Active theoretical research program

A discrete framework in which spacetime, gravity, and physical constants emerge from Planck-scale coherence.

The Sobolev–Ozok Lattice (SOL) proposes that physical reality is built from discrete cells whose coherence and resolution dynamics generate geometry, motion, and structure across scales.

Instead of assuming spacetime as a continuous background, SOL treats it as an emergent result of local interactions. The framework is developed to connect quantum behavior, gravitational structure, cosmology, and particle-scale organization within one discrete picture.

Why it matters It offers a route toward deriving geometry and dynamics from discrete first principles rather than taking them as given.

What it targets Gravity, Planck-scale structure, physical constants, galaxy-scale behavior, and compact-object phenomena.

How to read it Start with the overview below, then move to predictions and papers depending on how technical you want to go.

Start here See predictions Read papers

Discrete Planck-cell lattice Emergent geometry Coherence and resolution dynamics Testable deviations

Conceptual SOL Planck-cell lattice with coherence gradient — **Figure 1.** Conceptual illustration of the SOL lattice. Spatial variations in inter-cell coherence define an effective geometric structure at larger scales.

Start here

If this is your first time visiting the project, this is the shortest way to understand what SOL is trying to do.

1. Core premise

Spacetime is modeled as a discrete lattice of Planck-scale cells rather than a fundamentally continuous arena.

2. Generating geometry

Coherence gradients between cells produce an effective geometric structure, so curvature is treated as emergent.

3. Physical behavior

Quantum and large-scale behavior arise from resolution dynamics, coherence structure, and their higher-order corrections.

Why SOL is different

Not just another abstract description

It starts from a discrete cell picture at the Planck scale.
It treats geometry as a result of coherence rather than a prior stage.
It aims to derive structure, not only fit observations afterward.

Built around falsifiability

Planetary precession and solar-system tests
Galaxy rotation behavior
Black hole and shadow-related phenomena
Higher-order coherence corrections beyond leading behavior

What the framework aims to explain

Geometry Metric structure from inter-cell coherence

Dynamics Resolution processes instead of assumed postulates

Constants Physical constants linked to lattice structure

Predictions Observable deviations at multiple scales

Choose your reading path

Different visitors need different entry points. Use the path that matches your level of interest.

Level 1

Understand the idea

Get the conceptual overview of the framework, its motivation, and its main physical picture.

Read philosophy

Level 2

See the testable side

Review the observational hooks, falsifiability, and the phenomena SOL claims should be distinguishable.

Open predictions

Level 3

Go technical

Access the papers and manuscripts, including archived Zenodo records and ongoing theoretical development.

Browse papers

Core conceptual structure

Three layers shown visually

k = 1: conformal or scaling-like behavior
k = 2: intrinsic curvature behavior
k = 3: shell or interface structure linked to higher organization

This layered picture is part of how SOL organizes the transition from local cell interactions to larger physical effects.

SOL metric visualization showing k=1 scaling, k=2 curvature, and k=3 shell or interface structure — **SOL metric orders (3D render):** k=1 conformal scaling, k=2 intrinsic curvature, and k=3 curvature-gradient shell or interface structure.

Credibility and research status

Project status

SOL is maintained as an active theoretical research program with papers archived and expanded over time.

Access points

Read manuscripts, track development, and review the project through the papers page, GitHub repository, and ORCID profile.

Zenodo papers GitHub repository ORCID profile