The Communication–Coherence Framework (CCF)
Date: October 2025
Preface
The Communication–Coherence Framework (CCF) proposes that coherence—the organizing principle underpinning systems from the quantum to the cognitive—propagates through communication, which serves as its transfer medium across scales. Time itself emerges from this flow: as coherence moves, time advances; when coherence halts, temporal progression ceases. Because coherence cycles through formation, stabilization, and dissipation, its rhythms refine systemic order. CCF thus describes a self-organizing universe in which coherence, communication, and time evolve toward integrated complexity.
Abstract
CCF investigates whether coherence—expressed as quantum purity, neuronal synchrony, or thermodynamic order—acts as a unifying descriptor across complex systems. Communication is treated as the process mediating coherence transfer between organizational levels, defining when coherence is preserved, transformed, or lost. By linking coherence, energy, and information flow, CCF provides a theoretical foundation for integrating inquiry across physics, neuroscience, and thermodynamics.
1. Introduction
Recent research in physics and information theory reveals deep connections among energy, information, and systemic order. CCF explores coherence as a universal metric of organization and communication as the mechanism enabling its propagation through scale hierarchies.
2. Limits and Regimes of Coherence Conservation
While physical conservation laws derive from continuous symmetries (Noether’s theorem), coherence is not universally conserved. Quantum systems lose purity through decoherence, and classical or biological systems degrade coherence through feedback, interaction, and noise. CCF posits that coherence exhibits only conditional or approximate conservation, maintained under symmetry-preserving or closed conditions.
3. Coherence Across Domains
Coherence appears under diverse measurable forms:
- Quantum mechanics: purity Tr(ρ²), entanglement
- Neuroscience: phase synchrony, cross-spectral coherence
- Thermodynamics: order parameters, entropy gradients
CCF views these as contextual manifestations of a single relational property, exploring whether coherence metrics in different domains obey consistent transformation laws.
4. Quantized Communication Principle
Incremental information–energy coupling is described by:
q(E) = dI/dE
This parameter expresses the information–energy gradient within a communicating system. Treated as a heuristic, q(E) guides exploration of interdependence between coherence maintenance and energetic exchange.
5. Communication and Coherence Transfer
In neuroscience, “communication through coherence” describes how synchronized oscillations route information among neural populations. CCF generalizes this across physical, biological, and cognitive systems, defining communication as coherence redistribution through interaction, feedback, or coupling.
6. Empirical Directions
Key research questions:
- Under what conditions are coherence-like parameters conserved, transformed, or lost?
- How do coherence, energy flux, and information flow interact?
Potential experiments:
1. Compare coherence decay in isolated vs. open quantum systems.
2. Quantify coherence transfer and entropy flux in neural networks.
3. Evaluate coherence–energy coupling in engineered communication systems.
7. Philosophical Context
CCF tolerates speculative interpretations—for example, a universe oscillating between latent and manifest coherence—but treats them metaphorically, not as physical claims. The “value metric” V is introduced as a nonphysical quantity expressing alignment between local and global coherence flows.
8. Theoretical Objectives
- Formulate quantitative links among coherence, information, and entropy.
- Model communication as a process of coherence transfer.
- Identify falsifiable connections among physical, neural, and thermodynamic phenomena.
Core hypothesis: communication universally represents coherence exchange.
9. Conclusions
CCF establishes:
- A theoretical structure connecting coherence, communication, and time.
- Recognition that coherence is conditionally sustained, not absolutely conserved.
- A cross-disciplinary basis for empirical and mathematical unification.
10. Communication–Coherence Continuity Relation
∂C/∂t + ∇·JC = α(∂I/∂t + ∇·JI) – κ(∂S/∂t + ∇·JS) + βP
Definitions:
C: coherence density
I: information density
S: entropy density
JC, JI, JS: respective fluxes
α, κ, β: coupling coefficients
P: external power
This continuity-style equation mirrors transport laws in non-equilibrium systems, reinterpreted in informational space: communication is the flux of coherence through time.
Compact operator form:
DtC = αDtI – κDtS + βP
DtX = ∂X/∂t + ∇·JX
10.1 Coherence Field Equation
At microscale, coherence is represented by a complex field Φ(r,t):
iħ∂Φ/∂t = [–ħ²/2m ∇² + V + Scoh]Φ
where Scoh models stabilization against decoherence. For Scoh = 0, the standard Schrödinger equation is recovered; Scoh ≠ 0 predicts extended coherence lifetimes or emergent order.
The continuity expression:
∂C/∂t + ∇·JC = 2Re[Φ*∂Φ/∂t]
links microscopic field dynamics with macroscopic coherence flux.
10.2 Dimensional Transition Symmetry
Cross-domain coherence transformations are defined through parameter ξ:
Φrel = Tξ[Φquant]
where Tξ maps curvature-encoded information into coherence geometry. This expresses a conjectured duality: spacetime curvature and informational order may be complementary manifestations of conserved coherence.
11. Systemic Autonomy
dCtotal/dt = dCinternal/dt + dCexternal/dt = 0
Open systems:
dCinternal/dt = –Φc + σC
with communication flux Φc and internal regeneration σC.
Equilibrium requires σC = Φc; autonomy arises when σC > Φc.
Entropy couples inversely:
dS/dt ∝ –dCinternal/dt
Decision processes maximize total coherence:
Choice = argmaxpath_i Ctotal(path_i)
modeling adaptive selection under informational and energetic constraints.
11.1 Entropy–Coherence Resistance
Define resistance coefficient:
η = –(dS/dt)/(dCinternal/dt)
High η indicates strong feedback-driven coherence maintenance; low η implies vulnerability to noise. η can be experimentally estimated via synchrony or variance reduction measures.
12. Open Research Questions
- How does Scoh alter empirical decoherence rates?
- Can coherence-field formulations yield observable deviations from standard models?
- What roles do dimensional transitions play in unifying quantum and relativistic regimes?
- How can η be operationalized within biological feedback systems?
13. Experimental Scenarios
The following experimental domains test the Communication–Coherence Framework’s prediction that active feedback (“communication”) can stabilize or extend coherence by coupling informational and energetic flow.
1. Quantum Optics – Controlled Feedback on Entangled Pairs
Introduce a tunable coherence-stabilization field S_coh through adaptive optical feedback to entangled photons.
Measure coherence time, purity (Tr ρ²), and interference visibility as functions of feedback strength.
Objective: Determine whether informational feedback serves as an energetic input (βP term) sustaining coherence.
2. Interferometry – Communication-Modulated Phase Coupling
In a Mach–Zehnder interferometer, apply phase modulation linked to the information–energy gradient q(E) = dI/dE.
Monitor fringe contrast and phase stability across modulation regimes.
Objective: Test how coherent information transfer affects the coherence flux (J_C) and overall temporal stability.
3. Condensed Matter – Coherence Feedback in Cold-Atom Lattices
Engineer feedback-coupled optical traps to modulate internal coherence stabilization (S_coh).
Quantify emergent patterns using coherence tomography and phase-space entropy reduction.
Objective: Examine coherence transfer across local and collective degrees of freedom, linking micro- and mesoscale communication processes.
4. Biological or Artificial Networks – Entropy–Coherence Resistance (η)
Apply controlled noise and feedback in neural or synthetic oscillator networks to estimate
η = –(dS/dt)/(dC_internal/dt).
Objective: Empirically evaluate entropy–coherence coupling and identify conditions that produce sustained internal coherence (autonomy regime).
Expected Outcome
Detection of feedback-dependent stabilization or reduced decoherence across these systems would support the hypothesis that communication acts as coherence exchange, grounding CCF’s informational continuity equation in measurable dynamics.
Research Proposal Summary
Core Question: How does Scoh stabilize coherence and modify interference or decoherence behavior?
Method: Conduct parallel experiments across optical, interferometric, condensed-matter, and network domains using controlled feedback and coherence-spectrum analysis.
Impact: Empirical validation would suggest that coherence is an actively regulated informational quantity underlying both physical and temporal structure.
Appendix C – Mathematical Notes and Symbol Reference
1. Dimensional Structure
All quantities are expressed in generalized informational–thermodynamic units.
C – coherence density [bits m⁻³] or [entropy reduction rate]; degree of systemic order or phase alignment.
I – information density [bits m⁻³]; stored or transmitted information.
S – entropy density [J K⁻¹ m⁻³] or dimensionless Shannon entropy; disorder or uncertainty.
J_C, J_I, J_S – fluxes of coherence, information, and entropy respectively (quantity × velocity); spatial transport.
P – external power input [J s⁻¹ m⁻³]; energetic drive sustaining coherence.
α, κ, β – dimensionless coupling coefficients; weight information, entropy, and power influence on coherence evolution.
Φ_c – communication flux [coherence rate]; net outward coherence exchange.
σ_C – internal regeneration rate [coherence s⁻¹]; feedback‑based restoration of coherence.
η – entropy–coherence resistance (dimensionless); system’s ability to resist decoherence through feedback.
S_coh – coherence‑stabilization potential [J]; feedback potential maintaining field order.
q(E) – information–energy gradient [dI/dE]; rate of informational change with energy expenditure.
Φ(r,t) – coherence field (complex amplitude); wave‑like representation of local coherence.
ξ – dimensional transition parameter; maps quantum to relativistic representations.
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2. Continuity and Field Relations
Generalized continuity relation:
∂C/∂t + ∇·J_C = α(∂I/∂t + ∇·J_I) − κ(∂S/∂t + ∇·J_S) + βP
Analogous to non‑equilibrium thermodynamic transport equations, this expression defines communication as the flow of coherence, balancing informational gain (+α), entropic resistance (−κ), and energetic input (+βP).
Microscopically, coherence follows:
iħ ∂Φ/∂t = [−ħ²/2m ∇² + V + S_coh] Φ
S_coh introduces stabilization feedback opposing decoherence.
When S_coh = 0, the formulation reduces to the standard Schrödinger equation.
The macroscopic continuity form emerges via:
∂C/∂t + ∇·J_C = 2 Re[Φ* ∂Φ/∂t],
linking field‑level evolution to measurable coherence flux.
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3. Energetic and Informational Couplings
α – information‑to‑coherence conversion (α > 0 ⇒ adaptive gain).
κ – coherence degradation via entropy; high κ ⇒ rapid decoherence.
β – energetic support sustaining coherence; β > 0 ⇒ driven systems.
Approximate energy balance per volume:
Ė_coh = ħ (dC/dt) ≈ α (dI/dt) − κ (dS/dt) + βP.
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4. Autonomy Criterion and Entropy Resistance
Open‑system coherence evolution:
dC_internal/dt = −Φ_c + σ_C
Autonomy arises when σ_C > Φ_c, meaning feedback exceeds external coherence loss.
Entropy couples inversely:
dS/dt ∝ − dC_internal/dt
Define resistance coefficient:
η = − (dS/dt) / (dC_internal/dt)
High η implies stable feedback; low η indicates susceptibility to noise.
Empirically, η may be estimated from variance reduction or increased synchrony under perturbation.
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5. Temporal Reciprocity
Reciprocal operators:
T_C(C) = ∂C/∂t
C_T(t) = ∂t/∂C
When coherence flux J_C = 0, temporal differentiation collapses.
Therefore, communication flow and time progression are co‑generative.
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6. Dimensional Transition Parameter
Transformation rule:
Φ_rel = T_ξ[Φ_quant]
The parameter ξ (0 ≤ ξ ≤ 1) maps quantum coherence amplitude to relativistic curvature representation, suggesting spacetime curvature and informational order are dual manifestations of conserved coherence.
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7. Measurement and Operationalization
Observable counterparts to theoretical variables:
– Quantum optics: coherence time, interference visibility, stabilization potential S_coh.
– Neuroscience: phase synchrony, entropy rate, feedback‑derived η.
– Thermodynamics: order parameters, entropy flux related to κ and Φ_c.
– Systems engineering: feedback gain, signal variance, and noise suppression associated with σ_C, Φ_c, and η.
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8. Summary
These mathematical notes define the symbolic and dimensional foundations of the Communication–Coherence Framework.
They clarify how coefficients (α, κ, β) and parameters (S_coh, η, ξ) correspond to measurable properties of coherence behavior across quantum, biological, and cognitive domains.
Together, they form a bridge between the formal continuity relation and potential empirical verification of coherence as a conserved informational quantity.
Communication–Coherence Framework (CCF)
Date: October 2025
Abstract
The Communication–Coherence Framework (CCF) explores whether coherence—expressed as quantum purity, phase synchrony, or statistical order—acts as a unifying descriptor across complex systems. CCF proposes that communication mediates coherence transfer between levels of organization and examines the conditions under which coherence is preserved, transformed, or lost. The framework also proposes hypothetical correspondences among coherence, information, and energy flow, establishing a conceptual foundation for unifying inquiry across physics, neuroscience, and thermodynamics.
1. Introduction
Advances in physics and information theory reveal profound connections among energy, information, and order across physical and biological systems. The Communication–Coherence Framework (CCF) investigates coherence as a general descriptor of system organization. Communication is treated as the mechanism enabling coherence to propagate across scales, raising the question of when coherence is maintained or dissipated.
2. Limits and Possible Regimes of Coherence Conservation
Conservation laws in physics—such as those for energy or momentum—arise from continuous symmetries (Noether’s theorem). Coherence, however, is not universally conserved:
• Quantum systems lose purity (Tr ρ²) through decoherence caused by environmental coupling.
• Classical or biological systems may gain or lose coherence through interaction, feedback, or noise.
CCF Position: Coherence is not a fundamental conservation law. Instead, approximate conservation may occur under closed or symmetry‑preserving conditions. Identifying when and how this occurs defines a primary scope of investigation.
3. Coherence Across Domains
Coherence takes different measurable forms depending on the system context:
• Quantum mechanics: purity (Tr ρ²), entanglement measures
• Neuroscience and signal processing: phase synchrony, cross‑spectral coherence
• Thermodynamics: order parameters, entropy gradients
CCF Position: Coherence is a contextual construct. CCF does not claim these measures are identical but studies whether coherence transformations exhibit consistent relational structures across domains.
4. Quantized Communication Principle
A proposed parameter q(E) = dI/dE links changes in information and energy. The parameter remains theoretical and currently unverified.
CCF Position: q(E) is adopted as a hypothetical metric for exploring coherence–information coupling. It may guide analysis rather than define a universal physical property.
5. Communication and Coherence Transfer
In neuroscience, the concept of “communication through coherence” refers to dynamic synchronization among brain networks. CCF extends this idea generally, suggesting communication may sometimes correspond to coherence transformations.
CCF Position: The extension is conceptual, not universal. Evidence for coherence‑based communication beyond neural systems remains to be established empirically.
6. Empirical Questions and Directions
Key inquiries for testing CCF include:
• Under what conditions do coherence‑like parameters display conservation, transformation, or decay?
• Are there measurable relationships among coherence, energy exchange, and information flow?
Potential empirical approaches:
1. Compare coherence dynamics in isolated versus open quantum systems.
2. Quantify coherence transfer and entropy flux in biological or neural networks.
3. Analyze energy–information exchange behavior in engineered communication systems.
7. Philosophical Considerations
Speculative interpretations—such as viewing the universe as oscillating between latent and manifest coherence—are philosophical in nature. The value metric V, representing fidelity between local and global coherence flows, offers an interpretive metaphor for alignment rather than a measurable physical parameter.
8. Theoretical Objectives
CCF seeks to:
• Formulate cross‑domain analogies among coherence, information, and entropy flows;
• Develop quantitative frameworks to describe communication as coherence transfer;
• Establish falsifiable links among physics, neuroscience, and thermodynamic systems.
The goal is to determine whether the concept of communication can systematically express coherence exchange across scales.
9. Conclusions
The Communication–Coherence Framework offers:
• A disciplined, context‑sensitive account of coherence and communication;
• A recognition that coherence is conditionally preserved, not universally conserved;
• A multidisciplinary approach connecting empirical testing to theoretical modeling.
CCF remains an active research proposal aimed at discovering whether coherence underlies the informational structure of physical reality.
10. Central Governing Equation (Communication–Coherence Continuity Relation)
The Communication–Coherence Framework is grounded in a continuity‑style equation that governs how coherence evolves and is exchanged through communication. This relation formalizes coherence as a quantity that can flow, couple, or dissipate through interaction with information and entropy fluxes:
∂C/∂t + ∇·J_C = α(∂I/∂t + ∇·J_I) − κ(∂S/∂t + ∇·J_S) + βP
Here, C denotes coherence density, I information density, S entropy density, J_x their respective fluxes, P external power input, and α, κ, β are system‑specific coupling coefficients. This form parallels non‑equilibrium transport equations but generalizes them to the informational domain: communication is treated as the flux of coherence through time. In compact operator form: 𝒟_t C = α𝒟_t I − κ𝒟_t S + βP, where 𝒟_t X = ∂X/∂t + ∇·J_X.
This continuity relation serves as the central mathematical principle of CCF, linking coherence evolution to information flow, entropy resistance, and energy exchange.
11. Open Research Questions for Future Investigation
The following questions highlight emerging directions for empirical and theoretical research based on the Communication–Coherence Framework (CCF):
• How does the inclusion of coherence stabilization (S_coh) in quantum systems alter measurable decoherence rates compared to predictions from standard quantum theory?
• How does coherence stabilization (S_coh) influence quantum system behavior beyond conventional decoherence models?
• What measurable effects arise in quantum experiments when the Communication–Coherence Framework’s coherence field is actively modeled?
• How does the introduction of dimensional transitions in the CCF modify predictions for emergent structure in quantum and relativistic systems?
Appendix A. Notation and Symbols
Symbol Definition
C Coherence measure
I Information
S Entropy
q(E) Hypothetical information–energy rate dI/dE
ρ Density matrix
J_C, J_I, J_S Fluxes of coherence, information, entropy
α, κ, β Coupling coefficients
P Power input
T_C(C), C_T(t) Time–coherence operators
V Value metric (interpretive)
Appendix B. Time–Communication Reciprocity
If communication represents coherence transfer, time can be treated as its ordered progression:
∂C/∂t = ∇·J_C ⇒ communication exists.
In the absence of coherence flux (J_C = 0), time loses operational meaning locally. The reciprocal operator pair,
T_C(C) = ∂C/∂t
C_T(t) = ∂t/∂C
suggests temporal continuity and communication are mutually generative processes. At equilibrium, time degenerates; under increasing communication, time structure differentiates. This speculative symmetry offers a possible bridge between dynamical systems, causality, and temporal cognition.
12. Illustrative Experimental Scenarios and Refinement Strategy
The following conceptual experimental designs demonstrate how the Communication–Coherence Framework (CCF) could be empirically explored through measurable deviations, coherence modulation, and emergent structure formation:
Example 1: Decoherence Rate Deviation in Quantum Optics
• Objective: Test if introducing coherence stabilization S_{coh} affects quantum decoherence rates beyond environmental contributions.
• Setup: Use a photonic quantum optics system with entangled photons.
• Method: Prepare entangled photon pairs, then introduce controlled environmental noise with and without coherence stabilization via engineered feedback or interaction protocols.
• Measurement: Detect photon coherence times and entanglement visibility using interferometric methods.
• Expected Outcome: Observable deviations in decoherence rates or entanglement decay with S_{coh} present versus baseline models.
Example 2: Interference Pattern Modulation in an Interferometer
• Objective: Determine if CCF’s coherence field modulates interference fringes in a Mach–Zehnder interferometer.
• Setup: Mach–Zehnder interferometer with controllable phase shifts.
• Method: Implement mechanisms mimicking coherence stabilization effects in one arm, for example via dynamic phase modulation tied to predicted S_{coh} parameters.
• Measurement: Record interference patterns with high‑resolution photodetectors, analyze fringe contrast and phase shifts.
• Expected Outcome: Detectable changes in fringe visibility or phase consistent with CCF predictions.
Example 3: Emergent Structure Observation in Condensed Matter
• Objective: Observe emergent coherence‑driven structures consistent with dimensional transitions proposed by CCF.
• Setup: Utilize cold atom lattices or Bose–Einstein condensates.
• Method: Manipulate coherence parameters via external fields or inter‑particle interactions.
• Measurement: Use time‑of‑flight imaging or coherence tomography to capture emergent structure formation dynamics.
• Expected Outcome: Novel structural coherence signatures differing from current models, validating CCF mechanisms of emergence.
Refinement Strategy
• Tailor experimental parameters quantitatively based on CCF’s mathematical formulations.
• Collaborate with experimental physicists to assess technical feasibility and instrumentation.
• Prepare simulation models to predict expected results and refine hypotheses iteratively.
Research Proposal: Empirical Validation of the Communication–Coherence Framework (CCF)
1. Introduction
The Communication–Coherence Framework (CCF) proposes an integrative model unifying quantum mechanics and relativity through coherence as a fundamental informational field. Unlike conventional theories that treat coherence as a derivative property, CCF conceptualizes it as a dynamic quantity whose stabilization mechanisms mediate transitions between quantum and relativistic domains. This approach introduces the novel term coherence stabilization (S_coh) to describe processes that preserve quantum order against decoherence, offering new explanatory power for phenomena such as quantum stability, dimensional transitions, and emergent structure formation.
2. Research Questions
This study seeks to empirically test CCF predictions through the following core question:
How does coherence stabilization (S_coh) affect decoherence rates and interference patterns in quantum systems beyond standard quantum theory predictions?
Supplementary lines of inquiry include:
• Does the inclusion of S_coh alter measurable decoherence dynamics in quantum optics?
• Can modulation of interference patterns in interferometry validate CCF’s predicted coherence field effects?
• How do coherence-driven dynamics contribute to emergent structure formation in condensed-matter systems?
3. Theoretical Background
CCF introduces theoretical elements that extend established physics while maintaining continuity with known principles:
• Coherence Field (Φ): a generalized representation combining the quantum wavefunction and spacetime curvature as manifestations of a unified coherence field.
• Dimensional Transition: reframes spacetime projection as an information–coherence flow across domains.
• Coherence Stabilization (S_coh): an energy-based stabilizing term that modifies standard Hamiltonian dynamics.
• Emergence: interpreted as a macroscopic expression of coherence dynamics under dimensional transitions.
The governing equation integrating these concepts is proposed as:
iħ ∂Φ/∂t = [ −ħ²/2m ∇² + V + S_coh ] Φ
Here, S_coh represents the coherence stabilization term, hypothesized to influence decoherence behavior and emergent ordering beyond conventional quantum mechanical expectations.
4. Experimental Design and Methodology
Three primary experimental domains are proposed to evaluate measurable effects of S_coh:
1. Quantum Optics (Decoherence Rate Deviation)
• Objective: Examine whether introducing coherence stabilization alters photon decoherence rates.
• Setup: Entangled photon pairs subjected to environmental noise with and without engineered S_coh feedback.
• Measurement: Photon coherence times and entanglement visibility via interferometric methods.
2. Interferometry (Fringe Modulation Study)
• Objective: Determine whether a modeled coherence field modulates fringe patterns in a Mach–Zehnder interferometer.
• Setup: One arm includes dynamic phase modulation linked to predicted S_coh parameters.
• Measurement: Fringe visibility, phase shifts, and contrast analyzed through high-resolution photodetectors.
3. Condensed Matter (Emergent Coherence Structures)
• Objective: Observe coherence-driven emergent patterns in cold atom lattices or Bose–Einstein condensates.
• Setup: Manipulate coherence parameters via external field control or inter-particle coupling.
• Measurement: Time-of-flight imaging and coherence tomography for structure and phase analysis.
5. Measurement and Data Analysis
Data collection will employ photonic detectors, interferometric sensors, and coherence tomography to quantify coherence-related deviations. Statistical analyses (e.g., variance reduction, ANOVA, and spectral coherence mapping) will assess the significance of observed differences between CCF-based models and conventional quantum theory predictions.
6. Challenges and Mitigation Strategies
Challenges:
• Distinguishing S_coh-induced effects from environmental or instrumental noise.
• Achieving sufficient measurement sensitivity to detect subtle coherence field variations.
• Maintaining reproducibility across quantum and condensed-matter systems.
Mitigation Approaches:
• Implement high-fidelity controls and environmental isolation.
• Apply iterative refinement based on simulation models aligned with CCF equations.
• Collaborate with quantum optics and condensed-matter research groups for technical validation.
7. Expected Outcomes and Impact
The proposed research aims to provide the first empirical assessment of the Communication–Coherence Framework (CCF) by testing for deviations in coherence behavior beyond standard quantum predictions. Evidence supporting S_coh-related effects would suggest the presence of a stabilizing coherence field—potentially bridging the conceptual divide between quantum mechanics and general relativity and contributing to a deeper understanding of informational structure in physical reality.