docs: tighten reward section into table

docs/writeup.md

@@ -38,28 +38,17 @@ Each episode: the environment samples random parameters and initial conditions,
 
 ## Reward Design
 
-Five components are summed per rollout. All are computed from `scipy.odeint` output — no model-in-the-loop scoring.
+All reward is computed from `scipy.odeint` output — no model-in-the-loop scoring. Five components are summed per rollout:
 
-### `reward_match` — R² (coefficient of determination)
-The primary signal. Compares the agent's simulated trajectory against the observed one using R². R² = 1 means perfect fit; R² = 0 means no better than predicting the mean. This is a continuous, differentiable signal that gives GRPO a smooth gradient to follow.
+**R²** (coefficient of determination) measures trajectory fit: R² = 1 is a perfect match, R² = 0 is no better than predicting the mean, R² < 0 is actively wrong.
 
-### `reward_match_dense` — √R²
-R² is near-zero for most early rollouts, making the gradient vanishingly small. Taking the square root stretches the low end of the range: `√0.05 ≈ 0.22` instead of `0.05`. This gives GRPO a non-trivial gradient even when the model is far from the right equation, speeding up early learning.
-
-### `reward_correctness` — binary cliff at R² ≥ 0.70
-A binary 0/1 bonus that fires when the trajectory is "good enough". This creates a sharp cliff in reward space that the policy is incentivised to climb. In practice it helps push past local plateaus where `match` and `match_dense` flatten out — the model learns to specifically target the 0.70 threshold rather than settling for partial credit.
-
-### `reward_simplicity` — prefer shorter equations
-Computed as `1 − (operator_count / 12)`. Shorter equations that explain the data are physically preferable to long, overfit ones. **Gated on R² ≥ 0.10** — if the equation is wrong, simplicity doesn't score. Without this gate the model would learn to output `d2y/dt2 = 0` (zero operators, simplicity = 1) and farm 20% reward for a completely wrong trajectory.
-
-### `reward_format` — syntactic and numerical validity
-1.0 only if the output (a) parses against the whitelisted ODE grammar, **and** (b) `odeint` integrates it to completion without NaN or overflow. Without the NaN check, a valid-looking but explosive equation like `d2y/dt2 = exp(vy**10)` would earn format reward despite being physically nonsense.
-
----
-
-### Why these five together
-
-The three correctness-shaped signals (`match`, `match_dense`, `correctness`) dominate the GRPO advantage, ensuring physical accuracy drives the gradient. `simplicity` prevents equation bloat. `format` ensures the output is always usable by the verifier. Together they make reward hacking significantly harder than any single signal would.
+| Component | Formula | What it rewards | Why it's needed |
+|-----------|---------|-----------------|-----------------|
+| `match` | R² | Continuous fit quality | Primary learning signal |
+| `match_dense` | √R² | Same, stretched | R² ≈ 0 early on; √R² gives a non-zero gradient (√0.05 ≈ 0.22) so GRPO isn't blind in early steps |
+| `correctness` | 1 if R² ≥ 0.70 else 0 | Binary "good enough" | Creates a cliff the policy actively climbs; helps escape plateaus where the dense signal flattens |
+| `simplicity` | 1 − operators/12, gated on R² ≥ 0.10 | Shorter equations | Without the gate, `d2y/dt2 = 0` scores simplicity = 1 for free despite being completely wrong |
+| `format` | 1 if parses **and** `odeint` succeeds without NaN | Valid, simulatable output | Without the NaN check, explosive equations like `exp(vy**10)` parse successfully and claim format reward |
 
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