diff --git a/docs/exporting_bayesflow_models.md b/docs/exporting_bayesflow_models.md
index 22b7eae..dd8b3ed 100644
--- a/docs/exporting_bayesflow_models.md
+++ b/docs/exporting_bayesflow_models.md
@@ -1,5 +1,8 @@
 # Exporting bayesflow-trained networks to ONNX
 
+> The artifact rules every exporter here satisfies are collected in
+> [The ONNX likelihood contract](https://lnccbrown.github.io/HSSM/how_to/custom_onnx_likelihoods/).
+
 LANfactory's [`transform_bayesflow_to_onnx`](api/onnx.md) is the bayesflow
 sibling of [`transform_sbi_to_onnx`](exporting_sbi_models.md). It wraps a
 trained [`bayesflow`](https://github.com/bayesflow-org/bayesflow)
@@ -220,7 +223,7 @@ the caller.
 | Non-identity adapters | Numpy-only operations can't be baked into ONNX; see Constraint 4 above. Pointwise tensor adapter ops (log, sqrt, scale) are a candidate for v1.x. |
 | Transformer / attention summary networks | Contain `LayerNormalization` (no jaxonnxruntime handler) and dynamic-shape attention. |
 | FlowMatching, DiffusionModel, ConsistencyModel inference networks | `log_prob` requires ODE integration, not ONNX-exportable. |
-| `KERAS_BACKEND=jax` workflows | Use the bayesflow LRE-style in-memory JAX callable path (see [`bayesflow_lre_integration.ipynb`](https://github.com/lnccbrown/HSSM/blob/main/docs/tutorials/bayesflow_lre_integration.ipynb) in HSSM). |
+| `KERAS_BACKEND=jax` workflows | Use the bayesflow LRE-style in-memory JAX callable path (see [`bayesflow_lre_integration.ipynb`](https://lnccbrown.github.io/HSSM/tutorials/bayesflow_lre_integration/) in HSSM). |
 
 ## Numerical guarantees
 
diff --git a/docs/exporting_sbi_models.md b/docs/exporting_sbi_models.md
index 051b90e..c45e539 100644
--- a/docs/exporting_sbi_models.md
+++ b/docs/exporting_sbi_models.md
@@ -3,7 +3,8 @@
 LANfactory's [`transform_sbi_to_onnx`](api/onnx.md) wraps a trained
 [`sbi`](https://github.com/sbi-dev/sbi) estimator and writes a single-trial
 ONNX file that HSSM's `loglik_kind="approx_differentiable"` path can consume
-exactly like a LAN export. Use it to bring sbi-trained NLE density estimators
+exactly like a LAN export (the artifact rules are collected in
+[The ONNX likelihood contract](https://lnccbrown.github.io/HSSM/how_to/custom_onnx_likelihoods/)). Use it to bring sbi-trained NLE density estimators
 or NRE ratio classifiers into a [HSSM](https://github.com/lnccbrown/HSSM) model.
 
 ## Installation
diff --git a/docs/index.md b/docs/index.md
index 1a63fba..d8b34a8 100755
--- a/docs/index.md
+++ b/docs/index.md
@@ -93,7 +93,8 @@ transform-onnx --network-config-file <network_config.pickle> \
 ```
 
 The resulting file can be used directly with
-[HSSM](https://lnccbrown.github.io/HSSM/). Networks trained outside LANfactory
+[HSSM](https://lnccbrown.github.io/HSSM/) — see
+[The ONNX likelihood contract](https://lnccbrown.github.io/HSSM/how_to/custom_onnx_likelihoods/) for the artifact rules. Networks trained outside LANfactory
 can be exported the same way — see the
 [sbi](exporting_sbi_models.md) and [bayesflow](exporting_bayesflow_models.md)
 export guides.
diff --git a/docs/tutorials/exporting_bayesflow_to_onnx.ipynb b/docs/tutorials/exporting_bayesflow_to_onnx.ipynb
index 90e0818..80e96e9 100644
--- a/docs/tutorials/exporting_bayesflow_to_onnx.ipynb
+++ b/docs/tutorials/exporting_bayesflow_to_onnx.ipynb
@@ -202,8 +202,11 @@
     "\n",
     "`transform_bayesflow_to_onnx` bakes the standardizer's accumulated mean/std\n",
     "into the graph as constants (sidestepping the dynamic-shape ops the live Keras\n",
-    "layer would emit) and writes a **rank-1** single-trial graph, opset 17 — the\n",
-    "same contract as the sbi and LAN exporters, so HSSM consumes it identically."
+    "layer would emit) and writes a **rank-1** single-trial graph, opset 17. It satisfies the same\n",
+    "contract as the sbi and LAN exporters — **every input dim concrete, no dynamic\n",
+    "axes** ([canonical statement](https://lnccbrown.github.io/HSSM/how_to/custom_onnx_likelihoods/)) — though rank differs by tracer:\n",
+    "the LAN exporters emit rank-2 `(1, D)` Gemm graphs; rank-1 is required here\n",
+    "because the flow graph slices its input."
    ]
   },
   {
@@ -394,7 +397,8 @@
    "source": [
     "## 4. Consume it in HSSM\n",
     "\n",
-    "The `.onnx` file drops into HSSM exactly like a LAN or sbi export:\n",
+    "The `.onnx` file drops into HSSM exactly like a LAN or sbi export\n",
+    "(full rules: [The ONNX likelihood contract](https://lnccbrown.github.io/HSSM/how_to/custom_onnx_likelihoods/)):\n",
     "\n",
     "```python\n",
     "import jax\n",
@@ -412,7 +416,7 @@
     "```\n",
     "\n",
     "For the consumption side end to end, see HSSM's\n",
-    "[Build HSSM models starting from ONNX files](https://github.com/lnccbrown/HSSM/blob/main/docs/tutorials/blackbox_contribution_onnx_example.ipynb)\n",
+    "[Build HSSM models starting from ONNX files](https://lnccbrown.github.io/HSSM/tutorials/blackbox_contribution_onnx_example/)\n",
     "tutorial. The **NRE** path is analogous: train a `RatioApproximator` and pass\n",
     "`mode=\"nre\"` to `transform_bayesflow_to_onnx`."
    ]
diff --git a/docs/tutorials/exporting_sbi_to_onnx.ipynb b/docs/tutorials/exporting_sbi_to_onnx.ipynb
index 40c6f3c..49aff29 100644
--- a/docs/tutorials/exporting_sbi_to_onnx.ipynb
+++ b/docs/tutorials/exporting_sbi_to_onnx.ipynb
@@ -512,8 +512,10 @@
     "## 2. Export to ONNX\n",
     "\n",
     "`transform_sbi_to_onnx` wraps the trained estimator into a **rank-1**\n",
-    "single-trial graph (parameters first, observations second; opset 17). The\n",
-    "rank-1 contract is what lets HSSM `vmap` the graph over trials."
+    "single-trial graph (parameters first, observations second; opset 17). The graph is\n",
+    "rank-1 because flow/ratio graphs *slice* their input — a `(1, D)` trace bakes\n",
+    "`Slice` axes that fail under HSSM's `vmap`. The contract invariant itself is\n",
+    "**concrete dims, no dynamic axes** ([canonical statement](https://lnccbrown.github.io/HSSM/how_to/custom_onnx_likelihoods/))."
    ]
   },
   {
@@ -699,7 +701,8 @@
     "## 4. Consume it in HSSM\n",
     "\n",
     "The `.onnx` file drops into HSSM exactly like a LAN export — HSSM handles\n",
-    "the `vmap` over trials and (recent versions) the x64 flag:\n",
+    "the `vmap` over trials and (recent versions) the x64 flag —\n",
+    "the full rules are in [The ONNX likelihood contract](https://lnccbrown.github.io/HSSM/how_to/custom_onnx_likelihoods/):\n",
     "\n",
     "```python\n",
     "import jax\n",
diff --git a/src/lanfactory/onnx/jax_export.py b/src/lanfactory/onnx/jax_export.py
index 2b4f397..bfcbbda 100644
--- a/src/lanfactory/onnx/jax_export.py
+++ b/src/lanfactory/onnx/jax_export.py
@@ -5,8 +5,10 @@
 convert — ``transform-onnx`` only reads torch state dicts, and HSSM consumes
 ONNX exclusively.
 
-The export follows the ecosystem's single-trial ONNX contract (see HSSMSpine
-CLAUDE.md): the graph is traced with a **concrete** ``(1, input_dim)`` dummy
+The export follows the ecosystem's single-trial ONNX contract; the canonical
+statement lives in HSSM's docs:
+https://lnccbrown.github.io/HSSM/how_to/custom_onnx_likelihoods/
+The graph is traced with a **concrete** ``(1, input_dim)`` dummy
 and no dynamic axes, exactly like the torch MLP exporter and the production
 networks on franklab/HSSM. Every dim is static, so HSSM's load-time check
 passes, and HSSM's rank-1-per-trial + ``jax.vmap`` consumption works because
diff --git a/src/lanfactory/onnx/sbi.py b/src/lanfactory/onnx/sbi.py
index 236c8ac..3e9bfb3 100644
--- a/src/lanfactory/onnx/sbi.py
+++ b/src/lanfactory/onnx/sbi.py
@@ -9,9 +9,10 @@
 exporter): "train a network and emit an ONNX HSSM can read" stays a single
 conceptual home in LANfactory regardless of which library trained the network.
 
-The exported graph follows the LAN-and-HSSM convention: a single concatenated
-input of **rank 1, shape ``(theta_dim + x_dim,)``**. Inside the graph the
-input is split into ``theta`` and ``x``, upranked to ``(1, …)`` to satisfy
+The exported graph takes a single concatenated single-trial input of
+**rank 1, shape ``(theta_dim + x_dim,)``**. The contract invariant is concrete
+dims; rank is tracer-specific (the LAN exporters emit rank-2 ``(1, D)``
+``Gemm`` graphs). Inside the graph the input is split into ``theta`` and ``x``, upranked to ``(1, …)`` to satisfy
 sbi's batched ``log_prob`` API, and routed through the trained estimator.
 HSSM vmaps this graph over trials, so the per-call input rank from HSSM is 1
 — matching the export. Tracing with a 2D ``(1, D)`` dummy would emit ``Slice``