# 🧭 Universal Hex Relationships (UHR) **UHR** is the relationship layer of the Universal Hex (UHX) framework. It encodes how two UHT-encoded entities relate to each other using a fixed-width, 8-bit **semantic fingerprint**. Each bit corresponds to a distinct relational trait, enabling **self-describing links** in system models. --- ## 🔗 UHR Basics - **Length:** 8 bits (1 byte) - **Format:** Binary (`10100101`), Hex (`A5`), or trait list - **Purpose:** Describes the **type and nature** of the relationship between two entities - **Use:** Attach UHR codes to links in semantic graphs or system models --- ## 🧠 UHR Trait Table | **Bit** | **Trait Name** | **Description** | | ------: | ------------------------------- | -------------------------------------------------------------------- | | 1 | **Directional** | Relationship flows one way (A → B). If false, the link is symmetric. | | 2 | **Causal / Influential** | A causes or influences B. | | 3 | **Hierarchical / Containment** | A contains or dominates B structurally. | | 4 | **Symbolic / Representational** | A stands for or models B. | | 5 | **Governed / Constrained** | The link is defined or limited by external rules or systems. | | 6 | **Temporal / Sequence-bound** | Relationship depends on time or order. | | 7 | **Context-sensitive** | Only valid in certain conditions, environments, or perspectives. | | 8 | **Non-reciprocal** | B does not reciprocate the relationship. | --- ## 📘 Examples ### 1. **Feeds →** ```text UHR: 11000001 (binary) = C1 (hex) Traits: Directional, Causal, Non-reciprocal Meaning: A provides input or effect to B, unidirectionally. ``` ### 2. **Symbolizes →** ```text UHR: 10001001 = 89 Traits: Directional, Symbolic, Non-reciprocal Meaning: A represents or encodes B. ``` ### 3. **Constrains →** ```text UHR: 10100101 = A5 Traits: Directional, Governed, Non-reciprocal Meaning: A limits or regulates B under some policy or rule. ``` ### 4. **Belongs to** ```text UHR: 00100000 = 20 Traits: Hierarchical only Meaning: A is a part or component of B. ``` --- ## 📐 Use in Modeling ### In UHX Graphs ```markdown Sensor [UHT: C3F20000] Controller [UHT: C2FA3FDF] Sensor --> Controller [UHR: C1 | Feeds →] ``` ### In SDRs ```yaml required_links: - relation: "Feeds →" uhr: "C1" target_must_have: [11] # Logic processor ``` --- ## 🔄 Relationship Logic - **Symmetry**: If `Directional = 0`, the link is bidirectional (e.g., symbolic reflection) - **Asymmetry**: `Non-reciprocal = 1` → A affects B, but not vice versa - **Structural Semantics**: Hierarchy, containment, and symbolic relations can all be encoded --- ## 📎 When to Use UHR Use UHR when you want to: - **Model how entities interact** - **Specify required relationships in an SDR** - **Infer emergent system behavior** - **Document architecture patterns with meaning** --- ## 🧹 Example Relationship Network ```text User --[C1 | Triggers →]--> Light Switch Light Switch --[C1 | Activates →]--> Light Bulb Power Supply --[C1 | Feeds →]--> Light Switch ``` Each arrow carries **semantic type information** — not just a line on a diagram. --- ## ✅ Summary - **UHR** gives **meaning** to links in a system graph - Each UHR code is a compact semantic descriptor (8 bits) - Combine UHT + UHR to build fully self-describing models - Enables **traceability, explainability, and validation** of system relationships