# NPC Reason — SFT result vs frozen baseline + PREREG (Dispatch 2, Stage 4)

NPC-Reason-SFT = R1-Distill-1.5B + LoRA (r64), distilled on **7,546 V4 chains that the FROZEN
verifier confirmed verifiable AND correct**. Evaluated on the frozen EVAL.lock (500 held-out
GSM8K+MATH), same greedy decoding as the baseline (apples-to-apples), scored by the frozen
verifier (VERIFIER.lock d5d146cf).

## Result (format-prompt = the committed comparator)

|                        | base (format) | NPC-Reason-SFT | delta   |
|------------------------|--------------:|---------------:|--------:|
| verifiable-rate        |        0.0%   |     **76.8%**  | +76.8pp |
| accuracy               |       61.6%   |     **65.8%**  |  +4.2pp |
| verified-and-correct   |        0.0%   |     **58.0%**  | +58.0pp |
| mean assertions/chain  |        0.0    |       3.44     |    —    |

Plain-prompt (native, no format instruction): verifiable 0.0%, accuracy 64.8%. The model emits
the `<<EXPR=RESULT>>` format under the format prompt it was trained on, not unprompted — expected,
and the format prompt is the committed comparator.

## PREREG verdict (committed bars, frozen b5a49437 — graded honestly)

| Criterion | Bar | Result | Verdict |
|---|---|---|---|
| 1. Primary lift (verified-and-correct over format baseline) | ≥ +15pp | **+58.0pp** | **SUPPORTED** |
| 2. Verifiable-rate | ≥ 90% | 76.8% | **NOT SUPPORTED** |
| 3. Accuracy guard (no regression > 5pp) | ≥ −5pp | **+4.2pp** (improved) | **SUPPORTED** |

**2 of 3 SUPPORTED.** The all-three gate is not met (criterion 2 missed).

## Honest read

- **The central thesis is validated, strongly.** Distilling *only mechanically-verified* teacher
  chains moved a model that produced **zero** checkable reasoning (0% verifiable, even when asked)
  to **76.8% verifiable / 58% verified-and-correct** — a +58pp jump on the headline metric, far
  past the +15pp bar. The grounding transferred.
- **Accuracy did not regress — it rose** (+4.2pp). Verifiability was not bought by sacrificing
  correctness; the strict-basis corpus improved both. (Some of the rise is reduced greedy
  repetition vs the base; attributed, not overclaimed.)
- **The one missed bar is verifiable-rate (76.8% vs 90%).** ~23% of format-prompt chains still
  fail full verification — a step that doesn't verify, doesn't compose, or the model reverts to
  prose on harder MATH items. This is exactly the gap RL-with-verifier-reward is designed to close.

## RL gate

The committed gate is: RL proceeds if SFT clears its bar **OR** produces a high verifiable-rate
so RL has signal to sharpen. All-three bar: **NOT cleared** (verifiable 76.8 < 90). High-signal
condition: **MET** — 76.8% verifiable / 58% verified-and-correct gives RL (verifier = reward, the
same frozen code) dense signal to push toward ≥90%. So the RL phase is **warranted**, entered with
eyes open that criterion 2 is the explicit target. A null at SFT would have been valid; this is not
a null — it is a large, real lift that misses one of three bars.

Frozen: `sft/SFT_RESULT.lock`. Raw per-item outputs: `eval/eval_raw.jsonl`.