourced from the Superluminal Graviton Condensate Vacuum (SGCV). These off-lattice graviton fields, $G^\mu(x)$, respond dynamically to entropy gradients introduced by the neutron's curvature mass and stabilize the phase dynamics of the system:

$$ \delta C^{\mu\nu}(x, t) = \int G^\mu(x') G^\nu(x, x') dx', \qquad (15) $$

where $G^\nu(x, x')$ represents the coherence propagator from point $x'$ to $x$ across the SGCV background. This integration distributes curvature-induced tension nonlocally and realigns phase distortions across the qubit framework, allowing metastable configurations to emerge without immediate decoherence.

### Graviton-Driven Interface Realignment

Let $H_2$ represent a stable dodecahedral configuration and $H_3$ a metastable one with added neutron curvature. The SGCV mediates the transition by minimizing entropy-induced misalignment across qubit paths via:

$$ \delta\phi_{ij}(x, t) = \frac{\partial}{\partial t} \arg(\langle\psi_i|\psi_j\rangle) \rightarrow 0, \qquad (16) $$

where $\delta\phi_{ij}$ is the relative qubit phase between vertices $i$ and $j$. Stability is reached when phase diffusion is redistributed by graviton-corrected coherence tension [3].
<figure><img src="image_7.png" /><figcaption>Figure 6: Schematic transition from Hydrogen-2 to Hydrogen-3. Off-lattice graviton fields sourced from the SGCV rebalance phase tension and redirect entropy gradients, enabling metastable coherence at the H-3 state.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 7: Time evolution of the coherence tensor $\delta C^{\mu\nu}(t)$ in the presence and absence of graviton mediation. Without SGCV support, coherence rapidly decays. With graviton field correction, the decay is buffered, enabling longer-lived coherence necessary for isotopic metastability in H-3.</figcaption></figure>

The metastability of Tritium is thus not a product of weak force delay alone, but a geometric encoding of coherence struggle between curvature and entropy. The SGCV graviton fields act as informational curvatures that enforce balance within a qubit-string system until eventual decoherence triggers the Valamontes–Markoulakis Coherence Collapse
Mechanism (VM-CCM) process.

This mechanism represents a boundary condition within the broader Dodecahedral String-Graviton Coherence Framework (DSGCF), whereby isotopic transitions can be geometrically encoded as curvature-tension interfaces stabilized by graviton rebalancing fields [4].

## 8. Graviton Mass and Quantum Interaction

In conventional physics, the graviton is modeled as a massless, spin-2 tensor boson that mediates gravitational interactions via the linearized field equations of General Relativity. Its role in quantum field theory is conceptual, as no direct detection has been made [7]. In this classical view, gravitons neither couple directly to quantum coherence nor influence localized qubit states.

However, within the Dodecahedral String-Graviton Coherence Framework (DSGCF)—which integrates the Dodecahedron Linear String Field Hypothesis (DLSFH) with the Superluminal Graviton Condensate Vacuum (SGCV)—the graviton is reinterpreted not as a propagating particle, but as a phase-corrective field operator responsible for modulating curvature tension across coherent qubit-string networks [6, 3].

### Effective Mass from Entropy-Curvature Interaction

In this framework, the graviton possesses an effective mass $m_g^{\text{eff}}$ that arises dynamically from its coupling to local entropy gradients and spacetime curvature flux. We define this emergent quantity as:

$$m_g^{\text{eff}}(x, t) = \alpha \cdot \frac{|\nabla S(x, t)| \cdot R(x, t)}{c^2}, \qquad (17)$$

where:

* $\nabla S(x, t)$ is the spatial entropy gradient,

* $R(x, t)$ is the local Ricci scalar curvature,

* $\alpha$ is a graviton-curvature susceptibility constant tied to SGCV background properties.

This mass does not appear in free-particle propagation but manifests in the graviton's phase-regulation capacity. Unlike the Standard Model's inert quanta, this SGCV-mediated graviton dynamically adjusts the phase alignment of string-qubit interactions without transferring momentum, thus enabling gravitational coherence without traditional force-carrier exchange.

### Curvature-Corrective Operator Dynamics

The graviton operator $G^\mu(x)$ acts on the coherence tensor $C^{\mu\nu}$ and the qubit state field $\psi_i$ as a nonlocal curvature modulator:

$$G^\mu(x) = -\frac{\partial}{\partial x^\mu} (\mathcal{F}_{\text{SGCV}}(x) \cdot \phi_{ij}(x, t)), \qquad (18)$$

where $\phi_{ij}(x, t)$ is the phase misalignment between qubit nodes i and j, and $\mathcal{F}_{\text{SGCV}}(x)$ is the entropy-weighted coherence correction factor introduced in Section 7. This operator functions analogously to a gauge field in Yang-Mills theory, but its curvature source is entropy, not charge.
## Beyond Traditional Quantum-Gravity Limits

In the Standard Model, quantum particles interact with gravity only through energy-momentum tensors. But in the Dodecahedral String-Graviton Coherence Framework (DSGCF), graviton fields interact with the coherence properties of quantum geometry. They modulate the quantum state via phase-field tension and entropy feedback—creating a bridge between informational geometry and macroscopic curvature.

This explains how coherence-preserving behavior—such as delayed decoherence in Tritium or regulated photon time-of-flight in GRB 221009A—may occur without requiring classical gravitational force. These phase-field gravitons, while non-energetic in the traditional sense, are responsible for geometric memory transfer through the SGCV medium [4, 5].

Thus, within the DSGCF, the graviton's role is neither forceful nor purely massless, but is fundamentally redefined as a curvature-sensitive coherence stabilizer. Its effective mass and action derive not from rest energy but from its entropy-curvature function—acting at the interface between quantum information and the gravitational fabric of spacetime.

# 9. Graviton-Induced Phase Delays and Validation from GRB 221009A

The DLSFH-SGCV model finds compelling empirical support in the photon time-of-flight data from Gamma-Ray Burst GRB 221009A. Observations from the Large High Altitude Air Shower Observatory (LHAASO) revealed a measurable energy-dependent delay, where TeV-scale photons arrived with a lag of up to 7 seconds after lower-energy photons during the burst onset [5].

## 9.1. Time Delay and LIV Interpretation

This time delay $\Delta t$ is interpreted as a Lorentz Invariance Violation (LIV) signature in both the DLSFH framework and effective field LIV models. The modified photon dispersion relation implies an energy-dependent speed of light. For photon energies $E_2 > E_1$, the LIV-induced delay is modeled as [5]:

$$ \Delta t_{\text{LIV}}(n, E_2, E_1) = S_n(E_2^n - E_1^n) \int_0^z \frac{dz'}{H(z')}, \qquad (19) $$

where:

* $n$ is the LIV index: $n = 1$ (linear) or $n = 2$ (quadratic),

* $S_n = \frac{1+n}{2H_0 E_{\text{QG}}^n}$ encapsulates the quantum gravity scale $E_{\text{QG}}$,

* $H(z)$ is the redshift-dependent Hubble parameter.

## 9.2. Energy Scale Constraints

The LHAASO collaboration applied two statistical analyses—Cross-Correlation Function (CCF) and Maximum Likelihood (ML)—to extract constraints on LIV energy scales. These are among the tightest to date:

* Linear case ($n = 1$): $E_{\text{QG},1} > 1.0 \times 10^{20}$ GeV (subluminal), $> 1.1 \times 10^{20}$ GeV (superluminal),

* Quadratic case ($n = 2$): $E_{\text{QG},2} > 6.9 \times 10^{11}$ GeV (subluminal), $> 7.0 \times 10^{11}$ GeV (superluminal).
### 9.3. DLSFH Framework Interpretation

In the Dodecahedron Linear String Field Hypothesis (DLSFH), such delays arise not from LIV per se, but from string-qubit coherence distortion modulated by graviton fields in the Superluminal Graviton Condensate Vacuum (SGCV). As described by Valamontes [4, 6], these graviton fields are off-lattice coherence regulators that redistribute curvature tension. They act to mediate information flow via phase correction—analogous to the neutron-induced transition in the H-2 to H-3 nuclear geometry.

### 9.4. Visual Comparison of Energy-Delay Scaling

To illustrate the energy-dependence of photon delays, Figure 8 shows the approximate curve for GRB 221009A. The nonlinear scaling of delay with energy qualitatively matches both LIV and DLSFH predictions.

<figure><img src="image_9.png" /><figcaption>Figure 8: Approximate photon time delay vs. energy observed in GRB 221009A, exhibiting non-linear delay growth above 1 TeV.</figcaption></figure>

### 9.5. Cross-Scale Theoretical Convergence

This empirical result supports a core thesis of the present study: graviton-induced coherence dynamics occur across scales—from qubit realignment in nuclear transitions to string-curvature phase shifts in astrophysical propagation. The coherence decay of $\psi_s^*$ described in Valamontes [4] also mirrors the dissipationless information transfer observed in GRB photons, where energy does not vanish but reconfigures across curvature gradients in SGCV space.

These findings elevate the DLSFH–SGCV model from a nuclear-level proposal to a testable cosmological framework, with GRB 221009A providing rare convergence of experimental astrophysics and theoretical quantum geometry.

## 10. Markoulakis–Valamontes Informational Carrier (MVIC)

Building on the curvature-corrective dynamics defined in previous sections, we introduce the Markoulakis–Valamontes Informational Carrier (MVIC), a proposed nonlocal mediator responsible for phase rebalancing across qubit-curvature geometries. Originally posited by Markoulakis [3] as a hidden informational particle propagating faster than light
without violating causality, the MVIC is here identified with the SGCV graviton field operator $G^\mu(x)$ in the DSGCF framework.

The MVIC does not transmit classical signals, but instead encodes entropy-weighted curvature modulation through a dynamically generated effective mass:

Effective Mass of the MVIC Field Operator

$$m_{\text{MVIC}}^{\text{eff}}(x, t) = \alpha \cdot \frac{|\nabla S(x, t)| \cdot R(x, t)}{c^2}$$

This field governs coherence rebalancing under spatial entropy gradients, aligning qubit phase angles without local force-based interaction. It represents a broader generalization of nonlocal informational structure in graviton-mediated systems.

MVIC Diagram: Informational Field Action Across Entangled Qubit Systems

<figure><img src="image_10.png" /><figcaption>Figure 9: MVIC diagram illustrating the role of the Markoulakis–Valamontes Informational Carrier field $G^\mu$ between two entangled qubit systems. The entropy gradient $\nabla S$ drives local curvature asymmetry $(R(x, t))$, while MVIC mediates phase alignment and coherence stabilization. The coherence tensor $C^{\mu\nu}$ remains resilient as graviton-field feedback propagates across time-evolving qubit geometries.</figcaption></figure>

This interpretation strengthens the theoretical coherence between graviton-phase feedback, entropy regulation, and curvature-based geometry—and offers an additional explanatory bridge between DSGCF dynamics and experimental observations of nonlocal entanglement phenomena.
## 11. Conclusion

This paper introduces a geometrical-coherence approach to nuclear transformations by embedding graviton influence directly into qubit-level dynamics. Leveraging the Dodecahedron Linear String Field Hypothesis (DLSFH) and the Superluminal Graviton Condensate Vacuum (SGCV), we construct a unified framework—termed the Dodecahedral String-Graviton Coherence Framework (DSGCF)—to explain coherence regulation, metastability, and decay across isotopic states.

At its core, the framework reveals that phase coherence in nuclear systems is not merely a byproduct of quantum interactions or nuclear binding energies, but can instead be understood as a gravitationally-mediated, curvature-sensitive tensor field process. The transition from Hydrogen-2 to Hydrogen-3 serves as a minimal working model, wherein the addition of a neutron introduces entropy-gradient curvature tension that must be redistributed to preserve partial coherence. This redistribution is shown to be governed by off-lattice graviton fields operating within the SGCV background, smoothing the isotopic transition without immediate collapse.

The Valamontes-Markoulakis Coherence Collapse Mechanism (VM-CCM) formalizes the entropy-threshold condition that triggers phase collapse, while the Valamontes-Markoulakis Identity (VMI) provides the corresponding differential law that dictates how the coherence tensor $C^{\mu\nu}$ decays over time. These tools together redefine beta decay not simply as a weak-force-mediated nuclear event, but as a topological coherence disintegration encoded into the geometry of the quantum field.

Our model also demonstrates that quantum coherence can persist at biologically relevant temperatures, such as 37°C, provided SGCV graviton fields are active. This opens the door to a possible unification of quantum biology, nuclear physics, and gravitational theory under a common geometrical-curvature language.

The DLSFH-SGCV mechanism thus reframes the understanding of isotopic behavior, coherence resilience, and gravitational modulation in quantum systems. Appendices A-C outline foundational terminology, glossary references, and a roadmap for future research, including SGCV quantization, gravitational phase fidelity in mesons, and entropy-driven memory in cosmological and biological qubit systems.

Overall, the Dodecahedral String-Graviton Coherence Framework (DSGCF) stands not only as a theoretical refinement of graviton roles in nuclear transitions, but also as a flexible platform for modeling quantum-gravitational interactions across disciplines.
Appendix A: Abbreviations

<table><caption>Table .1: Abbreviations Used Throughout This Paper</caption><thead><tr><td>Abbreviation</td><td>Full Term / Description</td></tr></thead><tbody><tr><td>DLSFH</td><td>Dodecahedron Linear String Field Hypothesis</td></tr><tr><td>SGCV</td><td>Superluminal Graviton Condensate Vacuum</td></tr><tr><td>DSGCF</td><td>Dodecahedral String-Graviton Coherence Framework (DLSFH + SGCV unification)</td></tr><tr><td>VM-CCM</td><td>Valamontes-Markoulakis Coherence Collapse Mechanism</td></tr><tr><td>VMI</td><td>Valamontes-Markoulakis Identity (entropy-controlled coherence decay)</td></tr><tr><td>C<sup>μν</sup></td><td>Coherence tensor between qubit-curvature states</td></tr><tr><td>ψ<sup>*</sup><sub>s</sub></td><td>Observable quantum coherence field in DLSFH geometry</td></tr><tr><td>G<sup>μ</sup></td><td>Graviton phase field operator in SGCV</td></tr><tr><td>∇S</td><td>Entropy gradient driving phase instability</td></tr><tr><td>m<sup>eff</sup><sub>g</sub></td><td>Effective graviton mass due to curvature and entropy coupling</td></tr><tr><td>GRB 221009A</td><td>Observed gamma-ray burst used for quantum gravity validation</td></tr></tbody></table>
## Appendix B: Glossary of Key Theoretical Terms

<table><caption>Table 2: Glossary of Theoretical Terms in the DSGCF Framework</caption><thead><tr><td>Term</td><td>Definition / Description</td></tr></thead><tbody><tr><td>DSGCF</td><td>Dodecahedral String–Graviton Coherence Framework: A unification of DLSFH and SGCV describing qubit-curvature coherence and graviton-regulated phase behavior [6].</td></tr><tr><td>VM–CCM</td><td>Valamontes–Markoulakis Coherence Collapse Mechanism: A phase-collapse mechanism triggered by entropy gradients, redistributing coherence into ghost curvature fields [4, 3].</td></tr><tr><td>VMI</td><td>Valamontes–Markoulakis Identity: Describes entropy-driven coherence decay. Equation: $\frac{dC^{\mu\nu}}{dt} = -\left(\frac{|\nabla S| - \sigma_c}{\sigma_c}\right)C^{\mu\nu}$</td></tr><tr><td>SGCV</td><td>Superluminal Graviton Condensate Vacuum: A nonlocal coherence field that stabilizes quantum systems via graviton phase modulation [3].</td></tr><tr><td>DLSFH</td><td>Dodecahedron Linear String Field Hypothesis: A model of nucleons as qubit-encoded vertices within a dodecahedral geometry [6].</td></tr><tr><td>$\psi_s^*$</td><td>Observable coherence field in DLSFH; collapses into curvature ghosts and vacuum fluctuations under decoherence.</td></tr><tr><td>$C^{\mu\nu}$</td><td>Coherence tensor measuring alignment between qubit pairs distributed across a dodecahedral lattice.</td></tr><tr><td>$G^\mu$</td><td>Graviton operator in SGCV: a curvature-sensitive field that corrects quantum phase without transferring force.</td></tr><tr><td>$m_g^{\text{eff}}$</td><td>Effective graviton mass due to curvature–entropy interaction. Defined as: $m_g^{\text{eff}}(x, t) = \alpha \cdot \frac{|\nabla S(x, t)| \cdot R(x, t)}{c^2}$</td></tr></tbody></table>

## Appendix C: Open Questions and Future Research Directions

Despite the theoretical robustness of the Dodecahedral String–Graviton Coherence Framework (DSGCF) and the coherence-collapse mechanisms formalized through the Valamontes–Markoulakis Coherence Collapse Mechanism (VM–CCM) and Valamontes–Markoulakis Identity (VMI), several open questions remain that require both mathematical refinement and empirical validation. These future pathways include:

### 1. Empirical Measurement of SGCV-Induced Phase Correction

Can graviton-regulated coherence be indirectly measured through photon arrival time patterns or quantum entanglement fidelity in warm environments? GRB 221009A offers a promising but still indirect constraint.
## 2. Quantization of the Graviton Operator $G^\mu$

Can the SGCV graviton operator be embedded in a larger quantized field theory—e.g., a curved-space extension of non-Abelian gauge theory or within a path integral over entropy-curvature manifolds?

## 3. Biophysical Validation of Warm-Environment Coherence

Can coherence longevity at 37°C predicted by SGCV graviton modulation be verified in biological qubit systems (e.g., microtubule arrays, DNA solitons, or artificial warm qubits)?

## 4. Coherence Topology of Exotic Baryons

Does the DSGCF predict alternate metastable coherence geometries for short-lived baryonic states (e.g., $Λ, Ξ, Ω$), and could their decay modes be modeled using graviton-mediated phase transition diagrams?

## 5. Topological Memory Transfer Across Qubit Layers

Is $\psi_s^*$ collapsible into curvature memory that can persist across disconnected qubit networks (e.g., between isotopes, or across early universe structures)? Can this be used to explain long-range coherence in quantum cosmology?

## 6. Entropy Gradient Geometry in Expanding Spacetime

How does $\nabla S$ evolve in cosmologically expanding backgrounds? Can it be used to refine the dynamic mass function $m_s^{\text{eff}}(x, t)$ of gravitons in early-universe inflation or post-recombination eras?

## 7. Extension to Meson–Photon Phase Collapse Models

Can VM-CCM and DSGCF be adapted to describe quark recombination, meson-gluon evaporation, and photon-driven meson phase collapse? How does $\delta C^{\mu\nu}$ behave in pion/kaon quantum string geometries?

## 8. Multiscale Entanglement Diagnostics

Can the decay of $\psi_s^*$ coherence be used to model multiscale quantum memory entanglement—from isotopic configurations to stellar neutrino flux—and potentially across biological systems?

## 9. SGCV–Inflaton Duality Hypothesis

Is it possible that SGCV curvature memory fields are remnants or duals of inflationary scalar fields? Could this lead to a unification of DLSFH geometry with early-universe inflation theory?
<figure><img src="image_11.png" /><figcaption>Figure .10: Color-coded roadmap of nine open research directions within the DSGCF framework. Fields are grouped by core domain: quantum gravity (blue), particle physics (green), biology (red), and cosmology (yellow). Each path is mapped to its associated equation, section, or figure.</figcaption></figure>

These directions offer opportunities for experimental design, simulation modeling (e.g., DSGCF tensor dynamics), cross-disciplinary applications (quantum biology, cosmology, and quantum computing), and new theoretical constructs that could deepen the role of graviton-regulated coherence in fundamental physics.

## Glossary

**Dodecahedral String-Graviton Coherence Framework (DSGCF)** A unified framework combining the Dodecahedron Linear String Field Hypothesis (DLSFH) and the Superluminal Graviton Condensate Vacuum (SGCV). DSGCF governs entropy-corrected coherence, qubit-curvature alignment, and graviton-mediated thermal stability across nuclear, cosmological, and biological systems

**Markoulakis-Valamontes Informational Carrier (MVIC)** A nonlocal informational field operator hypothesized to transmit curvature-phase alignment faster than light without classical signaling. In the Dodecahedral String-Graviton Coherence Framework (DSGCF) framework, it corresponds to the SGCV graviton operator $G^\mu(x)$ and acquires an effective mass given by $m_{MVIC}^{\text{eff}}(x, t) = \alpha \cdot (|\nabla S(x, t)| \cdot R(x, t))/c^2$

**Valamontes-Markoulakis Coherence Collapse Mechanism (VM-CCM)** A coherence decay mechanism describing entropy-gradient-induced phase disintegration in DLSFH qubit lattices. Triggered when the entropy gradient
exceeds a critical threshold, it leads to collapse of the coherence tensor and redistribution of coherence energy into ghost curvature, vacuum fluctuations, and Ricci memory. The mechanism was introduced by Valamontes and supported by SGCV-based entropy-curvature dynamics described by Markoulakis

**Valamontes–Markoulakis Identity (VMI)** A differential identity defining the entropy-gradient-driven decay of the coherence tensor $C^{\mu\nu}$ in DLSFH qubit-curvature networks. Formally expressed as $\frac{dC^{\mu\nu}}{dt} = -((|\nabla S| - \sigma_c)/\sigma_c) \cdot C^{\mu\nu}$ for $\nabla S > \sigma_c$, it serves as the mathematical core of the Valamontes–Markoulakis Coherence Collapse Mechanism (VM–CCM) within the Dodecahedral String–Graviton Coherence Framework (DSGCF) framework

**References**

[1] et al., N.L., 2013. Quantum biology. Nature Physics 9, 10–18. doi:10.1038/nphys2474.

[2] Hameroff, S., Penrose, R., 1996. Orchestrated reduction of quantum coherence in brain microtubules: A model for consciousness? Journal of Consciousness Studies 3, 36–53.

[3] Markoulakis, E.N., 2024. Superluminal graviton condensate vacuum. International Journal of Physical Research 12, 45–61. doi:10.14419/bmr9g725.

[4] Valamontes, A., 2025a. Persistence beyond decoherence: Tracing the fate of $\psi_s^*$ energy in mc–sgcv geometry. Kapodistrian Academy of Science URL: https://www.researchgate.net/publication/390271715.

[5] Valamontes, A., 2025b. Refining the time of flight, creation mechanism, and expansion of the universe using the dlsfh and data from grb 221009a. Kapodistrian Academy of Science URL: https://www.researchgate.net/publication/390228057.

[6] Valamontes, A., 2025c. A unified framework of light and quantum geometry. Kapodistrian Academy of Science URL: https://www.researchgate.net/publication/390201850.

[7] Weinberg, S., 1972. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. John Wiley & Sons.

[8] Zurek, W.H., 2003. Decoherence, einselection, and the quantum origins of the classical. Reviews of Modern Physics 75, 715–775. doi:10.1103/RevModPhys.75.715.