Update docs

Author: sean-kuzco

docs/METHODOLOGY.md

@@ -14,17 +14,21 @@ LOGIC utilizes log probability distributions as a unique "fingerprint" of a mode
 
 The verifier supports two matching strategies:
 
-#### Token ID Matching (Default)
+#### Token ID Matching (Primary Method)
 
 The standard approach uses token IDs to align tokens between the original and verification responses:
 
 - Most accurate for providers that return token IDs (e.g., vLLM with `return_tokens_as_token_ids`)
 - Ensures exact token-level correspondence
 - Recommended when both sample and verification sources support token IDs
 
+With vLLM, we can request token IDs with the `return_tokens_as_token_ids` parameter. The OpenAI API, however, does not support this parameter.
+
 #### Text-Based Matching (Fallback)
 
-For providers that don't return token IDs (e.g., OpenRouter, some OpenAI configurations), use the `--text-only-matching` flag:
+For providers that don't return token IDs (e.g., OpenRouter, OpenAI, etc.), the system can fallback to text-based matching. In this approach, we will reconstruct the context up to the position of a given token and then query the verification model with that specific context. We will then compare the original log probabilities with the fresh ones using direct text matching.
+
+We can use the `--text-only-matching` flag:
 
 ```bash
 uv run logprob-sample \