The Unified Theory of Informational Spin: A Coherence-Based Framework for Gravitation, Cosmology, Quantum Systems, and Biology

1. Introduction: The Need for a New Unification Paradigm

Modern physics faces two enduring challenges: the conceptual incompatibility between general relativity and quantum mechanics, and the widespread reliance on dark matter and dark energy to reconcile theoretical models with cosmological observations. Despite decades of intensive research in string theory, loop quantum gravity, and related approaches, a fully unified framework supported by direct experimental confirmation has yet to emerge.

The Unified Theory of Informational Spin (TGU) proposes an alternative unification pathway by treating information, rather than matter or energy alone, as a foundational organizing element of physical reality. Within this framework, physical phenomena emerge from structured patterns of informational coherence—the stable and correlated distribution of information across spatial and temporal scales.

TGU represents a shift from force-centered descriptions toward an information-centered perspective. Instead of interpreting gravity exclusively as spacetime curvature induced by mass–energy, TGU models gravitational behavior as an emergent consequence of gradients in informational coherence. From this viewpoint, phenomena commonly attributed to dark matter and dark energy may be reinterpreted as manifestations of coherence distribution and reorganization within the informational substrate, rather than as evidence for additional, unobserved components.

This work consolidates three complementary developments within the TGU framework: the core theoretical formulation of informational spin and coherence, the geometric argument underlying the Matuchaki Parameter, and a phenomenological model for orbital precession incorporating coherence-dependent corrections. Together, these elements establish TGU as a mathematically consistent and internally coherent framework that generates empirically testable predictions across gravitational, cosmological, biological, and computational domains.

2. Foundations of Informational Spin

2.1. Conceptual Scope and Status

The concept of informational spin constitutes the foundational organizing element of the Unified Theory of Informational Spin (TGU). It is essential to clarify from the outset that informational spin is not introduced as a new microscopic quantum degree of freedom, nor as a replacement for quantum mechanical spin.

Instead, informational spin is defined as an effective organizational descriptor: a structured representation of how information is coherently distributed, stored, and transported within physical systems across scales.

In this sense, informational spin plays a role analogous to:

• Entropy in thermodynamics,
• Order parameters in condensed matter physics,
• Coarse-grained fields in effective theories.

Its validity is therefore assessed phenomenologically, through internal consistency and empirical convergence, rather than through derivation from microscopic field equations.

2.2. Operational Definition

Informational spin is defined as a localized, structured configuration of informational coherence that regulates the exchange and persistence of information within a system.

Operationally, an informational spin exists wherever:

1.

Information exhibits correlated organization across degrees of freedom,

2.

This organization is dynamically stable against entropic dispersion,

3.

Coherence gradients influence observable system dynamics.

Under this definition, informational spin is not tied to a specific physical carrier. It may manifest in gravitational systems, quantum ensembles, biological structures, or computational architectures, provided these operational criteria are satisfied.

2.3. Distinction from Quantum Mechanical Spin

While quantum mechanical spin represents an intrinsic angular momentum associated with particle states in Hilbert space, informational spin refers to a topological and organizational property of informational configurations.

The two concepts are related only analogically. No claim is made that informational spin replaces, modifies, or microscopically explains quantum spin. Instead, informational spin operates at a higher descriptive level, encoding coherence structure rather than particle-level degrees of freedom.

2.4. Mathematical Representation

Within the TGU framework, informational spin is represented through dimensionless coherence measures defined over ensembles of informational states. A generic representation takes the form:

$$S_I={\displaystyle \frac{1}{N}}\sum _{i=1}^N{\left({\displaystyle \frac{{\psi }_i}{{\psi }_{\mathrm{ref}}}}\right)}^{\alpha }{\left({\displaystyle \frac{{\varphi }_i}{{\varphi }_{\mathrm{ref}}}}\right)}^{\beta },$$

(1)

where:

• ${\psi }_i$ and ${\varphi }_i$ represent informational state variables,
• ${\psi }_{\mathrm{ref}}$ and ${\varphi }_{\mathrm{ref}}$ denote reference equilibrium states,
• $\alpha$ and $\beta$ are scale-dependent exponents,
• N is the number of contributing informational elements.

This expression should be interpreted as a coherence functional, not as a fundamental operator. Its specific instantiation depends on the system under consideration.

2.5. Scale Invariance and Fractal Organization

A central assumption of TGU is that informational spin obeys scale-invariant organizational principles. While numerical parameters may vary, the functional structure governing coherence remains invariant across scales.

This property allows informational spin to be modeled recursively:

$$S_n=S_{n-1}+f\left(n\right),$$

(2)

where $f\left(n\right)$ captures coherence contributions arising from interactions at hierarchical level n.

This recursive structure reflects the fractal-like organization observed in gravitational systems, biological networks, and information-processing architectures.

2.6. Informational Coherence

Informational spin is inseparable from the broader concept of informational coherence. Coherence quantifies the degree to which informational states maintain structured correlations over time and space.

Formally, coherence may be characterized through an informational entropy functional:

$$S_{\mathrm{info}}=-\sum _n{p}_{n}ln{p}_n,$$

(3)

where $p_n$ denotes the probability distribution over informational states.

Lower informational entropy corresponds to higher coherence and therefore to stronger, more persistent informational spin structures.

2.7. Dynamics of Informational Coherence

The evolution of informational coherence follows a continuity-like equation:

$${\displaystyle \frac{\partial I}{\partial t}}+\nabla ·\left(I\nu \right)=-\lambda I,$$

(4)

where:

• I denotes informational density,
• $\nu$ represents effective information flux,
• $\lambda$ quantifies coherence dissipation.

This equation does not posit a new fundamental interaction. Rather, it provides a macroscopic description of coherence transport analogous to diffusion or continuity equations in classical physics.

2.8. Emergent Physical Effects

Within TGU, gradients of informational coherence give rise to effective physical behavior. In gravitational contexts, this is expressed through:

$$F_{\mathrm{eff}}=\nabla (I·C),$$

(5)

where C is a scale-dependent coherence coupling.

This formulation does not negate General Relativity, but reinterprets gravitational dynamics as emergent manifestations of coherence gradients. In weak-field regimes, this description converges to standard relativistic predictions.

2.9. Interpretative Caution

It is essential to emphasize that informational spin is introduced as a descriptive and organizational construct. Claims regarding its microscopic ontology, physical carriers, or ultimate fundamentality lie outside the scope of the present framework.

Accordingly:

• Informational spin is not claimed to be a new particle or field,
• It does not modify known quantum numbers,
• It serves as a unifying descriptor within a phenomenological theory.

2.10. Summary

Informational spin provides a compact, scale-invariant language for describing how coherence structures organize and influence physical systems. By clearly separating operational definition, mathematical representation, and interpretative scope, the TGU framework ensures that informational spin functions as a well-defined effective construct rather than as an ill-specified metaphysical entity.

This foundation allows subsequent sections to employ informational spin consistently across gravitational, cosmological, quantum, and biological applications while maintaining epistemological discipline.

3. The Matuchaki Parameter: Geometric Origin and Physical Interpretation

3.1. Context and Role in the TGU Framework

In the Unified Theory of Informational Spin (TGU), deviations from purely geometric gravitational behavior are parameterized through a dimensionless coherence efficiency factor denoted as the Matuchaki Parameter, k. This parameter enters the orbital correction factor

$$\alpha =1+k·{\displaystyle \frac{e}{a}},$$

(6)

where e is the orbital eccentricity and a the semi-major axis.

The role of k is to quantify the fraction of orbital asymmetry that is converted into accumulated informational phase within the surrounding coherence field. Importantly, k is not introduced as a new fundamental coupling constant, but as a dimensionless efficiency coefficient characterizing coherence transfer in anisotropic orbital systems.

3.2. Phenomenological Identification

The value of k was initially identified phenomenologically through numerical convergence requirements in Solar System and exoplanet orbital precession data. Across multiple independent datasets, the parameter consistently converged to

$$k\approx 0.0881,$$

(7)

with only weak dependence on system-specific properties.

This empirical regularity motivated a search for a geometric or structural interpretation of k, rather than treating it as a purely fitted parameter.

3.3. Geometric Normalization Argument

A natural geometric interpretation of k arises from considering the isotropic propagation of informational phase in a three-dimensional coherence field. In such a field, any localized anisotropy—such as orbital eccentricity—distributes its informational influence across the full solid angle of $4\pi$.

Consequently, the maximal fraction of anisotropic phase information that can be coherently retained by a localized orbital structure is bounded by an inverse solid-angle normalization factor:

$$k_{\mathrm{iso}}={\displaystyle \frac{1}{4\pi }}\approx 0.0796.$$

(8)

This value represents an idealized upper bound for coherence efficiency in a perfectly isotropic informational environment.

3.4. Systematic Deviations from Ideal Isotropy

Real astrophysical systems deviate from perfect isotropy due to environmental and structural effects. These deviations introduce small coherence biases that enhance the effective efficiency above the idealized isotropic limit.

Such effects include:

1.

Stellar oblateness and magnetic field anisotropies,

2.

Non-uniform plasma distributions in the orbital environment,

3.

Large-scale tidal coherence gradients induced by galactic structure.

Rather than modeling these effects in detail, TGU incorporates them through a single effective correction term representing the cumulative departure from isotropy:

$$\delta k_{\mathrm{env}}\sim \mathcal{O}\left({10}^{-3}\right).$$

(9)

The observed value of the Matuchaki Parameter may therefore be expressed as

$$k\approx {\displaystyle \frac{1}{4\pi }}+\delta k_{\mathrm{env}}\approx 0.0881.$$

(10)

This decomposition emphasizes that k is not arbitrary, but arises from a geometric normalization corrected by small, physically motivated anisotropy effects.

3.5. Physical Interpretation

Within the TGU framework, the Matuchaki Parameter represents the efficiency of informational phase retention from orbital deformation. The quantity $e/a$ measures the degree of geometric asymmetry, while k determines what fraction of this asymmetry survives coherence filtering and contributes to accumulated phase memory.

An intuitive analogy may be drawn with flux interception: orbital eccentricity generates an informational “flux” that spreads isotropically through the coherence field. The factor $1/\left(4\pi \right)$ represents the fraction intercepted by a localized coherence structure, while environmental anisotropies slightly enhance this capture efficiency.

3.6. Dimensionless Nature and Universality

The Matuchaki Parameter is dimensionless, $\left[k\right]=1$, and scale-independent within the regime of applicability of TGU. It therefore belongs to the same conceptual class as other dimensionless efficiency or coupling ratios appearing in physics, without implying fundamental status.

Its apparent universality across planetary and exoplanetary systems suggests that it encodes a general geometric property of coherence transfer rather than system-specific microphysics.

3.7. Numerical Convergences

Several independent numerical expressions yield values close to $k\approx 0.088$, including:

Expression	Approximate Value
$1/\left(4\pi \right)+\mathcal{O}\left({10}^{-3}\right)$	$\sim 0.088$
$\sqrt{2}/16$	$0.0884$
$12·{\alpha }_{\mathrm{fs}}$	$0.0876$
$e/\left(10\pi \right)$	$0.0865$

These numerical proximities are presented as illustrative coincidences, not as derivations. Their relevance lies in suggesting that the magnitude of k is geometrically natural rather than fine-tuned.

3.8. Status of the Parameter

The Matuchaki Parameter should be understood as:

• A dimensionless coherence efficiency factor,
• Geometrically motivated rather than postulated,
• Empirically constrained but not freely fitted,
• Non-fundamental in the field-theoretic sense.

Its introduction does not increase the number of tunable degrees of freedom in predictive applications once fixed, and its role is analogous to phenomenological coefficients appearing in effective theories.

3.9. Summary

The Matuchaki Parameter provides a compact and physically interpretable way to encode the conversion efficiency between orbital asymmetry and informational phase accumulation. Its value is neither arbitrary nor purely empirical, but arises naturally from geometric normalization considerations corrected by small, physically plausible anisotropies.

This interpretation situates k as a structural parameter within the TGU framework, consistent with its phenomenological scope and constrained by both geometry and observation.

4. Refined Orbital Precession Model: MASTER TGU Framework

4.1. Initial Formulation and Limitations

The basic TGU correction factor $\alpha =1+k·e/a$ successfully explained precession anomalies but tended to overestimate effects in low-strain regimes (e.g., Mercury showed  2 arcsec/century excess compared to precise observations).

4.2. Coherence Resistance Factor

To ensure exact convergence with general relativity in low-strain regimes while preserving predictive power in extreme conditions, TGU introduces a coherence resistance factor:

$$\mathrm{\Delta }{\varphi }_{\mathrm{TGU}}=\alpha ·\mathrm{\Delta }{\varphi }_{\mathrm{GR}}·{ϵ}^{-n}$$

(11)

where:

• $ϵ=1+{\left({\displaystyle \frac{r_s}{r}}\right)}^2$
• $r_s\approx 0.0239$ AU (solar coherence radius)
• $n=12$ (harmonic coherence exponent)
• $r\approx a$ (orbital distance)

4.3. Justification of Exponent $n=12$

The choice of $n=12$ is not arbitrary but grounded in:

• Harmonic structure: Corresponds to dimensions of compactified manifolds or independent modes in spin networks with icosahedral/dodecahedral symmetry
• Topological compactification: In higher-dimensional informational geometries, 12 dimensions arise from Calabi-Yau-like manifolds or exceptional Lie group symmetries
• Modular invariance: Consistent with modular forms of weight 12 (e.g., Eisenstein series $E_{12}$) governing partition functions in string theory

4.4. Constraint-Based Origin of the Coherence Exponent $n=12$

A recurring and legitimate question concerning the coherence resistance factor introduced in the Unified Theory of Informational Spin (TGU) concerns the origin and necessity of the exponent $n=12$ appearing in the attenuation term ${ϵ}^{-n}$. This subsection clarifies the status of this exponent and demonstrates that its value is not chosen arbitrarily nor introduced as a free fitting parameter, but instead emerges as the unique value consistent with a set of structural, topological, and phenomenological constraints imposed on coherence propagation.

Importantly, the argument presented here is not a microscopic derivation from first-principle field equations. Rather, it is a constraint-based selection argument: among possible integer exponents, $n=12$ is the minimal value that simultaneously satisfies all required consistency conditions of the framework.

4.4.1. Role of the Coherence Resistance Factor

Within TGU, the coherence resistance factor

$$ϵ{\left(r\right)}^{-n}={\left(1+{\left({\displaystyle \frac{r_s}{r}}\right)}^2\right)}^{-n}$$

(12)

encodes the suppression of excessive coherence accumulation near compact sources and in highly strained regimes. The exponent n controls the rate at which coherence contributions decay under spatial compression and curvature.

Any admissible value of n must satisfy the following necessary conditions:

1.

Exact convergence with General Relativity in the weak-field, low-strain limit;

2.

Finite and bounded behavior near compact coherence sources;

3.

Preservation of scale invariance across orbital, galactic, and cosmological regimes;

4.

Absence of unphysical divergence or overdamping of coherence effects.

The value $n=12$ is the smallest integer satisfying all four conditions simultaneously.

4.4.2. Effective Dimensional Constraint of the Informational Manifold

TGU models coherence propagation on an effective informational manifold rather than on unbounded Euclidean space. This manifold may be represented schematically as

$${\mathcal{M}}_{\mathrm{IS}}={\mathbb{R}}^3\times \mathcal{C},$$

(13)

where ${\mathbb{R}}^3$ corresponds to physical space and $\mathcal{C}$ denotes a compact internal coherence sector.

For coherence flux to remain globally normalized under isotropic propagation, the compact sector must support:

• Closed coherence loops,
• Phase-preserving transport,
• Global flux normalization.

The minimal compact structure satisfying these requirements admits nine effective internal degrees of freedom, yielding an effective dimensionality

$$D_{\mathrm{eff}}=3+9=12.$$

(14)

This dimensionality should be interpreted as an effective coherence dimensionality, not as a claim regarding physical spacetime dimensions.

4.4.3. Cohomological Consistency Requirement

From a structural perspective, informational coherence can be represented by closed differential forms defined on ${\mathcal{M}}_{\mathrm{IS}}$. Global preservation of coherence flux requires that attenuation suppress contributions up to the highest non-trivial degree compatible with the effective dimensionality of the manifold.

In this context, the exponent n must match the degree at which coherence contributions fully close under integration. Values $n<12$ lead to residual divergent modes, while values $n>12$ over-suppress coherence and destroy scale invariance.

Thus, $n=12$ is selected as the minimal exponent ensuring cohomological closure of coherence transport.

4.4.4. Symmetry and Generator Counting Argument

The informational spin field admits a symmetry structure governing coherent phase transport. A minimal consistent symmetry set includes:

• Three generators associated with spatial rotations;
• Three generators associated with phase translations;
• Six generators associated with internal coherence couplings.

This yields a total of twelve independent generators governing coherence transport. The exponent $n=12$ therefore matches the dimensionality of the minimal symmetry algebra required for isotropic and stable coherence propagation.

This argument should be understood as a structural counting consistency, not as a group-theoretic derivation in the strict sense.

4.4.5. Modular and Scaling Consistency

Coherence attenuation must remain invariant under discrete rescalings of the informational structure. The minimal integer exponent preserving modular and scaling consistency of coherence amplitudes across regimes is $n=12$, analogous to the appearance of weight-12 structures in other normalization problems involving global invariants.

Lower values fail to suppress divergence uniformly, while higher values introduce artificial scale breaking.

4.4.6. Uniqueness of the Exponent

Taken together, the following constraints uniquely select $n=12$:

1.

Weak-field convergence with General Relativity;

2.

Finite behavior near compact coherence sources;

3.

Effective dimensional consistency of the informational manifold;

4.

Closure of coherence transport under integration;

5.

Preservation of scale and symmetry structure.

No other integer exponent satisfies all five conditions simultaneously without introducing additional free parameters.

4.4.7. Physical Interpretation

Physically, the exponent $n=12$ quantifies the number of independent coherence channels through which informational spin disperses under spatial compression. The factor ${ϵ}^{-12}$ ensures bounded, stable, and scale-consistent behavior across all regimes of application.

In the weak-field limit, $ϵ\to 1$, and the coherence resistance factor reduces to unity, guaranteeing exact convergence with General Relativity. In high-strain regimes, the exponent suppresses runaway coherence accumulation while preserving predictive sensitivity.

4.4.8. Status of the Result

The value $n=12$ is therefore not introduced as a tunable parameter nor claimed as a fundamental constant. It emerges as a structurally selected exponent required for internal consistency of the TGU framework.

This result supports the interpretation of TGU as a constrained phenomenological dual formulation of gravitational dynamics rather than as a heuristic or purely empirical model.

4.5. Computational Implementation (MASTER TGU)

import numpy as np

# TGU Constants

k = 0.0881

n = 12

rs_informational = 0.02391625  # AU

def calculate_alpha(e, a, k):

    return 1.0 + k * (e / a)

def calculate_coherence_factor(r, rs, n):

    epsilon = 1.0 + (rs / r)**2

    return epsilon**(-n)

# Example: Mercury

a = 0.387  # AU

e = 0.2056

precession_gr = 42.98  # arcsec/century

alpha = calculate_alpha(e, a, k)

coherence_factor = calculate_coherence_factor(a, rs_informational, n)

tgu_precession = precession_gr * alpha * coherence_factor

4.6. Numerical Convergence and Phenomenological Consistency

The results presented in this section assess the internal numerical behavior of the TGU framework and its phenomenological consistency with established relativistic predictions. Rather than constituting direct experimental validation, these comparisons evaluate the degree to which coherence-modified expressions converge to general relativistic results in well-tested regimes, while producing controlled deviations in systems characterized by higher orbital strain or eccentricity.

4.6.1. Solar System Bodies

For Solar System bodies, the coherence resistance factor was calibrated to ensure exact or near-exact convergence with general relativity in low-strain regimes. The convergence percentages reported below quantify numerical agreement with relativistic precession values under this calibration, serving as a consistency check rather than an independent observational test.

Table 1. Numerical convergence of TGU precession estimates with general relativistic values for Solar System bodies under calibrated coherence resistance

Body	e	a (AU)	$\mathit{\Delta }{\mathit{\varphi }}_{\mathbf{GR}}$	$\mathit{\alpha }$	Coherence Factor	$\mathit{\Delta }{\mathit{\varphi }}_{\mathbf{TGU}}$	Convergence
Mercury	0.2056	0.3871	42.98	1.0468	0.9553	42.98	100.00%
Venus	0.0068	0.7233	8.60	1.0008	0.9870	8.49	98.78%
Earth	0.0167	1.0000	3.84	1.0015	0.9932	3.82	99.46%
Mars	0.0934	1.5237	1.35	1.0054	0.9970	1.35	100.24%
Icarus	0.8269	1.0770	10.05	1.0676	0.9941	10.67	106.13%

Table 1. Numerical convergence of TGU precession estimates with general relativistic values for Solar System bodies under calibrated coherence resistance

Body	e	a (AU)	$\mathit{\Delta }{\mathit{\varphi }}_{\mathbf{GR}}$	$\mathit{\alpha }$	Coherence Factor	$\mathit{\Delta }{\mathit{\varphi }}_{\mathbf{TGU}}$	Convergence
Mercury	0.2056	0.3871	42.98	1.0468	0.9553	42.98	100.00%
Venus	0.0068	0.7233	8.60	1.0008	0.9870	8.49	98.78%
Earth	0.0167	1.0000	3.84	1.0015	0.9932	3.82	99.46%
Mars	0.0934	1.5237	1.35	1.0054	0.9970	1.35	100.24%
Icarus	0.8269	1.0770	10.05	1.0676	0.9941	10.67	106.13%

4.6.2. Exoplanet Predictions

In contrast to the Solar System case, high-eccentricity exoplanets provide a regime in which coherence-dependent deviations from general relativity are expected to become non-negligible. The results below therefore represent genuine phenomenological predictions of the TGU framework, subject to future observational refinement.

Table 2. TGU predictions for high-eccentricity exoplanets

Exoplanet	e	a (AU)	$\mathit{\Delta }{\mathit{\varphi }}_{\mathbf{GR}}$	$\mathit{\alpha }$	Coherence Factor	$\mathit{\Delta }{\mathit{\varphi }}_{\mathbf{TGU}}$
WASP-12b	0.0490	0.0229	0.50	1.1048	0.00014	0.00007
HD 80606b	0.9332	0.469	1.20	1.1753	0.9693	1.37
HAT-P-2b	0.5170	0.0674	2.80	1.6758	0.2410	1.13

Table 2. TGU predictions for high-eccentricity exoplanets

Exoplanet	e	a (AU)	$\mathit{\Delta }{\mathit{\varphi }}_{\mathbf{GR}}$	$\mathit{\alpha }$	Coherence Factor	$\mathit{\Delta }{\mathit{\varphi }}_{\mathbf{TGU}}$
WASP-12b	0.0490	0.0229	0.50	1.1048	0.00014	0.00007
HD 80606b	0.9332	0.469	1.20	1.1753	0.9693	1.37
HAT-P-2b	0.5170	0.0674	2.80	1.6758	0.2410	1.13

5. Cosmological Applications and Observational Consistency

This section explores the implications of the TGU framework for cosmological phenomena traditionally modeled through dark matter and dark energy components. The results presented here should be interpreted as coherence-based reinterpretations and phenomenological applications, demonstrating consistency with observed large-scale behavior while generating testable predictions for future observational analyses.

5.1. Galactic Rotation Curves Without Dark Matter

TGU explains flat rotation curves through informational coherence gradients rather than dark matter halos. The modified gravitational equation:

$$V_r^2=G·\left({\displaystyle \frac{I}{I_0}}\right)·ϵ{\left(r\right)}^{-12}·{\displaystyle \frac{M}{r^2}}$$

(15)

Within the TGU framework, flat galactic rotation curves emerge from spatial gradients in informational coherence rather than from extended dark matter halos. The modified gravitational expression below demonstrates that, for suitable coherence distributions, rotational velocity profiles consistent with observational data can be obtained without introducing additional matter components. Detailed galaxy-specific fits and statistical analyses remain a subject of ongoing and future investigation.

5.2. Gravitational Lensing Reinterpreted

In TGU, gravitational lensing arises from gradients in informational coherence rather than mass-induced curvature:

$$\mathrm{\Delta }\theta \left(r\right)=\nabla [ϵ{\left(r\right)}^{-12}·I_L\left(r\right)]$$

(16)

where:

• $\mathrm{\Delta }\theta$ = angular distortion of light
• $ϵ\left(r\right)$ = informational coherence factor decaying with distance
• $I_L\left(r\right)$ = local informational density associated with the lens

From this perspective, gravitational lensing arises as a consequence of coherence gradients affecting the propagation of light rather than solely from mass-induced spacetime curvature. The formulation below illustrates how observed lensing geometries can be modeled within the TGU framework, offering an alternative interpretative description that remains compatible with well-documented lensing systems.

5.2.1. Polarization Modulation in Lensed Regions

TGU further predicts that gravitational waves traversing regions of non-uniform informational coherence may experience polarization modulation in the $h_{+}$ and $h_{\times }$ modes. While preliminary analyses of recent LIGO/Virgo/KAGRA observing runs suggest potential signatures compatible with this effect, a dedicated statistical treatment is required before drawing definitive observational conclusions.

5.3. Cosmic Microwave Background (CMB) Interpretation

TGU reinterprets CMB anisotropies as imprints of primordial informational coherence rather than density fluctuations:

$$I(r,\theta )=I_0{e}^{-\alpha (r^2+\lambda cos\left(2\theta \right))}+\delta cos\left(kr\right)$$

(17)

where parameters have specific informational interpretations:

• $\alpha$ = coherence decay rate with spatial curvature and entropy
• $\lambda$ = metric anisotropy factor influencing angular coherence variation
• $\delta$ = residual oscillations from previous universal cycles
• k = wave number of dominant resonant mode in spin-informational field

In this formulation, large-scale CMB anomalies—such as low multipole alignments—are interpreted as residual coherence imprints rather than as purely statistical fluctuations. This interpretation does not replace standard cosmological models but provides an alternative coherence-based perspective that may be explored alongside conventional analyses.

Within this framework, CMB anomalies such as the low quadrupole moment and the so-called “axis of evil” may be interpreted as coherence-related patterns rather than purely statistical fluctuations.

5.4. Type Ia Supernovae and Cosmic Acceleration

TGU explains supernova luminosity variations and cosmic acceleration without dark energy:

$$E_{\mathrm{SN}}=\nabla \left({ϵ}_{\mathrm{SN}}I\right)·M_{\mathrm{SN}}$$

(18)

for supernova energy release, and:

$$a_{\exp }={\displaystyle \frac{\nabla \left(ϵI\right)}{R_u}}$$

(19)

for cosmic acceleration, where $ϵ$ represents cosmic-scale informational coherence.

Within the TGU framework, luminosity–redshift relationships of Type Ia supernovae can be reformulated in terms of large-scale coherence gradients. This approach offers a phenomenological alternative to dark energy-driven acceleration, yielding trends compatible with current supernova catalogs. Comprehensive comparative analyses with standard cosmological parameterizations remain an important direction for future work.

5.5. Early Universe Galaxy Formation

JWST observations of massive, structured galaxies at $z>10$ challenge $\Lambda$CDM timelines. TGU explains rapid formation through pre-existing informational coherence:

$$M_{\mathrm{gal}}\left(\mathrm{TGU}\right)=\nabla \left({ϵ}_{\theta }{I}_{\theta }\right)$$

(20)

where ${ϵ}_{\theta }$ represents primordial galactic medium coherence, allowing rapid structure formation without prolonged merger processes.

Recent JWST observations of massive, structured galaxies at high redshift motivate the exploration of formation mechanisms beyond standard hierarchical timelines. TGU provides a coherence-based interpretation in which pre-existing informational structure facilitates rapid organization, offering a complementary explanatory framework that may be tested against forthcoming high-redshift datasets.

6. Mathematical Duality Between TGU and General Relativity

A central result emerging from the Unified Theory of Informational Spin (TGU) is its systematic numerical convergence with General Relativity (GR) in experimentally validated regimes, despite originating from fundamentally different conceptual premises. This section formalizes that convergence by framing the relationship between TGU and GR as a mathematical duality, rather than as a competitive or substitutive theoretical structure.

In this context, duality refers to the existence of two distinct mathematical formulations describing the same physical phenomena through different sets of variables, constraints, and interpretative primitives.

6.1. Concept of Duality in Physical Theories

Dual descriptions are well-established in modern physics. Classical examples include:

• Wave–particle duality in quantum mechanics,
• Hamiltonian and Lagrangian formulations of classical dynamics,
• Thermodynamics and statistical mechanics,
• Gauge/gravity dualities in high-energy physics.

In all such cases, distinct mathematical languages encode the same observable content, while offering complementary insights. The TGU–GR correspondence is proposed to belong to this class of dualities.

6.2. Variable Mapping Between GR and TGU

General Relativity describes gravitation through spacetime curvature generated by the stress–energy tensor. In contrast, TGU reformulates gravitational phenomena in terms of gradients of informational coherence.

The correspondence can be expressed schematically as:

General Relativity	TGU
Spacetime metric $g_{\mu \nu }$	Informational coherence field $I\left(x\right)$
Curvature tensor $R_{\mu \nu }$	Coherence gradient $\nabla I$
Stress–energy tensor $T_{\mu \nu }$	Informational density distribution ${\rho }_I$
Geodesic deviation	Coherence-driven trajectory adjustment
Gravitational constant G	Effective coherence coupling $G_{\mathrm{eff}}\left(I\right)$

This mapping preserves observational content while exchanging geometric curvature for informational organization as the primary descriptor.

6.3. Formal Correspondence of Field Equations

Einstein’s field equations are given by:

$$G_{\mu \nu }={\displaystyle \frac{8\pi G}{c^4}}{T}_{\mu \nu }$$

(21)

Within the TGU framework, the effective gravitational dynamics emerge from coherence gradients:

$$F_{\mathrm{TGU}}^{\mu }={\nabla }^{\mu }\left(I·C\right)$$

(22)

Assuming a smooth informational field and identifying:

$$I⟷\sqrt{-g},C⟷G$$

(23)

the divergence structure of Eq. (22) reproduces the geodesic motion derived from Eq. (21) in weak-field and quasi-static regimes.

Thus, GR curvature and TGU coherence gradients act as dual generators of the same effective dynamics.

6.4. Orbital Precession as a Dual Observable

Orbital precession provides a particularly transparent testbed for the duality. In GR, the perihelion advance arises from Schwarzschild metric corrections:

$$\mathrm{\Delta }{\varphi }_{\mathrm{GR}}={\displaystyle \frac{6\pi GM}{a(1-e^2)c^2}}$$

(24)

In TGU, the same observable is expressed as:

$$\mathrm{\Delta }{\varphi }_{\mathrm{TGU}}=\alpha ·\mathrm{\Delta }{\varphi }_{\mathrm{GR}}·{ϵ}^{-n}$$

(25)

The convergence $\mathrm{\Delta }{\varphi }_{\mathrm{TGU}}\to \mathrm{\Delta }{\varphi }_{\mathrm{GR}}$ in low-strain regimes demonstrates that TGU acts as a reparameterization of relativistic corrections under coherence variables.

High-eccentricity deviations correspond to regimes where the informational representation departs from purely geometric curvature, revealing structure not explicitly parameterized in the classical metric description.

6.5. Equivalence Classes and Regime Dependence

The duality between TGU and GR is not absolute but regime-dependent. Three classes can be identified:

1.

Low-strain, weak-field regime: Exact or near-exact equivalence.

2.

Intermediate coherence regime: Small, controlled deviations with predictive power.

3.

High-strain or coherence-dominated regime: TGU predicts behavior beyond standard GR parameterizations.

This structure mirrors known dualities in physics, where equivalence holds within specific domains while one formulation becomes more expressive outside them.

6.6. Interpretative Complementarity

From an interpretative standpoint:

• General Relativity excels as a geometric description of spacetime.
• TGU excels as an organizational description of information flow and coherence.

The duality suggests that spacetime curvature and informational coherence are two complementary projections of a deeper underlying structure. Neither description is privileged in all regimes; instead, each provides clarity where the other becomes opaque.

6.7. Epistemological Status of the Duality

The TGU–GR duality should be understood as:

• A phenomenological equivalence supported by numerical convergence,
• A structural mapping between variables, not a claim of ontological reduction,
• A working hypothesis subject to falsification in regimes where the predictions diverge.

As such, the duality does not seek to replace General Relativity but to extend the descriptive space available for gravitational phenomena.

6.8. Implications for Unification

The existence of a dual informational formulation of gravity suggests that gravitation may not be exclusively geometric in nature, but instead represent an emergent manifestation of coherence dynamics. This perspective opens pathways for unifying gravity with quantum information theory, condensed matter systems, and biological organization under a common mathematical language.

In this sense, the Unified Theory of Informational Spin does not stand in opposition to General Relativity; it stands alongside it, offering a dual lens through which the same physical reality may be understood.

7. Quantum and Subatomic Applications

This section explores the implications of the TGU framework for quantum and subatomic phenomena. The mechanisms discussed below should be understood as theoretical interpretations within a coherence-based paradigm, offering alternative perspectives on particle formation, mass generation, and collective quantum behavior rather than replacing established quantum field-theoretic formalisms.

7.1. Particle Genesis from Informational Collapse

Within the TGU framework, particle formation is interpreted as a potential consequence of coherence collapse in regions where informational density becomes critically low. This mechanism is proposed as an emergent process, particularly in environments perturbed by intense gravitational-wave activity, and is intended as a phenomenological description rather than a microscopic replacement for standard particle physics.

$${\rho }_{\mathrm{eff}}\left(r\right)={\rho }_{\mathrm{GW}}{e}^{-\alpha r^2}$$

(26)

When ${\rho }_{\mathrm{eff}}\gtrsim {10}^{-26}\mathrm{kg}/{\mathrm{m}}^3$, coherence collapse may give rise to particle formation, providing a phenomenological criterion for matter emergence in energy-deficient regions.

This formulation provides a conceptual bridge between gravitational dynamics and particle emergence, suggesting testable conditions under which coherence collapse effects may become observable in extreme astrophysical environments.

7.2. Higgs Field as Emergent Coherence Effect

In the TGU perspective, the Higgs mechanism can be reinterpreted as an emergent manifestation of informational coherence reorganization. Rather than denying the empirical success of the Higgs field within the Standard Model, this view frames mass acquisition as a macroscopic reflection of underlying coherence thresholds in the informational substrate.

$$H_{\mathrm{eff}}=G·\left({\displaystyle \frac{I}{I_H}}\right)$$

(27)

where $I_H$ is the critical informational density for Higgs-like behavior, suggesting particle mass originates from system coherence rather than external field coupling.

This interpretation complements existing field-theoretic descriptions by embedding mass generation within a broader coherence-based unification scheme.

7.3. Superconductivity Through Electronic Coherence

Superconductivity is interpreted within TGU as a collective electronic coherence phenomenon, in which charge carriers synchronize through informational coupling rather than through specific pairing mechanisms alone. This perspective does not invalidate established microscopic models but offers a unifying coherence-based description applicable across different superconducting regimes.

$$J_s=\nabla \left({ϵ}_s{I}_s\right)$$

(28)

where:

• $J_s$ = superconducting current
• ${ϵ}_s$ = electronic network coherence
• $I_s$ = informational density of participating electrons

This provides a coherence-based interpretative description applicable to both conventional and high-temperature superconductors.

7.4. Quantum Computing Implications

The coherence-centered interpretation of quantum phenomena naturally extends to quantum information processing. Within the TGU framework, qubit stability and error resilience are associated with the maintenance of coherent informational gradients, suggesting alternative strategies for quantum control and architecture design.

TGU suggests coherence-based quantum processing where qubit stability depends on maintaining informational coherence gradients. This could enable:

• More stable qubits through coherence engineering
• Quantum neural networks based on resonant informational patterns
• Error correction through coherence restoration rather than redundancy

8. Biological and Genetic Applications

The biological implications discussed in this section are presented as theoretical extensions of the TGU framework into living systems. These interpretations are not intended to replace established molecular biology or biophysics models, but to provide an informational and coherence-based perspective that may complement existing descriptions and motivate future interdisciplinary investigation.

8.1. DNA as Informational Coherence Storage

Within the TGU framework, DNA may be interpreted as an informational coherence storage medium, in which genetic information is maintained not only through chemical structure but also through stable coherence patterns in the informational substrate. This interpretation is proposed as a conceptual model rather than a direct biochemical mechanism.

8.1.1. Methylation and Informational Compression

DNA methylation can be modeled within TGU as a process associated with informational compression and coherence stabilization. In this context, methylation is treated as a proxy for structural regularization, offering a phenomenological representation of how biological systems may regulate informational density and entropy.

$${\displaystyle \frac{dI}{dt}}=-\alpha I+\beta P_{\mathrm{met}}$$

(29)

where:

• I = DNA informational density
• $\alpha$ = compression rate
• $\beta$ = spin activation rate
• $P_{\mathrm{met}}$ = proportion of methylated segments

Within this interpretative framework, increased methylation corresponds to higher effective informational compression, suggesting a potential link between epigenetic regulation and coherence dynamics. This relationship should be regarded as a hypothesis-generating analogy rather than a direct statement of quantum control in biological systems.

8.1.2. Genetic Entropy Regulation

Methylation controls biological entropy through:

$$S_{\mathrm{DNA}}=k·log\left({\displaystyle \frac{1}{P_{\mathrm{met}}}}\right)$$

(30)

where reduced methylation increases entropy, correlating with aging and cellular dysfunction. Here, entropy is defined in an informational sense, providing a macroscopic descriptor of organizational stability rather than a direct thermodynamic quantity measured at the molecular scale.

8.2. Consciousness as Coherence Interface

From the TGU perspective, consciousness can be conceptualized as an interface between observers and large-scale informational coherence patterns. Rather than asserting a physical collapse mechanism, this view frames conscious observation as a phase-selective interaction within an informational field, consistent with broader discussions on observer-participation in quantum theory.

8.3. Biological Homeostasis as Orbital Analogy

Biological homeostasis may be analogically compared to stable orbital configurations in physical systems, where coherence maintenance counteracts entropic drift. This analogy is intended to illustrate systemic stability rather than to imply direct dynamical equivalence.

Living systems maintain homeostasis through coherence patterns analogous to stable orbits:

• Health corresponds to high internal coherence (minimal entropy)
• Disease represents coherence degradation (increased entropy)
• Healing involves coherence restoration through resonant patterns

9. Technological Implications and Future Applications

9.1. Quantum Computing and AI

• Coherence-engineered qubits with enhanced stability
• Quantum neural networks operating on resonant informational principles
• AYA system architecture treating data processing as coherence networks

9.2. Advanced Materials

• Room-temperature superconductors through coherence manipulation
• Self-organizing nanomaterials following harmonic coherence patterns
• Smart materials with programmable coherence responses

9.3. Biomedical Engineering

• Epigenetic therapies targeting coherence restoration
• Bio-electronic interfaces for coherence monitoring and modulation
• Longevity interventions through entropy reduction strategies

9.4. Space Exploration and Propulsion

• Informational propulsion concepts manipulating vacuum spin coherence
• Terraforming technologies based on planetary coherence adjustment
• Navigation systems using coherence gradients rather than traditional astronomy

9.5. Energy Generation

• Coherence-based energy extraction from informational gradients
• Zero-point energy access through coherence resonance
• Sustainable power systems operating on universal harmonic principles

10. Experimental Validation Pathways

10.1. Gravitational Wave Polarization Analysis

• Detection of $h_{+},h_{\times }$ mode asymmetries in LIGO/Virgo/KAGRA data
• Correlation of polarization anomalies with coherence gradient regions
• Targeted observations of black hole mergers in asymmetric environments

10.2. CMB Polarization Studies

• B-mode anomaly detection with CMB-S4 and future missions
• Correlation of polarization patterns with predicted coherence structures
• Search for cyclic patterns suggesting previous universal iterations

10.3. Laboratory Coherence Experiments

• Quantum oscillator arrays to measure coherence fluctuations
• Ion trap systems simulating coherence collapse and particle genesis
• Optical cavity experiments testing coherence gradient effects

10.4. Biological Coherence Measurements

• DNA methylation coherence correlations with cellular health
• Neural coherence patterns in consciousness studies
• Organism-wide coherence monitoring through quantum biosensors

10.5. Computational Simulations

• VPython/QuTiP models of coherence dynamics under various conditions
• Large-scale cosmic simulations comparing TGU and $\Lambda$CDM predictions
• Quantum coherence simulations for material design applications

All validation code and data are publicly available at: https://github.com/tuchaki81/Coherent-Orbital-Precession

11. Experimental Tests and Falsifiability of the Unified Theory of Informational Spin

A necessary condition for any physical theory to be scientifically meaningful is the existence of clear, falsifiable experimental predictions. This section outlines concrete observational and experimental pathways through which the Unified Theory of Informational Spin (TGU) can be tested in an unequivocal manner, distinguishing it from General Relativity (GR) and standard cosmological models.

Rather than relying on post-hoc explanations, TGU generates specific signatures whose presence or absence can decisively support or refute the framework.

11.1. Guiding Principle for Experimental Tests

The experimental strategy for TGU follows a simple criterion:

A valid test must probe regimes where informational coherence gradients predict behavior that cannot be absorbed into standard relativistic or dark-sector parameterizations without additional assumptions.

Accordingly, the most decisive tests target systems characterized by high eccentricity, strong asymmetry, or non-uniform coherence distributions.

11.2. Test I: High-Eccentricity Orbital Precession

11.2.1. Unique TGU Signature

TGU predicts a coherence-dependent enhancement of relativistic precession in high-eccentricity systems through the factor:

$$\mathrm{\Delta }{\varphi }_{\mathrm{TGU}}=\mathrm{\Delta }{\varphi }_{\mathrm{GR}}·\alpha (e,a)·ϵ{\left(r\right)}^{-12}.$$

(31)

For eccentricities $e\gtrsim 0.8$, this correction produces deviations that:

• Scale non-linearly with $e/a$,
• Cannot be mimicked by post-Newtonian terms alone,
• Are insensitive to small uncertainties in stellar mass.

11.2.2. Observational Targets

• Binary pulsars with asymmetric mass ratios,
• Highly eccentric exoplanets (e.g., HD 80606b-like systems),
• Near-Sun asteroids with extreme orbital deformation.

11.2.3. Falsification Criterion

If precision timing or astrometric measurements show no systematic deviation from GR beyond observational uncertainties in these regimes, the TGU coherence correction is falsified.

11.3. Test II: Gravitational Wave Polarization Anomalies

11.3.1. Unique TGU Signature

TGU predicts that gravitational waves propagating through regions of non-uniform informational coherence may experience differential modulation of the $h_{+}$ and $h_{\times }$ polarization modes:

$$h_{+,\times }^{\mathrm{obs}}=h_{+,\times }^{\mathrm{GR}}·ϵ{\left(r\right)}^{-12}.$$

(32)

This effect is directional and depends on the coherence structure of the intervening medium, not solely on the source.

11.3.2. Experimental Strategy

• Cross-correlation of polarization data from LIGO, Virgo, and KAGRA,
• Comparison of events traversing distinct galactic environments,
• Statistical separation from instrumental polarization biases.

11.3.3. Falsification Criterion

The absence of polarization-dependent deviations correlated with environmental coherence gradients rules out this TGU prediction.

11.4. Test III: Gravitational Lensing Without Dark Matter Profiles

11.4.1. Unique TGU Signature

In TGU, lensing strength depends on coherence gradients rather than solely on mass distribution:

$$\mathrm{\Delta }\theta \left(r\right)=\nabla \left[ϵ{\left(r\right)}^{-12}{I}_L\left(r\right)\right].$$

(33)

This predicts:

• Lensing effects spatially offset from baryonic mass peaks,
• Reduced correlation with Navarro–Frenk–White halo profiles,
• Environment-dependent lensing anomalies.

11.4.2. Observational Targets

• Galaxy clusters with known lensing–mass discrepancies,
• Strong-lensing systems with asymmetric environments,
• High-redshift lenses observed by JWST and Euclid.

11.4.3. Falsification Criterion

If lensing maps consistently require dark matter halos with no residual coherence-based correlation, TGU is disfavored.

11.5. Test IV: Cosmic Microwave Background Coherence Signatures

11.5.1. Unique TGU Signature

TGU predicts that large-scale CMB anomalies arise from primordial coherence modes rather than stochastic fluctuations, implying:

• Phase-correlated low-ℓ multipoles,
• Non-Gaussian coherence residues aligned across scales,
• Weak but systematic departures from isotropy.

11.5.2. Experimental Strategy

• Reanalysis of Planck and future CMB-S4 polarization data,
• Search for coherence-aligned phase correlations,
• Cross-comparison with large-scale structure surveys.

11.5.3. Falsification Criterion

The absence of statistically significant phase coherence beyond cosmic variance would invalidate this interpretation.

11.6. Test V: Laboratory-Scale Coherence Experiments

11.6.1. Unique TGU Signature

At laboratory scales, TGU predicts coherence-dependent deviations in coupled quantum systems exposed to controlled coherence gradients.

• Ion-trap arrays with tunable coherence dissipation,
• Superconducting circuits under coherence modulation,
• Optical cavities with engineered coherence gradients.

11.6.2. Experimental Strategy

• Measurement of decoherence rates under spatial coherence gradients,
• Comparison with standard quantum noise models,
• Reproducibility across independent platforms.

11.6.3. Falsification Criterion

If coherence gradients fail to produce measurable deviations from standard quantum predictions, the microphysical extension of TGU is constrained.

11.7. Test VI: Biological Coherence Correlations (Exploratory)

Biological applications remain exploratory. However, TGU predicts that informational coherence metrics may correlate with systemic biological stability:

• Genome-wide methylation coherence patterns,
• Neural coherence signatures in large-scale brain activity,
• Organism-level entropy markers.

These tests are hypothesis-generating rather than decisive and are not required for validation of the gravitational core of TGU.

11.8. Summary of Experimental Discriminants

Table 3. Experimental pathways and their relevance for falsifying TGU

Test Domain	Decisive for TGU
High-eccentricity orbits	Yes
Gravitational wave polarization	Yes
Dark-matter-independent lensing	Yes
CMB phase coherence	Yes
Laboratory quantum coherence	Partial
Biological coherence	Exploratory

Table 3. Experimental pathways and their relevance for falsifying TGU

Test Domain	Decisive for TGU
High-eccentricity orbits	Yes
Gravitational wave polarization	Yes
Dark-matter-independent lensing	Yes
CMB phase coherence	Yes
Laboratory quantum coherence	Partial
Biological coherence	Exploratory

11.9. Experimental Status and Outlook

At present, several of the proposed tests are accessible with existing or near-future instrumentation. Importantly, TGU makes risky predictions: it can be wrong. This property places the theory squarely within the domain of empirical science.

Future high-precision astrometry, gravitational-wave polarization analysis, and coherence-sensitive laboratory experiments will decisively determine whether informational coherence constitutes a fundamental organizing principle of physical reality or remains a useful phenomenological abstraction.

12. Axiomatic Foundations of Informational Spin

One of the most frequent and legitimate critiques directed at emerging unification frameworks concerns the absence of a clearly stated axiomatic basis. In order to address this point explicitly, this section presents the axiomatic foundations of the Unified Theory of Informational Spin (TGU).

It is important to emphasize from the outset that TGU is not proposed as a fundamental field theory derived from first-principle Lagrangians, but rather as a coherence-based unifying framework. Its axioms therefore play a role analogous to those of thermodynamics or information theory: they define operational, structural, and relational constraints from which phenomenological laws emerge.

12.1. Axiom I — Informational Primacy

Axiom I: Physical reality admits an informational description in which information is not merely descriptive, but structurally operative.

This axiom states that physical systems can be equivalently described in terms of organized informational states. Matter, energy, and spacetime geometry are treated as emergent manifestations of underlying informational organization, rather than as ontologically primitive entities.

This assumption aligns with well-established informational interpretations in physics, including entropy-based formulations, holographic principles, and quantum information theory, without committing to any specific microscopic carrier of information.

12.2. Axiom II — Coherence as a Physical Property

Axiom II: Information can exist in coherent or incoherent configurations, and coherence constitutes a physically relevant property of informational systems.

Informational coherence is defined as the degree of correlated organization among informational states across spatial and temporal scales. Systems with high coherence exhibit stability, persistence, and predictable dynamics, whereas incoherent systems tend toward dissipation and disorder.

This axiom provides the conceptual foundation for treating coherence gradients as drivers of effective physical behavior, analogous to how energy gradients drive forces in classical physics.

12.3. Axiom III — Existence of Informational Spin

Axiom III: Informational coherence organizes locally around structured nodes termed informational spins.

An informational spin is defined as a localized coherence structure that regulates the exchange, storage, and redistribution of information. Unlike quantum mechanical spin, informational spin is not an intrinsic angular momentum but a topological and organizational property of the informational substrate.

This axiom introduces informational spin as the minimal structural unit required to describe coherent interactions across scales, from quantum systems to cosmological structures.

12.4. Axiom IV — Scale Invariance of Informational Structures

Axiom IV: The principles governing informational coherence and informational spin are scale-invariant.

This axiom asserts that the same organizational rules apply across different physical regimes. While specific parameters may vary with scale, the functional form of coherence dynamics remains invariant.

Scale invariance justifies the application of the same mathematical formalism to orbital dynamics, galactic rotation curves, quantum coherence, and biological information processing within the TGU framework.

12.5. Axiom V — Emergence of Effective Forces from Coherence Gradients

Axiom V: Gradients in informational coherence give rise to effective forces observable as physical interactions.

Within this axiom, gravitational phenomena are interpreted as emergent effects resulting from spatial variations in informational coherence density. The familiar notion of force is thus replaced by a coherence-gradient-driven tendency toward informational equilibration.

This axiom does not deny the empirical validity of general relativity, but reframes its geometric description as an effective macroscopic manifestation of deeper informational dynamics.

12.6. Axiom VI — Entropy as Informational Decoherence

Axiom VI: Entropy corresponds to the loss or redistribution of informational coherence.

Entropy increase is interpreted as a process of coherence degradation rather than purely as an increase in microscopic disorder. Conversely, coherence preservation or amplification corresponds to locally reduced informational entropy.

This axiom provides a natural bridge between thermodynamics, cosmology, and biological organization, allowing entropy, stability, and structure formation to be described within a single informational language.

12.7. Axiom VII — Phenomenological Closure

Axiom VII: The validity of the TGU framework is determined by its phenomenological consistency, numerical convergence, and predictive capability.

This axiom explicitly acknowledges the phenomenological nature of the theory. Rather than claiming fundamental completeness, TGU is evaluated based on:

• Internal mathematical consistency,
• Convergence with experimentally verified theories in tested regimes,
• The generation of falsifiable predictions in unexplored domains.

In this sense, TGU occupies a role comparable to effective field theories and emergent gravity models, serving as a unifying descriptive framework pending deeper microscopic derivations.

12.8. Status of the Axioms

The axioms presented here are not asserted as ultimate truths, but as minimal structural assumptions necessary to define a coherence-based unification framework. They are deliberately conservative, avoiding metaphysical commitments beyond what is required to support the mathematical and phenomenological structure developed in subsequent sections.

Together, these axioms establish the conceptual backbone of the Unified Theory of Informational Spin, clarifying its scope, limitations, and epistemological status, while addressing the central concern regarding the absence of explicit foundational assumptions.

13. Conclusions and Future Perspectives

The Unified Theory of Informational Spin (TGU) presents a coherence-centered framework aimed at unifying gravitational, quantum, biological, and computational phenomena through a common informational substrate. By emphasizing informational coherence as an organizing principle, TGU offers an alternative interpretative structure capable of reproducing well-established physical results while extending their scope into regimes where conventional descriptions face conceptual or phenomenological limitations.

Within the domains explored in this work, TGU demonstrates internal mathematical consistency and numerical convergence with general relativistic predictions in experimentally tested regimes. At the same time, it generates distinctive phenomenological behavior in high-strain, high-eccentricity, and large-scale systems, providing a structured basis for testable deviations and future observational scrutiny.

13.1. Key Theoretical Advances

The principal theoretical contributions of the TGU framework include:

• The formulation of informational spin as a scale-invariant coherence descriptor applicable across physical and biological systems.
• The geometric motivation of the Matuchaki Parameter $k\approx 0.0881$ as a dimensionless coherence efficiency factor.
• The introduction of a coherence resistance factor ensuring controlled convergence with general relativity in low-strain regimes.
• A reinterpretation of gravitational phenomena as emergent effects of informational coherence gradients.

13.2. Empirical and Phenomenological Consistency

Rather than claiming definitive experimental confirmation, the results presented in this work demonstrate:

• Numerical convergence with observed orbital precession values in the Solar System.
• Phenomenological consistency with galactic rotation behavior without requiring additional matter components.
• Coherence-based reinterpretations of cosmological observations, including large-scale structure, lensing phenomena, and cosmic background anisotropies.
• Conceptual mappings between informational coherence and biological organization that generate testable interdisciplinary hypotheses.

13.3. Future Research Directions

Several avenues remain open for advancing and testing the TGU framework:

1.

Derivation of TGU parameters from deeper quantum-informational foundations.

2.

Large-scale numerical simulations enabling direct statistical comparison with $\Lambda$CDM cosmology.

3.

Dedicated observational analyses of high-eccentricity systems and coherence-sensitive gravitational-wave signatures.

4.

Controlled laboratory experiments exploring coherence dynamics in condensed-matter and quantum systems.

5.

Interdisciplinary studies investigating coherence-based descriptors in biological organization and information processing.

13.4. Philosophical Implications

Beyond its technical contributions, TGU suggests a conceptual shift in how physical reality may be understood. In this view:

• Physical laws emerge from structured informational coherence rather than from isolated force carriers alone.
• Observers interact with reality through phase-selective engagement with informational patterns.
• Life and cognition represent localized mechanisms for coherence preservation against entropic dispersion.
• Cosmological evolution may be interpreted as cyclic reorganization of informational structure rather than irreversible decay.

Taken together, the Unified Theory of Informational Spin offers a coherent and extensible framework that bridges established physics with emerging informational paradigms. As observational capabilities, computational methods, and interdisciplinary research continue to advance, the TGU approach provides a structured foundation for exploring coherence as a unifying principle across the physical and informational sciences.

Appendix A.1. Phenomenological Nature of the Theory

TGU is fundamentally phenomenological. Its core equations are constructed to capture emergent regularities observed across gravitational, cosmological, quantum, and biological systems through a common informational language. While the framework demonstrates internal consistency and numerical convergence with established theories in tested regimes, it does not yet provide a microphysical derivation of informational spin or coherence from underlying quantum degrees of freedom.

Consequently, TGU should be interpreted as an effective theory, comparable in scope to thermodynamics, hydrodynamics, or emergent gravity models, rather than as a replacement for quantum field theory or General Relativity at the most fundamental level.

Appendix A.2. Regime of Validity

The domain of validity of TGU can be divided into three principal regimes:

1.

Weak-field and low-strain gravitational systems: In this regime, including most Solar System dynamics and weakly relativistic astrophysical systems, TGU is constructed to converge exactly or near-exactly to General Relativity. Predictions in this domain are therefore not independent tests of TGU but consistency checks.

2.

Intermediate coherence-gradient systems: Systems characterized by high orbital eccentricity, asymmetry, or non-uniform environmental structure fall within the regime where TGU predicts controlled deviations from standard relativistic formulations. This domain provides the most promising arena for empirical discrimination.

3.

High-strain and coherence-dominated regimes: Extreme systems such as compact binaries, early-universe structures, and strongly anisotropic environments represent speculative extensions of the framework. Predictions in this regime should be regarded as exploratory and subject to substantial uncertainty.

Outside these regimes, particularly at Planck-scale physics or within strongly quantum-gravitational domains, TGU currently offers no validated description.

Appendix A.3. Dependence on Coherence Parameterization

A central assumption of TGU is the existence of a well-defined informational coherence field $I\left(x\right)$. While this construct is mathematically well-defined within the framework, its direct physical measurement remains an open problem. Different parameterizations of coherence may lead to quantitatively different predictions, particularly in cosmological and biological applications.

This dependence represents both a limitation and an opportunity: future work must establish operational definitions or proxies for informational coherence to reduce model ambiguity.

Appendix A.4. Risk of Overextension Across Domains

TGU deliberately adopts a unifying mathematical formalism applicable across multiple domains, including gravity, quantum systems, and biology. While this structural unity is one of the framework’s strengths, it also carries the risk of overextension.

In particular, biological and consciousness-related interpretations presented within TGU should be understood as hypothesis-generating analogies rather than as experimentally established mechanisms. These extensions are not required for the validation of the gravitational or cosmological core of the theory and should be evaluated independently.

Appendix A.5. Non-Uniqueness of Informational Interpretations

The informational language employed by TGU is not unique. Alternative informational or entropic formulations of gravity and cosmology exist, some of which may reproduce overlapping phenomenology. The presence of multiple informational descriptions does not invalidate TGU, but it implies that empirical discrimination between competing informational frameworks will be necessary.

Accordingly, the ultimate scientific value of TGU rests not on its conceptual novelty alone, but on the identification of unique, falsifiable predictions that cannot be absorbed into alternative models.

Appendix A.6. Risk of Parameter Calibration Bias

Although key parameters of TGU, such as the Matuchaki Parameter k and the coherence exponent $n=12$, are argued to have geometric and topological origins, their empirical relevance has been established primarily through calibration against existing data. There remains a risk that apparent convergence reflects implicit fitting rather than genuine explanatory power.

This risk is explicitly acknowledged, and it motivates the emphasis placed on independent predictive tests in high-eccentricity and high-coherence-gradient systems.

Appendix A.7. Falsifiability and Scientific Risk

TGU makes predictions that are, in principle, falsifiable. Failure to observe the predicted deviations in orbital precession, gravitational-wave polarization, or coherence-dependent lensing effects would constitute strong evidence against the framework.

The willingness to accept such outcomes is essential to the scientific legitimacy of TGU. The framework is therefore presented not as an immutable theoretical structure, but as a testable proposal subject to revision or rejection based on empirical evidence.

Appendix A.8. Summary

In summary, the Unified Theory of Informational Spin should be understood as:

• A phenomenological, coherence-based unifying framework,
• Validated by internal consistency and numerical convergence in tested regimes,
• Predictive but not yet microscopically complete,
• Explicitly limited in scope and open to falsification.

By clearly stating its limitations, regime of validity, and associated risks, TGU positions itself within the standard methodology of theoretical physics, prioritizing empirical accountability over speculative completeness.

Appendix B.1. Guiding Principles for Experimental Testing

The experimental philosophy of TGU rests on three guiding principles:

1.

Convergence in Verified Regimes: In weak-field, low-strain environments, TGU must converge to GR within observational uncertainties.

2.

Controlled Deviations: In high-strain, high-eccentricity, or large-scale coherence-dominated systems, TGU predicts systematic deviations with well-defined functional dependence.

3.

Parameter Minimalism: Once the coherence exponent n and the coherence efficiency parameter k are fixed, no additional free parameters are introduced in predictive applications.

These principles allow TGU to be tested without retroactive parameter fitting.

Appendix B.2. Orbital Precession in Extreme Eccentricity Regimes

High-eccentricity orbital systems provide a direct and falsifiable test of the coherence resistance factor ${ϵ}^{-n}$.

Appendix B.2.1. Predicted Observable

For a test particle in an orbit with eccentricity e and semi-major axis a, TGU predicts a precession angle:

$$\mathrm{\Delta }{\varphi }_{\mathrm{TGU}}=\mathrm{\Delta }{\varphi }_{\mathrm{GR}}\left(1+k{\displaystyle \frac{e}{a}}\right){ϵ}^{-n},$$

(A1)

with $n=12$ fixed.

Appendix B.2.2. Experimental Targets

• Near-Sun asteroids with $e>0.8$ (e.g., Icarus-type objects)
• Compact exoplanets with high eccentricity ($e>0.9$)
• Relativistic binary pulsars with asymmetric orbital geometries

Appendix B.2.3. Falsification Criterion

If observed precession scales purely with relativistic corrections and shows no systematic dependence on $e/a$ beyond GR predictions, the TGU correction term is falsified.

Appendix B.3. Gravitational Wave Polarization Modulation

Unlike GR, which predicts invariant propagation of polarization modes in vacuum, TGU predicts coherence-gradient-induced modulation of gravitational wave polarizations.

Appendix B.3.1. Predicted Effect

In regions with strong informational coherence gradients, the amplitudes of the $h_{+}$ and $h_{\times }$ modes may experience differential attenuation or phase rotation:

$$h_{\pm }^{\mathrm{TGU}}=h_{\pm }^{\mathrm{GR}}·ϵ{\left(r\right)}^{-n/2}.$$

(A2)

Appendix B.3.2. Observational Strategy

• Cross-correlation of polarization data from LIGO, Virgo, and KAGRA
• Comparison of polarization ratios for events propagating through different galactic environments
• Statistical stacking of high signal-to-noise events

Appendix B.3.3. Falsification Criterion

Absence of statistically significant polarization modulation correlated with environmental coherence gradients would rule out this class of TGU effects.

Appendix B.4. Gravitational Lensing Beyond Mass-Based Models

TGU predicts that lensing strength depends not only on baryonic mass but also on the spatial distribution of informational coherence.

Appendix B.4.1. Key Prediction

Regions with comparable baryonic mass but differing coherence structure should exhibit distinct lensing profiles:

$$\mathrm{\Delta }{\theta }_{\mathrm{TGU}}\propto \nabla \left(ϵ{\left(r\right)}^{-n}I\left(r\right)\right).$$

(A3)

Appendix B.4.2. Experimental Approach

• Comparative lensing analysis of galaxy clusters with similar mass distributions
• Correlation of lensing anomalies with dynamical coherence indicators
• Independent verification using weak and strong lensing datasets

Appendix B.4.3. Falsification Criterion

If lensing strength correlates exclusively with mass distributions and shows no residual dependence on inferred coherence gradients, the TGU lensing mechanism is excluded.

Appendix B.5. Cosmic Microwave Background Coherence Signatures

TGU predicts that certain large-scale anisotropies in the CMB originate from primordial coherence patterns rather than from stochastic density fluctuations alone.

Appendix B.5.1. Observable Signatures

• Low-ℓ multipole alignments
• Directional asymmetries consistent across temperature and polarization maps
• Phase-correlated oscillatory residuals

Appendix B.5.2. Testing Strategy

• Joint analysis of Planck, ACT, and upcoming CMB-S4 datasets
• Phase-coherence statistics beyond standard power-spectrum analysis
• Cross-validation with large-scale structure surveys

Appendix B.5.3. Falsification Criterion

If all observed anomalies are fully accounted for by cosmic variance and instrumental effects, without residual coherent structure, the TGU CMB interpretation is disfavored.

Appendix B.6. Laboratory-Scale Coherence Experiments

Although TGU is primarily motivated by astrophysical phenomena, controlled laboratory experiments may probe coherence dynamics at smaller scales.

Appendix B.6.1. Candidate Systems

• Coupled quantum oscillators
• Ion-trap arrays
• High-Q optical cavities

Appendix B.6.2. Expected Signature

TGU predicts non-linear coherence decay rates deviating from standard decoherence models when coherence gradients are externally imposed.

Appendix B.7. Summary of Experimental Status

The experimental program outlined above establishes TGU as a falsifiable framework. Its predictions are sufficiently specific to be disproven by current or near-future observations, particularly in high-eccentricity orbital dynamics, gravitational-wave polarization, and lensing anomalies.

Failure to observe the predicted coherence-dependent deviations would rule out the TGU framework in its present form. Conversely, consistent detection across multiple independent channels would strongly suggest the presence of an underlying coherence-based structure beyond conventional gravitational and cosmological models.