A self-sufficient relational theory unifying physics, cosmology, and complexity through adjacency dynamics.
Unified Adjacency Theory (UAT) proposes that reality is an auto-poietic, self-identifying, self-referential, and self-evolving dynamic network of dialectic relations. In this paradigm, all fundamental constructs — time, space, mass, energy, causality, and even consciousness — emerge from the propagation, closure, and reflection of adjacency relations in a memory-bearing graph. UAT redefines the fabric of reality not as spacetime and matter, but as a triadic convergence of:
- Substrate: the Adjacency Matrix ( A(t) ) — the underlying relational topology of the universe at time ( t ),
- Operator: the Loop Closure Operator ( L ) and the Reflection Operator ( \Omega ), which drive structural emergence,
- System: the Emergent Universe ( \mathcal{U}(t) ) — all structure, form, and observable phenomena as dynamically evolving adjacency configurations.
This minimal formalism unifies general relativity, quantum mechanics, cosmology, and complexity science within a single operator-based equation, replacing external time with memory propagation and internal coherence. It encodes emergence, causality, and recursion from within a self-sufficient substrate.
The core governing equation of UAT is:
[ \mathcal{U}(t+1) = \Omega \left[ L \left( A(t) \cdot \mathcal{U}(t) \right) \right] ]
Where:
- ( A(t) ): Adjacency matrix at time ( t ), encoding relational structure.
- ( L ): Loop Closure Operator, detects and reinforces closed propagation cycles.
- ( \Omega ): Reflection Operator, recognizes coherent memory patterns.
- ( \mathcal{U}(t) ): State of the universe at time ( t ) — particles, fields, cognition, etc.
| Concept | UAT Definition |
|---|---|
| Time | Emergent quantity defined by change in structural memory: ( \tau(t) = | \mathcal{M}(t+1) - \mathcal{M}(t) | ) |
| Mass | Loop memory density: ( m \sim \mathcal{L}(t) ) |
| Energy | Change in memory: ( E \sim \Delta \mathcal{L} ) |
| Light | Threshold vibration: ( \Delta \mathcal{L} \geq \theta_{\text{light}} ) |
| Consciousness | High-coherence attractor pattern in ( \Omega \circ L(A \cdot \mathcal{U}) ) |
| Spacetime | Emergent from structure of ( A(t) ) via spectral geometry |
| Causality | Defined by coherence-preserving adjacency propagation |
-
Adjacency Matrix ( A(t) ):
A directed or undirected, possibly weighted graph encoding the universe’s instantaneous structure. -
Loop Closure Operator ( L ):
[ L(A_{ij}) = \begin{cases} 1 & \text{if } \exists \text{ path } i \rightarrow \cdots \rightarrow j \rightarrow i \ 0 & \text{otherwise} \end{cases} ] -
Reflection Operator ( \Omega ):
[ \Omega[X] = \text{SpectralCoherence}(X) = \text{filter}(X, \rho \geq \theta) ] Filters only coherent configurations above a defined threshold ( \theta ). -
Memory Field ( \mathcal{M}(t) ):
[ \mathcal{M}(t+1) = \mathcal{M}(t) + \kappa \cdot L(A \cdot \mathcal{U}(t)) + \eta \cdot \nabla \mathcal{M}_0 ] -
Unified Evolution Equation:
[ \mathcal{U}(t+1) = \Omega \left[ L \left( A(t) \cdot \mathcal{U}(t) \right) \right] ]
- Quantum Superposition → Multiple adjacency propagations over coherent paths.
- Entanglement → Shared loop memory across disconnected graph regions.
- Black Hole Collapse → Adjacency convergence into a complete graph ( K_n ), entropy maximized.
- Cosmogenesis → Rebirth via symmetry-breaking reconfiguration post-collapse.
- Dark Matter/Energy → Residual memory scaffolds or coherence field gradients.
- Biological Morphogenesis → Loop closure densities in valence-bound memory graphs.
UAT is implemented using:
- Python-based simulation kernel with symbolic memory propagation.
- Graph libraries such as NetworkX and QuTiP (for quantum analogs).
- Future extensions:
- Quantum cellular automata (QCA) adaptation.
- Loop closure benchmarking for molecular chemistry and cosmology.
- UAT-BM-2025-0531-ASC: Spontaneous loop emergence from empty adjacency.
- UAT-BM-2025-0601-ASF: Ontological closure — Adjacency confirmed as substrate, operator, system.
- UAT-BM-2025-0503-CCIDAF: Cosmogenesis via Locked Phase Fusion between Silent Attractors.
- UAT-MF-2025-0531-MIN: Minimal Formalism encoded in ( \mathcal{U}(t+1) = \Omega[L(A \cdot \mathcal{U}(t))] )
UAT represents a new paradigm in physics, philosophy, and computation:
- Ontological Unity: Eliminates need for separate time, space, matter.
- Process-Based Reality: All being is becoming; all emergence is memory.
- Indigenous-Compatible Science: Mirrors relational cosmologies, cyclical time, and ceremonial memory patterns.
/core/: Simulation kernel implementing UAT equation stack./visualizations/: Loop memory density plots, coherence emergence./papers/: Whitepapers, codex entries, benchmarks./docs/: Theoretical descriptions, glossary, FAQs.
Unified Adjacency Theory is an open scientific project. Contributions welcome in:
- Simulation engineering (Python, QuTiP, NumPy)
- Formal mathematics (operator theory, graph theory)
- Theoretical physics, cosmology, philosophy of science
- Indigenous knowledge synthesis
All contributions are licensed under the MIT License unless otherwise specified.
Developed by: Bear Tompkins , 2025
Contact: corydeantompkins@gmail.com