Fix `BroadcastReceiver` lag counts

`BroadcastReceiver.receive_nowait()` treated `seq` as a deque index
but subtracted `BroadcastState.maxlen` without counting the first
invalid index. A one-slot queue thus claimed it dropped zero values
after its subscriber missed one.

Include that first displaced value in the count. Preserve the
existing Tokio-style reset to the oldest retained item.

Also, cover exact loss reporting and recovery for one- and
three-slot retention windows.

Prompt-IO: ai/prompt-io/opencode/20260811T233833Z_7cbd64ee_prompt_io.md

(this patch was generated in some part by `opencode` using `gpt-5.6-sol` (`openai`))

ai/prompt-io/opencode/20260811T233833Z_7cbd64ee_prompt_io.md

@@ -0,0 +1,30 @@
+---
+model: openai/gpt-5.6-sol
+service: opencode
+session: ses_0799212ebffe42arY96czXn89F
+timestamp: 2026-08-11T23:38:33Z
+git_ref: 7cbd64ee
+scope: code
+substantive: true
+raw_file: 20260811T233833Z_7cbd64ee_prompt_io.raw.md
+---
+
+## Prompt
+
+Open a new isolated worktree in the local Tractor repository and draft a fix
+for `BroadcastReceiver` reporting that a lagged one-slot consumer dropped
+zero values when one value had actually been displaced.
+
+## Response summary
+
+Corrected the off-by-one lag count while preserving cursor recovery and added
+deterministic narrow- and wider-window regressions for exact loss reporting.
+
+## Files changed
+
+- `tractor/trionics/_broadcast.py` - exact broadcast overrun count.
+- `tests/test_task_broadcasting.py` - lag count and recovery regression.
+
+## Human edits
+
+None - generated output follows the user's diagnosed edge case.

ai/prompt-io/opencode/20260811T233833Z_7cbd64ee_prompt_io.raw.md

@@ -0,0 +1,50 @@
+---
+model: openai/gpt-5.6-sol
+service: opencode
+timestamp: 2026-08-11T23:38:33Z
+git_ref: 7cbd64ee
+diff_cmd: git diff HEAD~1..HEAD
+---
+
+The user asked for a Tractor fix in a new isolated worktree after a live piker
+failure reported:
+
+```text
+tractor.trionics._broadcast.Lagged:
+Task `piker.brokers.ib.broker.handle_order_requests` overrun and
+dropped `0` values
+```
+
+Inspection showed the lag exception was valid but its count was off by one.
+`BroadcastReceiver.receive_nowait()` treats `seq` as a deque index. With a
+one-entry queue, index zero is the only retained value and `seq == 1` already
+means one value was displaced. The old `seq - maxlen` calculation therefore
+reported zero instead of one.
+
+> `git diff HEAD~1..HEAD -- tractor/trionics/_broadcast.py`
+
+Adjusted the lag count to `seq - maxlen + 1` and documented why the first
+invalid deque index must be included. The existing Tokio-style cursor reset
+remains unchanged.
+
+> `git diff HEAD~1..HEAD -- tests/test_task_broadcasting.py`
+
+Added a deterministic parameterized regression covering a one-slot queue
+with one dropped value and a three-slot queue with two dropped values. The
+test keeps the root receiver idle while a child subscriber synchronously
+drains each produced value, asserts the exact `Lagged` message, and proves the
+next receive resumes at the oldest retained item.
+
+Verification output:
+
+```text
+..                                                                       [100%]
+2 passed in 0.04s
+
+..........                                                               [100%]
+10 passed in 4.65s
+```
+
+The targeted import resolved to the new Tractor worktree. Python compilation
+and `git diff --check` passed. Adversarial review found no actionable issues;
+zero-capacity channels remain a pre-existing untested edge outside this fix.

tests/test_task_broadcasting.py

@@ -307,6 +307,48 @@ def test_subscribe_errors_after_close():
     trio.run(main)
 
 
+@pytest.mark.parametrize(
+    ('size', 'sent', 'dropped'),
+    [
+        (1, 2, 1),
+        (3, 5, 2),
+    ],
+)
+def test_lagged_reports_exact_drop_count(
+    size: int,
+    sent: int,
+    dropped: int,
+) -> None:
+    '''
+    `Lagged` must report every value outside the retained window.
+
+    `BroadcastReceiver.receive_nowait()` previously subtracted the
+    queue length from an already-invalid deque index without counting
+    that first displaced value. A one-slot queue therefore claimed it
+    dropped zero values after two sends. Keep one root receiver idle
+    while a child subscriber drains every produced value, then prove
+    the lag error reports the exact overrun and positions the root at
+    the oldest value still retained by `BroadcastState.queue`.
+
+    '''
+    async def main() -> None:
+        tx, rx = trio.open_memory_channel(size)
+        brx = broadcast_receiver(rx, size)
+
+        async with brx.subscribe() as fast:
+            for value in range(sent):
+                await tx.send(value)
+                assert await fast.receive() == value
+
+            match = rf'dropped `{dropped}` values'
+            with pytest.raises(Lagged, match=match):
+                await brx.receive()
+
+            assert await brx.receive() == sent - size
+
+    trio.run(main)
+
+
 def test_ensure_slow_consumers_lag_out(
     reg_addr,
     start_method,

tractor/trionics/_broadcast.py

@@ -237,7 +237,10 @@ class BroadcastReceiver(ReceiveChannel):
                 # https://docs.rs/tokio/1.11.0/tokio/sync/broadcast/index.html#lagging
 
                 mxln = state.maxlen
-                lost = seq - mxln
+                # `seq == mxln` is already one past the final
+                # valid deque index, so include that first
+                # displaced value in the loss count.
+                lost = seq - mxln + 1
 
                 # decrement to the last value and expect
                 # consumer to either handle the ``Lagged`` and come back