The Coherence Expansion Principle: A Universal Constraint on Informational Systems

Kevin L. Brown, Independent Researcher
Published: December 2025
DOI: 10.5281/zenodo.17771878

Informational Physics Ontology Paper

Abstract

This work introduces the Coherence Expansion Principle (CEP) — a universal, substrate-independent constraint governing the evolution of informational systems. CEP formalizes the empirically observed tendency of complex systems to transition toward higher internal coherence over time. The principle applies to any system representable as an informational manifold

I=(M,F,O),I = (M, F, O),I=(M,F,O),

where MMM is a differentiable substrate, FFF are informational fields, and OOO are the allowable operators (recursion, projection, scalar-time evolution).

CEP asserts that the coherence functional

C[F]=1Z∫MΦI dμ,\mathcal{C}[F] = \frac{1}{Z} \int_M \Phi_I \, d\mu,C[F]=Z1∫MΦIdμ,

is monotonically non-decreasing under admissible transformations. This functional depends on gradient alignment, suppression of second-order irregularity, and local informational curvature. The paper defines:

• the coherence density ΦI\Phi_IΦI,

• the informational metric gijg_{ij}gij,

• the informational Laplacian ΔI\Delta_IΔI,

• and the informational curvature scalar Rinfo\mathcal{R}_{\text{info}}Rinfo,

providing a unified mathematical structure for coherence-driven dynamics.

CEP is strictly informational and non-causal: it does not describe forces, agency, or purpose. Instead, it identifies a universal invariance condition required for any system to preserve structure under internal evolution. The principle is falsifiable through tests in quantum state relaxation, biological phase synchrony, dynamical attractor formation, and large-scale structure stability.

This manuscript provides the first cross-domain mathematical formalization of coherence expansion, enabling coherent comparison across quantum, biological, dynamical, and astrophysical systems.

Core Structure of the Framework

1. The Informational Manifold I=(M,F,O)I=(M,F,O)I=(M,F,O)

The paper constructs a general informational geometry incorporating:

• a metric space MMM,

• informational fields FFF (entropy, coherence, coupling modes),

• operator sets OOO governing recursion, projection, and phase evolution.

This structure generalizes prior work on informational substrates and harmonic evolution.

2. The Coherence Functional C[F]\mathcal{C}[F]C[F]

CEP centers on a dimensionless functional quantifying informational organization:

ΦI=∣∇SI∣1+∣ΔISI∣,C[F]=1Z∫MΦI dμ.\Phi_I = \frac{|\nabla S_I|}{1 + |\Delta_I S_I|}, \quad \mathcal{C}[F] = \frac{1}{Z} \int_M \Phi_I \, d\mu.ΦI=1+∣ΔISI∣∣∇SI∣,C[F]=Z1∫MΦIdμ.

The model supplies explicit rules for:

• coherence gradient alignment,

• suppression of irregular informational curvature,

• integration over the manifold,

• normalization and stability bounds.

3. Informational Curvature and Stability

The informational curvature scalar:

Rinfo=α∣∇SI∣2+βΔISI+γφ2,\mathcal{R}_{\text{info}} = \alpha |\nabla S_I|^2 + \beta \Delta_I S_I + \gamma \varphi^2,Rinfo=α∣∇SI∣2+βΔISI+γφ2,

provides a cross-domain measure of coherence concentration and attractor formation. This term unifies structural stabilization phenomena across scales in a single geometric quantity.

4. The Coherence Expansion Principle (CEP)

The central invariance:

C[Ft+δt]≥C[Ft]\mathcal{C}[F_{t+\delta t}] \geq \mathcal{C}[F_t]C[Ft+δt]≥C[Ft]

holds under all admissible operators in OOO. This condition replaces domain-specific coherence mechanisms with a single informational constraint applicable to:

• quantum projections and eigenstate stabilization,

• biological synchronization and feedback networks,

• dynamical-system attractor convergence,

• boundary formation and stabilization in complex physical systems,

• large-scale structural organization.

CEP is a structural consistency law: systems that decrease coherence decay or depersist; systems that maintain or increase coherence remain stable under recursion.

5. Cross-Domain Consequences

CEP offers the first substrate-agnostic explanation for coherence phenomena across:

• Quantum systems: eigenstate stability and projection behavior

• Biological networks: synchronization, reflectivity, coherence cascades

• Dynamical systems: attractor contraction and stability

• Temporal domains: phase-modulated scalar-time signatures

• Astrophysical structures: large-scale boundary and stability formation

All are derived from a single informational framework rather than independent theories.

6. Falsifiability and Observational Pathways

CEP is empirically testable via:

• coherence maxima in quantum projections,

• failure or presence of phase-locking in biological networks,

• attractor non-convergence in dynamical systems,

• absence or presence of coherence modulation in temporal variability,

• cross-domain coherence alignment measurements.

The paper provides explicit conditions whose violation would refute CEP’s universality.

Key Contributions

1. A domain-independent definition of coherence

Built from informational gradients and curvature.

2. A universal invariance condition

Monotonic non-decrease of C[F]\mathcal{C}[F]C[F].

3. A unifying informational geometry

Applicable from quantum states to large-scale structures.

4. A fully falsifiable theoretical framework

Grounded in measurable coherence behaviors.

5. The first mathematical structure explicitly linking multi-scale coherence

without invoking new forces, particles, or metaphysical claims.

Reviewer Guidance

Reviewers are encouraged to evaluate:

• mathematical rigor of the coherence functional and curvature definitions,

• internal consistency of the informational manifold formulation,

• clarity of variational stability arguments,

• generality across domains without overreach,

• completeness of the falsifiability criteria,

• distinction between informational constraints and physical laws.

CEP is intended as a descriptive and structural framework, not a modification of existing physical theory.

Keywords

Coherence Expansion Principle,
Informational Geometry,
Coherence Functional,
Informational Curvature,
Complex Systems,
Quantum Coherence,
Dynamical Stability,
Nonlinear Systems,
Informational Manifold,
Structural Invariance,
Gradient Alignment,
Temporal Modulation,
Cross-Scale Coherence,
Variational Stability,
Information-Theoretic Dynamics