docs: corrected the graph-agent parallel reducer gotcha

Graph-Agents.md

@@ -1065,6 +1065,48 @@ parallel super-step but no reducer is declared for 'summary'. Add
 node's output.
 ```
 
+The load-time check covers **declared** writes only. The runtime applies the
+same contention rule to every key a branch actually wrote (writes are
+extracted by diffing branch state; see
+[Branch isolation](#branch-isolation)), including keys the load-time
+validator does not model. The most important of these is the implicit
+`output` key:
+
+### The implicit `output` key (gotcha)
+
+Every LLM (and agent) node stores its raw completion in the `output` state
+key. That is what `{{output}}` in `state_updates` templates against. In a
+parallel super-step this counts as a write from every LLM/agent branch, so
+a fan-out of **two or more LLM/agent nodes always contends on `output`**,
+even when every declared `state_updates` key is distinct.
+
+Because the load-time validator only computes declared write sets
+(`state_updates` ∪ `output_schema`), this conflict surfaces at **runtime,
+at the join**, after the branches have already executed:
+
+```
+Key 'output' was written by 5 parallel branches but has no reducer
+declared. Add a reducer for 'output' to the graph's `reducers:` block, or
+rename one writer.
+```
+
+The fix is one declaration at the graph root. When (as is typical) each
+branch captures its real result into its own key via `state_updates` and
+nothing reads `output` after the join, `overwrite` is the idiomatic
+choice:
+
+```yaml
+reducers:
+  output: overwrite   # implicit LLM completion key; unused after the join
+```
+
+Merge order is deterministic (branches sorted by
+`(node_id, invocation_index)`), so even `overwrite` reproducibly keeps the
+last-sorted branch's completion across runs.
+
+Rule of thumb: **any parallel super-step containing 2+ LLM/agent nodes
+needs a reducer for `output`.**
+
 ## Branch isolation
 
 Each parallel branch runs against an **independent state fork**. Writes
@@ -1075,8 +1117,11 @@ merges them via the reducer pipeline.
 
 This means:
 
-- Branches can freely mutate `output`, internal counters, etc. without
+- Branches can freely mutate state **during** the super-step without
-  worrying about siblings
+  stepping on siblings — but every key a branch wrote participates in the
+  join, including the implicit `output` key every LLM/agent node sets, so
+  any key written by 2+ branches needs a declared reducer (see
+  [the implicit `output` key](#the-implicit-output-key-gotcha))
 - Race conditions are impossible since there is no shared mutable state during
   the parallel phase
 - Branches cannot communicate with each other mid-super-step. If you