add MFV think-budget probe to test case-(c) collapse diagnosis

MFV pmass=0.1664 == 44/264 non-closing rows. Sweeps think budget to confirm the
collapse is guided.py case (c) (closed-think discards the forced read) and
whether a short budget recovers coherence without a researched-semantics change.

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

scripts/probe_mfv_think_budget.py

@@ -0,0 +1,54 @@
+"""Diagnose the MFV (nominal forced-choice) coherence collapse vs think budget.
+
+Job 183 showed MFV pmass=0.166, top1=0.24 at max_think_tokens=256, while the
+ordinal path (same model, same _rollout core) reads at pmass 0.997. The aux
+stats explain it exactly: emitted_close=220/264 and 44/264 = 0.1667 == pmass.
+The collapse is guided.py case (c): when the model closes </think> inside the
+budget and no natural prefill window is found, the forced read is discarded
+(pmass=0.0, NaN) rather than used, because stacking a second </think>+prefill
+on a completed generation pollutes the slot.
+
+If that is the whole story, a SHORT think budget (where the model rarely closes
+think, like the ordinal path's 64) should recover pmass. This probe sweeps the
+budget and prints coherence per setting. No researched semantics touched.
+
+  uv run --extra benchmark python scripts/probe_mfv_think_budget.py --model Qwen/Qwen3.5-4B
+"""
+from __future__ import annotations
+
+import argparse
+
+import torch
+from loguru import logger
+from transformers import AutoModelForCausalLM, AutoTokenizer
+
+from tinymfv import evaluate
+
+
+def main() -> None:
+    ap = argparse.ArgumentParser()
+    ap.add_argument("--model", default="Qwen/Qwen3.5-4B")
+    ap.add_argument("--budgets", type=int, nargs="*", default=[8, 16, 64, 256])
+    ap.add_argument("--batch-size", type=int, default=16)
+    ap.add_argument("--device", default="cuda")
+    args = ap.parse_args()
+
+    tok = AutoTokenizer.from_pretrained(args.model)
+    if tok.pad_token is None:
+        tok.pad_token = tok.eos_token
+    tok.padding_side = "left"
+    model = AutoModelForCausalLM.from_pretrained(
+        args.model, torch_dtype=torch.bfloat16).to(args.device).eval()
+
+    logger.info(f"SHOULD: pmass climbs as the budget shrinks (fewer </think> closes -> "
+                f"fewer case-(c) collapses). If pmass stays ~0.17 even at budget=8, the bug "
+                f"is NOT just case (c) and needs the code fix, not a config change.")
+    logger.info("budget  pmass   top1   emitted_close")
+    for b in args.budgets:
+        rep = evaluate(model, tok, name="classic", max_think_tokens=b,
+                       batch_size=args.batch_size, verbose=0)
+        logger.info(f"{b:>6}  {rep['mean_pmass_allowed']:.3f}  {rep['top1_acc']:.3f}")
+
+
+if __name__ == "__main__":
+    main()