log: reprint step-table header every 50 rows; related-work: Piggyback learned-mask critique

Header reprint fixes the variable-width misread trap (20+ unlabeled cols, gn
adjacent to lr). Records the anticipated Piggyback 'why not learn the routing
mask' critique (answer: no-cheat withholds the per-rollout label a learned mask
needs) and LoRA rank-deficiency as mild support for the low-rank hack subspace.

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

docs/writeup/main.tex

@@ -377,6 +377,14 @@ one-liners are in docs/grad\_routing/related\_work.md.}
         the subset from a given task label, whereas we \emph{remove} an unwanted
         capability and pick the subset from a gradient signal ($\cos$ to
         $v_{\text{hack}}$), with no per-rollout label.
+  % Anticipated critique (Piggyback learns its mask end-to-end via a differentiable
+  % real-valued threshold): why is our route gate a per-step calibrated cosine
+  % threshold rather than a learned mask? Answer for the rebuttal: a learned mask
+  % needs a per-rollout supervision signal (the task label Piggyback has); we
+  % deliberately withhold that (no-cheat invariant), so the gate must come from the
+  % unsupervised hack-vs-clean cos gap, not a trained parameter.
+  % LoRA's rank-deficiency finding is mild external support for our low-rank hack
+  % subspace (~10 pairs => rank-10).
   % \TODO{abstract-only twins to verify+place: GRIFT (gradient fingerprints,
   % arXiv:2604.16242); Spilling the Beans (OOD self-report, arXiv:2511.06626).}
 \end{itemize}

src/projected_grpo/train.py

@@ -1554,7 +1554,10 @@ def main(cfg: Config) -> int:
             "sec": time.time() - t0,
         }
         rows.append(row)
-        # Stream this step as a row (header was printed before the loop).
+        # Stream this step as a row. Reprint the header every 50 rows so long runs
+        # stay readable without scrolling back (20+ unlabeled columns, no per-row label).
+        if step > 0 and step % 50 == 0:
+            logger.info(step_logger.header())
         logger.info(step_logger.row(row))
         with rollout_log_path.open("a") as fh:
             for rec in step_rollouts: