diff --git a/brainpy/dyn/rates/populations.py b/brainpy/dyn/rates/populations.py
index 8ae90fdc8..efa82a92e 100644
--- a/brainpy/dyn/rates/populations.py
+++ b/brainpy/dyn/rates/populations.py
@@ -1043,23 +1043,23 @@ def update(self, inp_e=None, inp_i=None):
             input_e = inp_e if (inp_e is not None) else 0.
             input_i = inp_i if (inp_i is not None) else 0.
 
-        de = -self.e + self.beta_e * bm.maximum(input_e, 0.)
+        de = (-self.e + self.beta_e * bm.maximum(input_e, 0.)) / self.tau_e
+        de = self.e + de * dt
         with jax.ensure_compile_time_eval():
             has_noise = bm.any(self.noise_e != 0.)
-
         if has_noise:
-            de += bm.random.randn(*self.varshape) * self.noise_e
-        de = de / self.tau_e
-        self.e.value = bm.maximum(self.e + de * dt, 0.)
+            # Euler-Maruyama: the stochastic term scales as sqrt(dt), not dt, so the
+            # noise intensity is independent of the integration step (P10-M1).
+            de += self.noise_e / self.tau_e * bm.sqrt(dt) * bm.random.randn(*self.varshape)
+        self.e.value = bm.maximum(de, 0.)
 
-        di = -self.i + self.beta_i * bm.maximum(input_i, 0.)
+        di = (-self.i + self.beta_i * bm.maximum(input_i, 0.)) / self.tau_i
+        di = self.i + di * dt
         with jax.ensure_compile_time_eval():
             has_noise = bm.any(self.noise_i != 0.)
-
         if has_noise:
-            di += bm.random.randn(*self.varshape) * self.noise_i
-        di = di / self.tau_i
-        self.i.value = bm.maximum(self.i + di * dt, 0.)
+            di += self.noise_i / self.tau_i * bm.sqrt(dt) * bm.random.randn(*self.varshape)
+        self.i.value = bm.maximum(di, 0.)
         return self.e.value
 
     def clear_input(self):
diff --git a/brainpy/dyn/rates/rates_test.py b/brainpy/dyn/rates/rates_test.py
index 1147cc44f..dfb9f14f1 100644
--- a/brainpy/dyn/rates/rates_test.py
+++ b/brainpy/dyn/rates/rates_test.py
@@ -15,10 +15,13 @@
 # ==============================================================================
 from unittest import TestCase
 
+import jax.numpy as jnp
+import numpy as np
 from absl.testing import parameterized
 
 import brainpy as bp
 import brainpy.math as bm
+from brainpy.context import share
 from brainpy.dyn.rates import populations
 
 
@@ -54,6 +57,43 @@ def test_tlm(self):
         self.assertTrue(tlm.tau_e is not None)
 
 
+class TestThresholdLinearModelNoise(TestCase):
+    """P10-M1: noise must follow Euler-Maruyama ``sqrt(dt)`` scaling."""
+
+    @staticmethod
+    def _noise_increment_std(dt):
+        # Drive a fresh model with no drift (beta_e=0, tau_e=1) from e=0 so that one
+        # step gives e = max(noise_e/tau_e * sqrt(dt) * randn, 0). Measure the std of
+        # the (clamped) increment; the positive-half std is proportional to the
+        # increment std, so its ratio across dt isolates the dt scaling.
+        bm.random.seed(0)
+        bm.set_dt(dt)
+        m = bp.rates.ThresholdLinearModel(20000, noise_e=1.0, beta_e=0.0, tau_e=1.0)
+        m.reset_state()
+        share.save(t=0.0, dt=dt, i=0)
+        out = np.asarray(m.update(inp_e=0.0))
+        pos = out[out > 0]
+        return float(pos.std())
+
+    def test_threshold_linear_model_noise_scales_as_sqrt_dt(self):
+        s_small = self._noise_increment_std(0.01)
+        s_large = self._noise_increment_std(0.1)
+        ratio = s_large / s_small
+        # sqrt(dt): ratio ~ sqrt(0.1/0.01) = sqrt(10) ~ 3.162.
+        # The buggy dt scaling gives ratio ~ 10.
+        self.assertAlmostEqual(ratio, np.sqrt(10.0), delta=0.2)
+
+    def test_threshold_linear_model_noise_finite(self):
+        bm.random.seed(0)
+        bm.set_dt(0.1)
+        m = bp.rates.ThresholdLinearModel(8, noise_e=1.0, noise_i=0.5)
+        m.reset_state()
+        share.save(t=0.0, dt=0.1, i=0)
+        out = jnp.asarray(m.update(inp_e=1.0, inp_i=1.0))
+        self.assertEqual(out.shape, (8,))
+        self.assertTrue(bool(jnp.isfinite(out).all()))
+
+
 class TestPopulation(parameterized.TestCase):
     @parameterized.named_parameters(
         {'testcase_name': f'noise_of_{name}', 'neuron': name}
diff --git a/brainpy/dyn/rates/rnncells.py b/brainpy/dyn/rates/rnncells.py
index eae8b6fc4..b07c4507d 100644
--- a/brainpy/dyn/rates/rnncells.py
+++ b/brainpy/dyn/rates/rnncells.py
@@ -124,7 +124,7 @@ def __init__(
             self.state[:] = self.state2train
 
     def reset_state(self, batch_or_mode=None, **kwargs):
-        self.state.value = parameter(self._state_initializer, (batch_or_mode, self.num_out,), allow_none=False)
+        self.state.value = variable(self._state_initializer, batch_or_mode, self.num_out)
         if self.train_state:
             self.state2train.value = parameter(self._state_initializer, self.num_out, allow_none=False)
             self.state[:] = self.state2train
@@ -236,7 +236,7 @@ def __init__(
             self.state[:] = self.state2train
 
     def reset_state(self, batch_or_mode=None, **kwargs):
-        self.state.value = parameter(self._state_initializer, (batch_or_mode, self.num_out), allow_none=False)
+        self.state.value = variable(self._state_initializer, batch_or_mode, self.num_out)
         if self.train_state:
             self.state2train.value = parameter(self._state_initializer, self.num_out, allow_none=False)
             self.state[:] = self.state2train
@@ -372,7 +372,7 @@ def __init__(
             self.state[:] = self.state2train
 
     def reset_state(self, batch_or_mode=None, **kwargs):
-        self.state.value = parameter(self._state_initializer, (batch_or_mode, self.num_out * 2), allow_none=False)
+        self.state.value = variable(self._state_initializer, batch_or_mode, self.num_out * 2)
         if self.train_state:
             self.state2train.value = parameter(self._state_initializer, self.num_out * 2, allow_none=False)
             self.state[:] = self.state2train
diff --git a/brainpy/dyn/rates/rnncells_test.py b/brainpy/dyn/rates/rnncells_test.py
index b8fbd9bf8..ce3ea8129 100644
--- a/brainpy/dyn/rates/rnncells_test.py
+++ b/brainpy/dyn/rates/rnncells_test.py
@@ -170,5 +170,38 @@ def test_Conv3dLSTMCell_NonBatching(self):
         output = layer(input)
 
 
+class Test_Rnncells_reset_state(parameterized.TestCase):
+    """Regression tests for P10-H1: ``reset_state(None)`` must not crash."""
+
+    @parameterized.product(cls=['RNNCell', 'GRUCell', 'LSTMCell'])
+    def test_rnn_cells_reset_state_none_unbatched(self, cls):
+        # P10-H1: explicit reset_state(None) on a non-batching cell used to raise
+        # ``ValueError: Do not support type <class 'NoneType'>: None`` because the
+        # state shape was built as ``(None, num_out)``.
+        bm.random.seed()
+        cell = getattr(bp.dyn, cls)(num_in=3, num_out=4)
+        cell.reset_state(None)
+        expected = (8,) if cls == 'LSTMCell' else (4,)
+        self.assertTupleEqual(tuple(cell.state.shape), expected)
+
+    @parameterized.product(cls=['RNNCell', 'GRUCell', 'LSTMCell'])
+    def test_rnn_cells_reset_state_via_bp_reset_state(self, cls):
+        # P10-H1: the public ``bp.reset_state`` path passes ``batch_or_mode=None``.
+        bm.random.seed()
+        cell = getattr(bp.dyn, cls)(num_in=3, num_out=4)
+        bp.reset_state(cell)
+        expected = (8,) if cls == 'LSTMCell' else (4,)
+        self.assertTupleEqual(tuple(cell.state.shape), expected)
+
+    @parameterized.product(cls=['RNNCell', 'GRUCell', 'LSTMCell'])
+    def test_rnn_cells_reset_state_int_batch(self, cls):
+        # The int-batch path must still produce a leading batch axis.
+        bm.random.seed()
+        cell = getattr(bp.dyn, cls)(num_in=3, num_out=4, mode=bm.batching_mode)
+        cell.reset_state(2)
+        expected = (2, 8) if cls == 'LSTMCell' else (2, 4)
+        self.assertTupleEqual(tuple(cell.state.shape), expected)
+
+
 if __name__ == '__main__':
     absltest.main()
diff --git a/docs/issues-found-20260619-dyn-rates-base.md b/docs/issues-found-20260619-dyn-rates-base.md
new file mode 100644
index 000000000..f32eb30f9
--- /dev/null
+++ b/docs/issues-found-20260619-dyn-rates-base.md
@@ -0,0 +1,146 @@
+# Audit — dyn/rates + dyn/outs + dyn/others + dyn base/utils (P10)
+
+Date: 2026-06-19
+Branch: `fix/audit-20260619-dyn-rates-base`
+Scope: `brainpy/dyn/rates/{nvar,populations,reservoir,rnncells}.py`,
+`brainpy/dyn/outs/{base,outputs}.py`, `brainpy/dyn/others/{common,input,noise}.py`,
+`brainpy/dyn/{base,utils,_docs}.py` (+ co-located `*_test.py`).
+
+## Summary
+
+A prior audit pass (2026-06-18, see `dev/issues-found-20260618.md`) already fixed
+the bulk of the verified Critical/High bugs in this slice and left regression tests
+in `brainpy/dyn/rates/dyn_rates_dynold_fixes_test.py`. Those fixes are present and
+green in the current tree:
+
+- C-15 `ThresholdLinearModel` `randn(*shape)` — fixed (`populations.py:1051,1060`).
+- C-16 `StuartLandauOscillator.dy` `+w*x` rotational coupling — fixed (`populations.py:721`).
+- H-36 `LSTMCell` `h`/`c` setters slice the last axis — fixed (`rnncells.py:401,412`).
+- H-37 `Reservoir` recurrent noise `uniform(-1, 1)` — fixed (`reservoir.py:228`).
+- H-38 `Reservoir` bias added in `update()` — fixed (`reservoir.py:223-224`).
+
+This pass performs a fresh review and fixes the still-present
+correctness/robustness issues (M-20, M-21), re-examines the previously-recorded
+M-18/M-19 (both turn out NOT to be bugs in the current brainstate 0.5 stack), and
+records remaining Low items.
+
+---
+
+### P10-H1 — `RNNCell`/`GRUCell`/`LSTMCell.reset_state()` crashes in default usage  [High]
+- File: `brainpy/dyn/rates/rnncells.py:127, 239, 375`
+- Category: edge/error, api-drift
+- What: `reset_state` builds the state via
+  `parameter(self._state_initializer, (batch_or_mode, self.num_out), allow_none=False)`.
+  With the default `batch_or_mode=None` (the value supplied by `bp.reset_state(node)`
+  and by a bare `node.reset_state()` in non-batching mode) the shape tuple becomes
+  `(None, num_out)`, and `tools.size2num(None)` raises
+  `ValueError: Do not support type <class 'NoneType'>: None`.
+- Why it's a bug: `bp.reset_state(net)` / `node.reset_state()` is the standard reset
+  API. Any network containing an unbatched `RNNCell`/`GRUCell`/`LSTMCell` crashes on
+  reset. `__init__` already builds the state correctly with
+  `variable(jnp.zeros, self.mode, self.num_out)`, which handles `None`; only
+  `reset_state` regressed to `parameter((None, ...))`.
+- Repro:
+  ```python
+  import brainpy as bp
+  cell = bp.dyn.RNNCell(num_in=3, num_out=4)   # NonBatchingMode
+  bp.reset_state(cell)                          # ValueError: ... None
+  ```
+- Fix: use `variable(self._state_initializer, batch_or_mode, self.num_out)` (matching
+  `__init__`), which yields `(num_out,)` for `None`, `(B, num_out)` for an int `B`,
+  and the mode-aware shape for a `Mode`. Applied to all three cells (LSTM uses
+  `num_out * 2`).
+- Tests: `test_rnn_cells_reset_state_none_unbatched`,
+  `test_rnn_cells_reset_state_via_bp_reset_state`,
+  `test_rnn_cells_reset_state_int_batch` in `rnncells_test.py`.
+- Status: fixed
+
+### P10-M1 — `ThresholdLinearModel` noise scales as `dt`, not `sqrt(dt)`  [Medium]
+- File: `brainpy/dyn/rates/populations.py:1046-1062`
+- Category: numerics
+- What: the Euler update folds the Gaussian noise into the drift
+  (`de += randn(*shape) * noise_e`, then `de = de / tau_e`, then
+  `e = max(e + de * dt, 0.)`). The noise increment therefore scales linearly with
+  `dt`. A correct Euler–Maruyama step for `tau de = (-e + beta·[I]_+) dt + noise·dW`
+  needs the stochastic term to scale as `sqrt(dt)` (`dW ~ sqrt(dt)·N(0,1)`).
+- Why it's a bug: the effective noise intensity is `dt`-dependent — halving `dt`
+  changes the realized noise standard deviation by 2x instead of `sqrt(2)`, so the
+  stationary statistics of the simulated rate change with the integration step.
+  Measured: noise std ratio for `dt=0.1` vs `dt=0.01` is exactly `10` (the `dt`
+  scaling); the correct Euler–Maruyama ratio is `sqrt(10) ≈ 3.16`.
+- Repro: static + measured (see commit message / regression test).
+- Fix: move the noise out of the `dt`-scaled drift and add it as a separate
+  `sqrt(dt)` Euler–Maruyama increment:
+  `e = max(e + (-e + beta_e·[I]_+)/tau_e · dt + noise_e/tau_e · sqrt(dt)·randn, 0)`.
+- Tests: `test_threshold_linear_model_noise_scales_as_sqrt_dt` in `rates_test.py`.
+- Status: fixed
+
+### P10-L1 — `FeedbackFHN.reset_state` rebinds `self.input`/`input_y` instead of `.value=`  [Low] (recorded only — was M-18)
+- File: `brainpy/dyn/rates/populations.py:370-371`
+- Category: style
+- What: `reset_state` does `self.input = variable(...)` / `self.input_y = variable(...)`
+  whereas the sibling rate models (`FHN`, `QIF`, `StuartLandau`, `WilsonCowan`) use
+  `self.input.value = ...`.
+- Why not a bug here: under brainstate 0.5, assigning a fresh `Variable` to an
+  attribute that already holds a `State` performs an in-place value/shape update
+  (object identity is preserved, value resets, batched reshape works), so captured
+  references and monitors are not broken. Verified empirically.
+- Fix: recorded only (consistency nit; out of Critical/High/Medium scope).
+- Status: recorded-only
+
+### P10-L2 — Prior audit M-19 (`FeedbackFHN` delay "double-count") is not a bug  [Low] (recorded only)
+- File: `brainpy/dyn/rates/populations.py:374`
+- Category: correctness (false positive in prior audit)
+- What: 2026-06-18 M-19 claimed that because `state_delays={'x': self.x_delay}` is
+  registered with the integrator, querying `self.x_delay(t - self.delay)` in `dx`
+  double-counts the delay and should be `self.x_delay(t)`.
+- Why it's not a bug: `state_delays` only causes the integrator to call
+  `delay.update(new_x)` after each step (buffer maintenance). `TimeDelay.__call__`
+  takes an **absolute time** (see its docstring: `delay(-0.5)` → value at t=-0.5), so
+  `x_delay(t - delay)` is the correct way to read `x(t - delay)`. Querying
+  `x_delay(t)` would return the *current* value (no delay) and destroy the feedback.
+  Verified empirically: the query returns the historical value ~`delay` ms in the
+  past, not the current value.
+- Fix: recorded only — leave `x_delay(t - self.delay)` as-is. Changing it (per the
+  earlier audit) would introduce a regression.
+- Status: recorded-only
+
+### P10-L3 — `OutputGroup.reset_state` signature uses `batch_size` not `batch_or_mode`  [Low] (recorded only)
+- File: `brainpy/dyn/others/input.py:102`
+- Category: style
+- What: `OutputGroup.reset_state(self, batch_size=None, ...)` while the rest of the
+  module (`InputGroup`, `SpikeTimeGroup`, `PoissonGroup`) uses `batch_or_mode`. The
+  body is a no-op `pass`, so callers passing positionally still work; no functional
+  impact.
+- Fix: recorded only.
+- Status: recorded-only
+
+### P10-L4 — NumPy-doc nonconformance across rates/outs docstrings  [Low] (recorded only)
+- File: `brainpy/dyn/rates/populations.py` (and `nvar.py`, `reservoir.py`,
+  `outs/outputs.py`), e.g. `Parameters::`, `References::`, `See Also::` literal-block
+  markers and bare `Reference` headings.
+- Category: style
+- What: CLAUDE.md mandates underlined NumPy-doc sections; these files use the legacy
+  `Section::` literal-block form (matching the rest of the repo, also flagged as L-14
+  in the 2026-06-18 audit).
+- Fix: recorded only (repo-wide cosmetic; out of scope).
+- Status: recorded-only
+
+---
+
+## Verified-correct (checked, no change)
+
+- `NVAR` feature construction: stride/`select_ids` picks exactly `delay` time points;
+  monomial `comb_ids` and constant/linear concatenation correct (matches 2026-06-18
+  Appendix B).
+- `Reservoir` spectral-radius rescaling (`Wrec *= spectral_radius / current_sr`) is
+  applied after connectivity masking and before sparse reduction — correct ordering.
+- `QIF` / `FHN` / `WilsonCowan` ODE right-hand sides match their docstrings.
+- `MgBlock` magnesium curve `1/(1 + [Mg]/β·exp(α(V_off - V)))` matches the documented
+  `g_inf`; `COBA`/`CUBA` outputs correct.
+- `OUProcess` uses `sdeint` with constant diffusion `g = sigma` → correct `sqrt(dt)`
+  scaling; `reset_state` initializes `x` at `mean`.
+- `PoissonGroup` spike probability `freqs · dt / 1000` (Hz·ms) correct.
+- `LSTMCell`/`GRUCell` gate equations match docstrings (forget-gate `+1` bias; GRU
+  reset/update split) — GRU confirmed correct by 2026-06-18 Appendix B.
+- `get_spk_type` mode → dtype mapping correct.