spec: fold external-review into pair-routing plan; default teacher_off_step=30

External review (Claude + deepseek-v4-pro) converged on the threshold being
circular (c_rej>c_cho holds by construction since vec=mean(g_rej-g_cho)) plus
scale-mismatched to live rollouts. Decisions added: leave-one-pair-out as the
real vec-generalizes diagnostic; quantile-tau to match flagged fraction in the
real-vs-random control; route the vec-component (erase-style) not the whole
rollout; degeneracy diagnostic (hkgap collapse); pre-register the science UAT
(n>=3 seeds, effect>random-baseline std).

teacher_off_step now defaults to 30 on the base Config so every arm runs pure
on-policy past step 30 (apples-to-apples deploy numbers; job 87 showed hacking
self-sustains after the cut).

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

docs/reviews/20260606_pairroute_review_deepseek.md

@@ -0,0 +1,37 @@
+```
+## Scientist Review
+
+### Central assumption
+The pair-derived gradient difference `vec` captures a universal hack-ward direction that separates hack from clean rollouts for unseen hack B.  
+**holds when:** the hack behavior shares a low-dimensional gradient signature across hack variants, and the pairs (A) faithfully sample that signature.  
+**fails when:** the vec overfits to superficial pair artifacts (e.g., phrasing, sequence length) that do not transfer to B; or the live cos separation is so weak that the random baseline produces similar suppression due to chance, yielding a false‑null (underpowered comparison).
+
+### Confounds
+1. **Overfitted threshold** – τ is computed as the midpoint of `cos` on the *same* pairs used to extract `vec`. This inflates the pair separation (`c_rej − c_cho`) and may not reflect live distributions, causing the gate to flag an inappropriate fraction of rollouts.  
+   → **Control:** leave‑one‑pair‑out τ (or use a separate calibration set), and ablate τ sensitivity via a sweep.
+
+2. **Differential flagged fraction** – Real and random `vec` may produce different fractions of flagged rollouts (due to distribution shapes), and the suppression difference might be driven by the amount of quarantined gradient updates, not directional accuracy.  
+   → **Control:** match the flagged fraction between real and random conditions (adjust threshold quantile), or compute suppression as a function of fraction.
+
+3. **Pair gradient drift / degenerate `vec`** – As the model is updated by routing, the hack‑completion gradients may weaken, making the refreshed `vec` degenerate or misleading.  
+   → **Control:** monitor `c_rej − c_cho` over time; if it collapses, freeze a pre‑routing snapshot for `vec` extraction or use an auxiliary model.
+
+### Algorithm issues
+- **`What we do INSTEAD`/pair‑calibrated τ:** using the same data (`g_rej[p]`, `g_cho[p]`) both to build `vec` and to calibrate τ yields an optimistic threshold; this breaks the assumption that τ separates live rollouts (overfitting). The correction is to at least apply a hold‑out within pairs or cross‑validate.
+- **Gradient direction computation:** `vec = unit(mean_p Δ[p])` – if `Δ[p]` stems from full‑parameter gradients, SVD top‑k is called but not specified in the pseudocode. Ensure that the shape after SVD reduction matches the per‑rollout `g_b` (the gate hook gradient) to avoid silent misalignment.
+- **No missing stop‑gradients** – the discrete `cos_b > τ` branch does not bleed gradients; routing is sound.
+
+### Experimental design
+- **Falsifiable:** Yes – the real‑vec > random‑vec suppression claim on B is testable.  
+- **n needed:** At least 5–10 independent seeds per condition (real/random) to detect a practical difference; single‑run comparisons are insufficient due to variance in hack‑rate metrics.  
+- **UAT gap:** The science UAT (“random‑vec does NOT suppress B as well as real‑vec”) lacks a statistical criterion – pre‑registration of an effect‑size threshold (e.g., difference in mean B‑solve rate > 2σ of the random baseline distribution) is necessary to avoid post‑hoc interpretation.
+
+### Section verdicts
+- **What we do INSTEAD (pair‑routed):** sound in concept, but τ calibration introduces overfitting that must be mitigated.
+- **Fork to decide (gradients vs activations):** reasonable investigation; gradients preserve the intervention thesis despite noise.
+- **Calibration risk to smoke‑test first:** essential sanity check, but not a full control—leave‑one‑pair‑out or external calibration needed.
+- **Smoke + UAT:** insufficiently specified for the science UAT; needs pre‑committed statistical success criterion and number of runs.
+
+### Single most important fix
+Replace the overfitted pair‑midpoint τ with a calibration procedure that does not reuse the exact pair data used to build `vec` (e.g., leave‑one‑pair‑out τ, or a quantile on a held‑out fraction of pairs, or calibrate on a set of clean/hack rollouts from a model variant not used for vec extraction). Without this, the threshold’s validity for live rollouts is unproven, and the real‑vs‑random comparison remains confounded by mis‑calibration.
+```