diag: count zero-variance-skipped GRPO groups per step (zerovar=)

Tests the post-saturation collapse mechanism for vanilla long runs: as a
loophole saturates, every rollout in a group hacks -> identical reward ->
group hits the Dr.GRPO zero-variance skip -> no learning signal. Prediction:
zerovar climbs toward max right as lp_s starts collapsing (~step 80 in job 85).
Surfaced on the existing per-step diag debug line, not the streaming table.

Co-Authored-By: Claudypoo <288921227+claudypoo@users.noreply.github.com>

src/projected_grpo/train.py

@@ -760,6 +760,9 @@ def main(cfg: Config) -> int:
         step_mode_hacks: dict[str, int] = {}  # THIS step's student hacks per mode (the hk_<mode> columns; reset each step so they don't grow)
         agg_logp: list[float] = []  # per-rollout mean per-token gen_logp (student's logp on rollout tokens)
         agg_comp_lens, agg_finished, n_skipped = [], [], 0
+        n_zerovar = 0  # groups skipped for zero reward variance (all rollouts same reward).
+        # Rises as a loophole saturates: every rollout hacks -> identical reward -> no
+        # GRPO signal. Tracks the post-saturation signal-sparsity that drives lp_s collapse.
         agg_loss = 0.0
         diag_tail = None
         # Per-source grad accumulators: each prompt's backward is split into
@@ -1054,6 +1057,7 @@ def main(cfg: Config) -> int:
                 # (extended above at line 770). Skipping the logπ_old forward
                 # here is the whole point of the zero-variance bail.
                 agg_logp.extend([float("nan")] * len(rs))
+                n_zerovar += 1
                 continue
             A = rewards - rewards.mean()                  # advantage; Dr.GRPO unbiased: no /σ_R
             if not cfg.unbiased:
@@ -1476,7 +1480,8 @@ def main(cfg: Config) -> int:
             f"clipped(no-eos)={n_clipped}/{n_rollouts}  "
             f"comp_lens(min/mean/max)={_min_len}/{_mean_len:.0f}/{_max_len}  "
             f"max_new={max_new}  fmt={sum(agg_fmt)}/{n_rollouts}  gt={sum(agg_gt)}/{n_rollouts}  "
-            f"hack={sum(agg_hack)}/{n_rollouts}  skipped={n_skipped}/{prompts_per_step}"
+            f"hack={sum(agg_hack)}/{n_rollouts}  skipped={n_skipped}/{prompts_per_step}  "
+            f"zerovar={n_zerovar}/{prompts_per_step}"
         )
         _tstep = time.time() - t0
         logger.debug(