What was measured. The complete probability distribution of the model's answer to the prompt "Pick a number between 10 and 30", computed as a best-first search over the model's own next-token probabilities — not sampling. Qwen3.8-27B-FP8 served by vLLM, 248,320-token vocab; each prefix expansion is one greedy decode step that returns the top-300 next-token logprobs (top-100 kept as children, per-node mass coverage ~99.5%).
Traversal. Starting from the prompt, a priority queue (Dial bucket queue, one decade per bucket, pointer only descends) always expands the highest-mass unexpanded prefix next. Every node carries its cumulative log-probability (sum of per-token logprobs along the path), so mass is exact up to top-100 truncation, which is booked into "dropped tail". 225,035 prefix expansions were performed; mass conservation was verified to float precision (total = 1.000000009).
Early stops (absorption). The moment a branch produces its first number, expansion of that branch stops: exactly one number in 10–30 → valid answer for that number; one number out of range → OUT_OF_RANGE (this kills degenerate digit-repeats like "1111…" in one step); a 15-token lookahead then checks for a second number → MULTIPLE_NUMBERS; no number at the 100-token cap → LEN_EXCEEDED. The active frontier therefore only ever contains "no-number-yet" prefixes, which self-limits its total mass.
Criteria. Strict: exactly one number token-sequence in the answer text, value 10–30. The model re-quoting your range ("between 10 and 30, I pick 17") counts as MULTIPLE_NUMBERS.
Result. 49.9% of total probability mass is a valid single in-range number; within that: 23 = 29.8%, 17 = 24.0%, 21 = 10.5%, 22 = 6.3%, 20 = 5.2%, 25 = 5.1%, 24 = 3.1%, 27 = 1.4%, 15 = 1.0%, rest <0.2% each (Panel 1, sums to 100%). Panel 2 is the full mass ledger: 21.7% MULTIPLE_NUMBERS (dominated by the range re-quote), 3.1% out-of-range, 0.8% dropped tail, 24.5% frontier not yet expanded. The run stopped at a crash (a unicode-digit tokenizer token
23²; fixed and relaunched as v6 targeting 1% unexplored), but the answer bars had been stable to <0.1pp for 90 minutes, so Panel 1 is settled; the remaining frontier feeds the long tail and MULTIPLE, not the top.Cross-validation note. Your 100 samples at temperature 1.0 put 17 at 61% — that's sampling noise (±8pp at n=100); the full-distribution walk shows the true mass is split 23/17 as near-twins, with 23 slightly ahead.