docs: record the live API URL and replace the streaming caveat with measured behaviour

Author: codebybilal18

README.md

@@ -5,16 +5,20 @@
 Upload documents, ask questions, get answers with citations you can click back to the source — and
 a measured comparison of which retrieval strategy actually works, and what it costs.
 
-> **Status: the code is complete and verified end-to-end; the numbers are not.** Every benchmark
-> table in this README is empty on purpose — filling them in with invented figures would defeat the
-> entire point of the project. [Reproduce them](#reproducing-the-benchmark): about twenty minutes
-> and a few dollars of API credit.
+> **Status: deployed and working; the benchmark has not been run.** Every results table below is
+> empty on purpose — filling them in with invented figures would defeat the entire point of the
+> project. [Reproduce them](#reproducing-the-benchmark): about twenty minutes and a few dollars of
+> API credit.
 >
-> Verified against Postgres 16 + pgvector 0.8.5: migrations apply, a PDF ingests, hybrid retrieval
-> returns ranked passages, the answer carries citations that resolve and verify at 100% coverage,
-> the SSE stream emits every event, and an unanswerable question is refused. `pytest`: 90 passing.
+> Verified in production (Vercel `sin1` + Neon Postgres 18 / pgvector 0.8.1): a PDF ingests, hybrid
+> retrieval returns ranked passages, the answer carries citations that resolve and verify at 100%
+> coverage, cost and latency are reported per request, an unanswerable question is refused, and the
+> SSE stream delivers tokens progressively rather than in one flush. `pytest`: 108 passing.
+>
+> Not yet exercised: the eval harness and benchmark table, the HNSW sweep, the Qdrant backend,
+> Langfuse tracing, and the Kubernetes manifests. All are written; none has been run.
 
-Frontend: **[documind-web](https://github.com/codebybilal18/documind-web)** · Live demo: _(add your Vercel URL)_
+**Live API: https://documind-api-theta.vercel.app** ([health](https://documind-api-theta.vercel.app/health) · [docs](https://documind-api-theta.vercel.app/docs)) · Frontend: [documind-web](https://github.com/codebybilal18/documind-web)
 
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@@ -366,9 +370,14 @@ boot, because two concurrent instances racing the same migration is worse than a
 `ACTIVE_CONFIG=serverless` is a **distinct config**, not config D, so the deployment never reports
 D's numbers for a reranker it is not running.
 
-Streaming: the Python runtime buffers responses in some configurations. The SSE stream is written
-correctly regardless — a buffered deployment delivers every event in one flush and the client
-parser handles it unchanged; only the progressive reveal is lost.
+Streaming works. Measured against the live deployment, 33 token events arrived over a 2.23 s
+spread rather than in a single flush, so the progressive reveal is real and not a local-only
+behaviour. (The client parser handles a buffered response identically, should that ever change.)
+
+Latency is the honest weak point: ~10 s to first token on a cold function, of which ~8 s is
+retrieval — cold start, query rewrite, embedding, hybrid search, and the LLM reranker, each a
+round trip to `ap-southeast-1`. Warm requests are far quicker. Cutting it means dropping the
+rewrite and rerank hops, which is exactly the trade the benchmark exists to quantify.
 
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