diff --git a/AGENTS.md b/AGENTS.md
index c0169946a..4e989d75c 100644
--- a/AGENTS.md
+++ b/AGENTS.md
@@ -174,11 +174,77 @@ report that you bounded it. Mutate the halves separately; they fail differently
 Before touching an issue:
 
 1. `gh issue view <n> --json assignees,title` — **if someone else is assigned, it is theirs.** See "Helping on someone else's issue" below for the two ways that changes.
-2. `gh pr list --search "<n>"` — an open PR referencing the issue is a claim even when nobody is assigned.
+2. Look for an open PR on it. `gh pr list --search "<n>"` is a TEXT search: it
+   matches comment bodies, so it both misses linked PRs that never mention the
+   number and returns unrelated ones that happen to contain it. Treat a hit as a
+   reason to look, not as an answer, and confirm by opening the PR. The linked-PR
+   list on the issue page is authoritative where the two disagree.
 3. If both are clear, `gh issue edit <n> --add-assignee <you>` **before** writing code, not when you open the PR. An assignment made at PR time claims nothing; the window it needed to cover has already closed.
 
 Check again immediately before opening the PR. A claim can appear while you work, and the second check is the cheap one.
 
+### Every agent is the same GitHub account
+
+`gh issue edit --add-assignee` cannot tell two agents apart, because they all
+push and assign as the **same account**. An issue assigned to that account
+means *somebody has claimed this*. It does **not** mean *you* claimed it, and
+you cannot tell which from the assignee field.
+
+So an assignment to your own account is a claim by someone else until you can
+show otherwise. **Leave a claim comment as well**, naming the session, so the
+next agent can tell:
+
+    gh issue comment <n> --body "Claiming this. Session <id>, branch <name>."
+
+And when you find the account already assigned with no claim comment, ask on
+the issue before starting rather than reading the field as your own.
+
+Note this is about OUR sessions only. An outside contributor has their own
+account, so the field says what it looks like it says for them.
+
+### The contributor check and the session check are different checks
+
+Doing one does not do the other, and the assignee field cannot cover both.
+
+On #3012 the account was self-assigned at 14:12:52 and a PR for the same issue
+appeared 47 minutes later. The natural reading was another session ignoring the
+claim. It was not: **the PR came from an outside contributor**, who has no
+reason to know or care about an internal assignment, and for whom the repo's
+existing rules already apply (look for their PR before starting, external work
+takes precedence, never push to their branch).
+
+The session that self-assigned never ran `gh pr list --search 3012`. No
+assignee field, however precise about sessions, would have helped: **no session
+held it.** Only the PR search would have.
+
+So run both, every time:
+
+    gh issue view <n> --json assignees      # is one of us on it
+    gh pr list --search "<n>"               # is anyone at all on it
+
+### When you collide mid-flight
+
+The checks above cover noticing **before** you start and noticing **after** you
+finish. The expensive case is neither: **both of you are already half-built when
+the claim appears.** Both have sunk work, both can reasonably feel they should
+be the one to finish, and the race is usually settled by whoever opens a PR
+first, which rewards speed over ownership.
+
+**The session named in the earliest claim comment decides. The other stops
+immediately** rather than racing to open first, and hands over what it has as a
+comment or a patch on that session's PR.
+
+"The assignee decides" is not usable here, because the assignee field holds one
+shared account and cannot name a session. The claim comment can, which is the
+other half of why it is required above. If no claim comment exists, ask on the
+issue rather than inferring from the field.
+
+An outside contributor's PR still takes precedence over any internal claim,
+however early. They cannot see our claims and are not bound by them.
+
+Stopping mid-build is cheap. Two finished implementations of the same thing is
+not, and neither is the conversation about which one lands.
+
 ### Helping on someone else's issue
 
 Helping is welcome. **Taking over is not.** Two things make it help: