Layered Network Framework
A 14D Ontology Anchored Network Framework
Canonical layered architecture structured into vertical semantic layers, each encoding a dimension class, while supporting horizontal integration via cross-links and interoperable functions.
Eng. Ivan Pasev
Founder, Digital Fabrica Theory
Abstract
The Layered Network Framework structures DFT visualization into vertical semantic layers, each encoding a dimension class, while also supporting horizontal integration via cross-links, signaling interoperable functions.
The system is anchored in both mathematical formalisms(set theory, graph theory, category theory, etc.) and real-world operational planes (cybernetics, governance, ethics, sustainability), using Mermaid graph logic as a dynamic visualization layer.
Layered Class Ontology (Vertical)
| Layer | Dimension Class | Semantic Role | Tensor / Logical Object |
|---|---|---|---|
| 0 | DFT-Core | Central orchestrating node | Digital Fabrica Theory ψ11411 |
| 1 | Pillar | Abstract invariants / fixed points | Ethical Kernel ζπθ, GU (14D) |
| 2 | Mathematical Foundations | Formal logic and construction base | ZFC, Knot Polynomials, Graph Laplacians |
| 3 | Application Plane | Use-cases, technological domains | AI, PQC, Energy, DAO |
| 4 | Institutional Grounding | GILC, partner networks, governance | ScrollTreaty, Charter, Logician Entity |
| 5 | Knowledge Embedding | Recursive representation of formal systems | ScrollDNA, ScrollWitness, 14D Lattice |
Example Formal Nodes and Their Role
| Node Label | Formal Role / Interpretation | Mathematical Binding |
|---|---|---|
| Ramanujan Graphs | Topological security base for FNS, PQ key routing | Expander Graph, Spectral Gap Tensor |
| Zeta-Regularized Voting | Governance logic based on infinite series convergence | ζ(s), s ∈ Re>1, Euler product variant |
| Modular Congruence | Ethical + legal invariant enforcement | Modular arithmetic, p-adic cohomology |
| 14D Hexagonal Lattice | Projection surface of GU framework | ℝ¹⁴ → ℝ²/ℝ³ projection tensor Π |
| Ethical Functor | Morphism class mapping governance | Functor F: Cat → Cat′, maintaining ethics logic |
| Recursive Subnet Generation | Self-similar propagation across ICP/DFDF mesh | f: ℕ → ℕ subgraph with self-indexing |
| Knot-Theoretic Policy | Logical encoding of policies | Knot diagrams, Reidemeister moves |
Expanded Dimensions Mapping (Grounded)
| Dim | Label | Real World Role | Tensor / Mapping |
|---|---|---|---|
| 1–3 | Spatial (x, y, z) | UI / UX / contract location | gμν – Metric Tensor |
| 4–7 | Topological | Contract graph relations | Laplacian, Spectral Gap Tensor |
| 8–10 | Governance | Voting, Compliance, Law | Modular Congruence, Knot Tensor |
| 11–14 | Economic | Tokenomics, Supply, Valuation | Zeta Tensor, Partition Function |
Mapping Function Φ
Φ : H₂D → ℝ¹⁴
- Injectivity: Unique location in 14D space
- Functoriality: Morphisms preserved in transformations
- Partial Invertibility: Reverse projection possible for traceability
Conclusion
The Layered Network Framework provides a canonical architecture that structures DFT visualization into vertical semantic layers, each encoding a dimension class, while supporting horizontal integration via cross-links.
By anchoring the system in both mathematical formalisms (set theory, graph theory, category theory) and real-world operational planes (cybernetics, governance, ethics, sustainability), the framework creates a bridge between abstract mathematics and practical implementation.
The Mapping Function Φ enables unique location assignment in 14D space, preservation of morphisms in transformations, and partial invertibility for traceability. This framework is ready for ScrollKernel integration, Infinite Knowledge Garden (IKG), GILC Whitepapers, and Motoko or Rust logic embedding for FNS.
Future implementations will focus on dynamic visualization layers using Mermaid graph logic, development of semantic class–dimension binding tables, and deployment of cross-link signaling systems for interoperable functions.
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