diff --git a/docs/_client/authorization.md b/docs/_client/authorization.md
index 13d28192..436332e4 100644
--- a/docs/_client/authorization.md
+++ b/docs/_client/authorization.md
@@ -97,7 +97,8 @@ Optional keyword arguments:
   (with `iss` set to the RFC 9207 `iss` parameter from the redirect, or `nil` when absent) opts into SEP-2468 issuer validation: a present `iss` must match
   the authorization server's issuer, and a missing one is rejected when the server advertises `authorization_response_iss_parameter_supported`.
   Omit it when the redirect arrives in a later request, as it does in a web application; see [Authorization in Web Applications](#authorization-in-web-applications).
-- `pending_authorization_max_age`: Integer seconds a pending authorization stays redeemable after the redirect when `callback_handler` is omitted. Defaults to 600.
+- `pending_authorization_max_age`: Integer seconds a pending authorization stays redeemable, counted from the moment `run!` saves it, when `callback_handler`
+  is omitted. Defaults to 600.
 - `scope`: Space-separated scopes to request when the server's `WWW-Authenticate` does not specify one.
 - `authorization_request_validator`: Callable invoked with an `MCP::Client::OAuth::AuthorizationRequest` before any authorization request is built.
   Returning a falsy value abandons the flow with `Flow::AuthorizationRefusedError`. See [Reviewing the authorization request](#reviewing-the-authorization-request).
@@ -185,7 +186,8 @@ by a different process, and relaying the code to a request held open for that lo
 1. When the transport meets a `401`, or a `403` step-up challenge, the flow runs discovery and registration as usual, saves a pending authorization in `storage`
    keyed by the `state` it generated, hands the authorization URL to `redirect_handler`, and raises `MCP::Client::OAuth::Flow::AuthorizationPendingError`
    instead of retrying. The error's `authorization_url` reader returns the same URL, so the application can send the user there from wherever is convenient.
-2. The request that receives the redirect calls `MCP::Client::OAuth::Flow#finish!` with the redirect's whole query. Requests made afterwards use the stored tokens.
+2. The request that receives the redirect calls `MCP::Client::OAuth::Flow#finish!` with the redirect's whole query. Pass the query as it arrived: an `iss`
+   the caller drops reads as absent, and the flow cannot tell the difference. Requests made afterwards use the stored tokens.
 
 ```ruby
 def mcp_oauth_provider(user)
@@ -232,16 +234,18 @@ so the storage should expire entries older than `pending_authorization_max_age`,
 `finish!` redeems the code the way the authorization began, and refuses anything else with `Flow::AuthorizationError`:
 
 - The pending authorization is looked up by `state` before any request is made. An unknown, already used, or malformed one is refused,
-  and one older than `pending_authorization_max_age` is discarded and refused.
+  and one older than `pending_authorization_max_age`, counted from when `run!` saved it, is discarded and refused.
 - `server_url` must name the MCP server the authorization began with.
-- The RFC 9207 `iss` parameter is validated against the recorded issuer before the pending authorization is consumed, so a forged callback carrying a valid `state`
-  cannot discard the verifier the legitimate callback needs. Because `finish!` sees the whole query, a missing `iss` is refused whenever the authorization server
-  advertises `authorization_response_iss_parameter_supported`.
+- The RFC 9207 `iss` parameter is validated against the recorded issuer before the pending authorization is consumed, so a callback from another authorization
+  server, as in a mix-up attack, is refused without consuming the entry the legitimate callback needs. The check establishes only that a present `iss`
+  matches the recorded issuer, not who sent the callback; a callback without `iss` passes it unless the authorization server advertises
+  `authorization_response_iss_parameter_supported`, in which case a missing `iss` is refused. Whoever holds the `state`, passes that check, and reaches
+  the consume first takes the entry, with an `error` or an unusable code as well as with the code itself, and the legitimate callback then finds nothing.
 - The pending authorization is then consumed through `delete_pending_authorization`, and only a callback that gets the entry back proceeds, so of two callbacks
   racing on the same `state`, such as a retried redirect, at most one redeems the code. An `error` response is raised with its `error` and `error_description`,
-  bounded as [token endpoint errors](#token-endpoint-errors) are; it is read only after the `iss` check, since in a mix-up those parameters are the attacker's.
+  bounded as [token endpoint errors](#token-endpoint-errors) are; it is read only after the `iss` check, since in a mix-up those parameters are another server's.
 - The code is redeemed at the recorded token endpoint, with the client registration, `resource`, and `redirect_uri` used when the authorization began,
-  without running discovery again (SEP-2352). A registration replaced in the meantime is refused.
+  without running discovery again (SEP-2352). A registration whose `client_id` or issuer changed in the meantime is refused; its other members may change.
 
 {: .important }
 > `state` proves that this SDK started the authorization, not which user did. Binding the callback to the user who started it is the application's responsibility:
diff --git a/lib/mcp/client/oauth/flow.rb b/lib/mcp/client/oauth/flow.rb
index 13298e5d..c79a271e 100644
--- a/lib/mcp/client/oauth/flow.rb
+++ b/lib/mcp/client/oauth/flow.rb
@@ -493,15 +493,20 @@ def refresh!(server_url:, resource_metadata_url: nil)
 
         # Finishes an authorization that `run!` left pending, in the request that receives the redirect to `redirect_uri`,
         # which may run in another process. `callback_params` is that redirect's whole query as a Hash (`code`, `state`, and,
-        # when present, `iss`, `error`, and `error_description`); passing all of it, rather than picking values out, is what
-        # lets the flow tell an absent `iss` from one the caller did not look for.
+        # when present, `iss`, `error`, and `error_description`); passing all of it, rather than picking values out, is
+        # the caller's part of the `iss` check: an `iss` the caller drops reads as absent, and the flow cannot tell the difference.
         #
         # The pending authorization is looked up by `state` before any request is made, and it binds the rest of the exchange:
         # the code is redeemed at the token endpoint recorded when the authorization began, with the client registration,
         # `resource`, and `redirect_uri` used then, and without discovery running again, so the code reaches the authorization
         # server the user was sent to (SEP-2352). The RFC 9207 `iss` is validated against the recorded issuer before the pending
-        # authorization is consumed, so a forged callback carrying a valid `state` cannot discard the verifier the legitimate
-        # callback needs, and before the callback's `error` is read, since in a mix-up those parameters are the attacker's.
+        # authorization is consumed, so a callback from another authorization server, as in a mix-up, is refused without
+        # consuming the entry the legitimate callback needs, and before the callback's `error` is read, since in a mix-up
+        # those parameters are the other server's. The check establishes only that a present `iss` matches the recorded issuer,
+        # not who sent the callback, and a callback without `iss` passes it unless the metadata advertises
+        # `authorization_response_iss_parameter_supported`: whoever holds the `state`, passes that check, and reaches
+        # the consume first takes the entry, and the legitimate callback then finds nothing.
+        #
         # Past that check the pending authorization is consumed with `delete_pending_authorization`, which returns the entry
         # it removed; only a callback that gets the entry back redeems the code, so of callbacks racing on the same `state`
         # (a retried redirect, say), at most one does.
@@ -1285,8 +1290,9 @@ def non_empty_string?(value)
         end
 
         # An RFC 6749 Section 4.1.2.1 error response, reported with the bounds a token endpoint error gets.
-        # Reached only after the `iss` check, so the values are the authorization server's own; they are still text it chose,
-        # so they are cut to a bounded length and confined to the printable ASCII the RFC permits.
+        # Reached only after the `iss` check, so any `iss` beside the values matched the recorded issuer; that does not
+        # prove who sent them, and they are text the sender chose, so they are cut to a bounded length and confined to
+        # the printable ASCII the RFC permits.
         def authorization_response_error(error, description)
           error = bounded_diagnostic(error, limit: TOKEN_ENDPOINT_ERROR_MAX_LENGTH)
           description = bounded_diagnostic(description, limit: TOKEN_ENDPOINT_ERROR_DESCRIPTION_MAX_LENGTH)
diff --git a/lib/mcp/client/oauth/provider.rb b/lib/mcp/client/oauth/provider.rb
index aab14ced..ddeff730 100644
--- a/lib/mcp/client/oauth/provider.rb
+++ b/lib/mcp/client/oauth/provider.rb
@@ -33,8 +33,8 @@ module OAuth
       #   Omit it when the redirect arrives in a later request, as it does in a web application:
       #   the flow then stops after `redirect_handler` with a pending authorization saved in `storage`,
       #   and the request that receives the redirect finishes it with `Flow#finish!`.
-      # - `pending_authorization_max_age` - Seconds a pending authorization stays redeemable after the redirect,
-      #   when `callback_handler` is omitted. Defaults to `DEFAULT_PENDING_AUTHORIZATION_MAX_AGE`.
+      # - `pending_authorization_max_age` - Seconds a pending authorization stays redeemable, counted from the moment
+      #   `run!` saves it, when `callback_handler` is omitted. Defaults to `DEFAULT_PENDING_AUTHORIZATION_MAX_AGE`.
       # - `scope`   - String of space-separated scopes to request when the server's
       #   `WWW-Authenticate` does not specify one.
       # - `storage` - Object responding to `tokens`, `save_tokens(tokens)`,