diff --git a/src/projected_grpo/train.py b/src/projected_grpo/train.py
index f2d6b15..e284fe3 100644
--- a/src/projected_grpo/train.py
+++ b/src/projected_grpo/train.py
@@ -165,6 +165,7 @@ class Config:
     v_hack_path: Path | None = None
     v_hack_extract_top_k: int = 12    # max k to save at extract; n_train_pairs caps it lower
     v_hack_k: int = 5                 # load-time slice; k=1 = mean-diff, k=k_max = full
+    v_hack_tau_axis: float = 0.0      # extract-time: zero axes where S_i/S_0 < tau_axis
     out_tag: str = ""                 # suffix for saved artifact, e.g. "_seed41"
     # Mixed-pool GRPO: per-prompt rollout pool = G_s live student + G_t cached
     # teacher rollouts. Teacher pool is a dir of prompt_NNNN.jsonl.gz produced by
@@ -364,8 +365,12 @@ def main(cfg: Config) -> int:
     # Slug: works for HF names ("Qwen/Qwen3-4B" -> "Qwen3-4B") and local paths
     # ("out/baked/qwen3_4b_rh25" -> "qwen3_4b_rh25").
     model_slug = model_name.rstrip("/").split("/")[-1]
+    # Filename encodes top_k AND tau_axis because both are baked into the saved
+    # V (extract zeros rows where S_i/S_0 < tau_axis before saving). If a future
+    # ablation varies pairs.py, add a pairs hash here too.
+    tau_tag = f"_tau{cfg.v_hack_tau_axis:g}" if cfg.v_hack_tau_axis > 0 else ""
     if cfg.v_hack_path is None:
-        v_hack_path = OUT_DIR / f"v_hack_{model_slug}_k{cfg.v_hack_extract_top_k}.safetensors"
+        v_hack_path = OUT_DIR / f"v_hack_{model_slug}_k{cfg.v_hack_extract_top_k}{tau_tag}.safetensors"
     else:
         v_hack_path = cfg.v_hack_path
     if not v_hack_path.exists():
@@ -376,14 +381,14 @@ def main(cfg: Config) -> int:
         model.eval()  # match standalone extract: deterministic backward, no dropout
         v_hack_cpu_dict, raw_grads, _diag = extract_v_hack(
             model, tok, wrappers, VHACK_PAIRS,
-            top_k=cfg.v_hack_extract_top_k, tau_axis=0.0,
+            top_k=cfg.v_hack_extract_top_k, tau_axis=cfg.v_hack_tau_axis,
             n_heldout=2, device=device,
         )
         OUT_DIR.mkdir(exist_ok=True)
         save_file(v_hack_cpu_dict, str(v_hack_path),
                   metadata={"model": model_name, "dtype": "bf16",
                             "top_k": str(min(cfg.v_hack_extract_top_k, len(VHACK_PAIRS) - 2)),
-                            "tau_axis": "0.0", "schema": "v2_with_sv"})
+                            "tau_axis": str(cfg.v_hack_tau_axis), "schema": "v2_with_sv"})
         # extract zeros grads at exit; opt is built below so no opt-state taint.
         model.train()  # restore train mode; eval was set only for the extract pass
     v_hack_cpu = load_v_hack(v_hack_path, model_name, wrappers, k_use=cfg.v_hack_k)