docs: add wiki content for Home.md

Author: ranafaraz

docs/wiki/Home.md

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+# PathwAI
+
+[![CI](https://github.com/ranafaraz/PathwAI/actions/workflows/ci.yml/badge.svg)](https://github.com/ranafaraz/PathwAI/actions/workflows/ci.yml)
+[![Live demo](https://img.shields.io/badge/live%20demo-pathwai.dexdevs.com-brightgreen?logo=rocket)](https://pathwai.dexdevs.com)
+[![Python](https://img.shields.io/badge/python-3.10%20%7C%203.11%20%7C%203.12-blue)](https://github.com/ranafaraz/PathwAI/blob/main/pyproject.toml)
+[![License: MIT](https://img.shields.io/badge/license-MIT-green)](https://github.com/ranafaraz/PathwAI/blob/main/LICENSE)
+
+**Wrap a fallible LLM in search and a verifier, and prove it plans like the optimum.**
+
+PathwAI turns an LLM into a deliberate planner. A language-model proposer estimates how far each state is from the goal; a best-first search uses that estimate as a heuristic; and a verifier rejects illegal or looping moves so the agent recovers from bad suggestions instead of executing them blindly. Every plan is scored against a built-in **A\* optimum**, so the claims are measured, not asserted.
+
+The whole benchmark — three planning domains, five planners, a null ablation — runs green in CI with **no API keys and no model downloads** using a deterministic stub proposer. Real LLM backends (Ollama, OpenAI) are opt-in via pip extras.
+
+## Architecture
+
+```mermaid
+flowchart LR
+    subgraph Domains["Domain (env-selectable)"]
+        GW[GridWorld]
+        BW[Blocksworld]
+        DL[Delivery]
+    end
+    subgraph Proposer["LLM proposer (env-selectable)"]
+        STUB[stub\nnoisy heuristic · offline]
+        RND[random\nablation]
+        REAL[ollama / openai\noptional extras]
+    end
+    Domains --> STATE[State + applicable actions]
+    STATE --> Proposer
+    Proposer --> EST[cost-to-go estimate]
+    EST --> SEARCH[Best-first search\npriority = g + estimate]
+    STATE --> SEARCH
+    SEARCH <--> VERIFY[Verifier\nlegal? not revisited?]
+    SEARCH --> PLAN[Plan]
+    Domains -.optimal A*.-> SCORE[Score vs. ground-truth optimum]
+    PLAN --> SCORE
+    SCORE --> M[solve rate · optimality ratio · expansions]
+```
+
+## Quick start
+
+```bash
+python -m venv .venv && source .venv/bin/activate   # Windows: .venv\Scripts\activate
+pip install -e ".[dev]"
+pytest -q                    # 77 tests
+pathwai compare --domain gridworld --seed 3
+```
+
+## Wiki pages
+
+| Page | What it covers |
+|---|---|
+| [Architecture](Architecture) | Domain representation, proposer, verifier, search engine, ablation design |
+| [Evaluation](Evaluation) | Benchmark setup, results table, ablation, reproduce commands |
+| [Configuration](Configuration) | Env vars, backend matrix, `.env.example` |
+| [Development](Development) | Setup, test commands, adding domains and proposers, code layout |