Add local velocity benchmark

Author: roackb2

docs/benchmarks/wikipedia/local-velocity/benchmark-local-velocity-wikipedia-navigation.md

@@ -0,0 +1,97 @@
+# Benchmark: Wikipedia Deep-Dive (Local Velocity Experiment)
+
+> **🧪 Experiment Context**
+> **Objective:** Evaluate the impact of **Local Instantaneous Velocity** vs. **Global Trajectory Smoothing** on agent navigation performance.
+> **Hypothesis:** We initially feared local velocity () would cause oscillation due to high-frequency noise in the embedding space.
+> **Reality:** Experiments reveal that Global Smoothing introduces "Semantic Inertia," causing the agent to cling to the starting concept. **Local Velocity allows for rapid context switching**, essential for multi-hop reasoning.
+> **Input Data:**,
+
+---
+
+## 1. Comparative Executive Summary
+
+This experiment compares the default "Global Heading" implementation against the experimental "Local Velocity" implementation.
+
+| Metric | Global Heading (Baseline) | Local Velocity (Experimental) | Improvement |
+| --- | --- | --- | --- |
+| **Tech Scenario Steps** | 23 Steps (77s) | **2 Steps (18s)** | **10x Efficiency** |
+| **Revolution Scenario Steps** | 12 Steps (35s) | **8 Steps (37s)** | **33% Fewer Steps** |
+| **Trajectory Characteristic** | High Inertia (Hard to switch topics) | **High Agility** (Snaps to new contexts) | **Eliminated Looping** |
+| **Outcome** | Prone to "Orbiting" the target | Direct Interception | **Validated** |
+
+---
+
+## 2. Scenario A: The "Zero-Inertia" Run (Jacquard Machine → CPU)
+
+**Challenge:** Trace the technological evolution from early looms to modern processors.
+**Key Difficulty:** Breaking away from the "Textile" semantic cluster to enter the "Computing" cluster.
+
+### 2.1 The Trajectory Comparison
+
+#### 🔴 Global Heading (Baseline) - *The Trap*
+
+The agent kept the "Jacquard Machine" (Start Node) in its heading vector too long. It reached computer hardware but kept circling back to specific components rather than the core concept.
+
+* *Path:* `Jacquard` -> ... -> `ACPI` -> `AMD Turbo Core` -> `Opteron` -> `X86-64` -> `Opteron` (Loop)
+
+#### 🟢 Local Velocity (Winner) - *The Snap*
+
+The agent moved based *only* on the previous step. Once it hit a "Gateway Node" (`History of computing hardware`), it immediately discarded the "Textile" context and drove full speed toward the CPU.
+
+```mermaid
+graph TD
+    Start("🧶 Jacquard machine") -->|Link: History| Step1["📜 History of computing hardware"]
+    Step1 -->|Link: CPU| EndNode("💻 Central processing unit")
+
+    style Start fill:#f9f,stroke:#333,stroke-width:2px
+    style Step1 fill:#ff9,stroke:#333,stroke-width:2px
+    style EndNode fill:#bbf,stroke:#333,stroke-width:4px
+
+```
+
+### 2.2 Technical Analysis
+
+* **Semantic Inertia:** Global Heading failed because `Jacquard machine` is semantically distant from `CPU`. By averaging the start vector, the agent was "held back" by its history.
+* **Gateway Exploitation:** `History of computing hardware` acts as a semantic bridge. Local Velocity allowed the agent to use this bridge to perform a **90-degree semantic turn** without penalty.
+
+---
+
+## 3. Scenario B: The "Temporal Bridge" (Coffee → French Revolution)
+
+**Challenge:** Find the connection between a beverage and a major political event.
+
+### 3.1 The Trajectory
+
+```mermaid
+graph TD
+    Start("☕ Coffee") -->|Association| Step1["⚔️ Battle of Vienna"]
+    Step1 -->|Context| Step2["⚔️ Great Turkish War"]
+    Step2 -->|Context| Step3["⚔️ Austro-Turkish War"]
+    Step3 -->|Exploration| Step4["⚔️ Anapa campaign (1788/1790)"]
+    Step4 -.->|Dead End?| Step5["📅 1790 (Year)"]
+    Step5 -->|Reflex Trigger| EndNode("🔥 French Revolution")
+
+    style Start fill:#f9f,stroke:#333,stroke-width:2px
+    style Step5 fill:#ff9,stroke:#333,stroke-width:2px
+    style EndNode fill:#bbf,stroke:#333,stroke-width:4px
+
+```
+
+### 3.2 Analysis of Agent Behavior
+
+* **The Historical Route:** Unlike the Global run (which went via `American Revolution`), the Local run took a fascinating historical detour: Coffee -> Vienna (Coffee House Culture origins) -> Ottoman Wars.
+* **The "Year" Bridge (Step 5):** The agent got stuck in obscure wars (`Anapa campaign`). However, because it relies on *local* signals, it identified the link `1790` (the year) as a high-potential node.
+* **The Pivot:** Once at `1790`, the `French Revolution` is a dominant semantic neighbor. The agent used a temporal node to bridge a gap between "Ottoman Wars" and "French Politics."
+
+---
+
+## 4. Architectural Conclusions
+
+### 4.1 "Forgetfulness" is a Feature
+
+In high-dimensional Knowledge Graphs (like Wikipedia), the path to the target is often **non-linear**.
+
+* Global Heading assumes a straight line (Geodesic).
+* Local Velocity acts like **Brownian Motion with Gradient Descent**.
+
+**Conclusion:** For semantic exploration, it is better to "forget" where you came from and focus entirely on where the current node can take you.