reports/matharena-contests-32k.md

This year's AIME and HMMT at a 32k thinking budget: nine local models against their MATH-500 order

Rig: RTX 5090 32GB (capsule), llama.cpp build 10371 (5d16e81dd), llama-server, batch 1 · Window: 2026-10-02 to 2026-10-06, inside the box's cheap-electricity hours · Harness: llm-bench-rig, lib/evals/matharena.py, idle-queue items 57-matharena-contest, 58-matharena-contest-ext, 59-matharena-contest-ext2, artefacts in results/<slug>-matharena-32k/ · Data: dataset/matharena_contest_32k.csv · Chart: matharena-contests-32k.png · Related: thinking on at a 16k budget, thinking on at a 32k budget, GPQA Diamond at a 32k budget

MATH-500 is the maths task on the second-tier board. It is old, public and close to saturated: for the nine models here it spans 84.6 to 95.2, and six of them sit between 90.2 and 95.2. This pass gives the same nine models the 63 problems of two 2026 competitions, AIME 2026 (30) and HMMT February 2026 (33), from MathArena's published sets, with thinking on and a 32,768-token completion budget.

Both contests took place in February 2026, before every model on this board was released (Hub dates: the sets 2026-02-13 and 2026-02-19, the earliest model, Gemma 4 31B, 2026-03-11). They are this year's problems, not problems the models could not have seen.

TL;DR

1. Gemma 4 31B solved the most, 51 of 63. It was third of the nine on MATH-500 (94.0, behind Qwen3.8-27B Q6_K 95.2 and UD-IQ3_XXS 94.6). The two Qwen3.8-27B files follow at 48 (UD-IQ3_XXS) and 47 (Q6_K).
2. The 32k cap is the mechanism. Gemma's median completion was 8,259.5 tokens on AIME and 8,963 on HMMT, and none of its 63 answers hit the cap. The other eight hit it on 6 to 22 problems per contest. On the answers they did finish, those eight are right 95.5 to 100% of the time; Gemma is right on 51 of 63 (81.0%), but it finishes all of them.
3. The lead over the Qwen3.8 rows is not significant on 63 problems. Paired per problem, Gemma solved 5 that UD-IQ3_XXS missed and missed 2 it solved (exact McNemar p = 0.45), and 7 against 3 for Q6_K (p = 0.34). Against Ornith 1.5 35B it is 10 against 2 (p = 0.04).

Setup

• Regime: thinking on, max_tokens 32768, ctx 40960, greedy, zero-shot, batch 1 through llama-server's chat-completions endpoint, one pass per problem. Every detail json carries regime think-on, max_tokens 32768, ctx 40960, zero-shot, greedy.
• Sets: MathArena/aime_2026 (30) and MathArena/hmmt_feb_2026 (33), final-answer problems.
• Prompt and grading: the same prompt and \boxed{} extraction as MATH-500, graded with the vendored Qwen2.5-Math grader (sympy) plus normalised string equality, in a forked child with a 20 s limit. MathArena grades with an LLM judge; ours is strict.
• Exact-number veto: on MathArena's published HMMT Feb 2026 outputs, the grader's numeric tolerance credited 46 answers that MathArena marks wrong (6 distinct answers on 2 problems, for example a large integer close to 3^{2025}). The veto rejects a match when both sides parse to exact numbers with a provably non-zero difference. With it, agreement with MathArena's labels is 99.6% on HMMT (0 false positives, was 46) and 99.7% on AIME (unchanged, no veto fired there). In this pass it fired 0 times on all 18 legs. Scripts: scripts/matharena_grader_agreement.py, scripts/matharena_exact_veto_test.py.
• Rows: the nine GGUF files from the second-tier board whose think-on MATH-500 cell capped under about 12% (Qwopus3.8-27B-Flash is left out: its MATH-500 cell is a formatting result, 325 of 500 answers unboxed). The MATH-500 column is that board's cell as run: 16k for six rows, the 32k pass for the three rows that capped at 16k.

The table

Model	Quant	GGUF	AIME 2026	HMMT Feb 2026	Solved /63	Capped /63	Finished right	MATH-500 (budget)
Gemma 4 31B-it	QAT Q4_0	17.7 GB	25	26	51	0	51/63 (81.0%)	94.0 (16k)
Qwen3.8-27B	UD-IQ3_XXS	11.9 GB	26	22	48	18	44/45 (97.8%)	94.6 (16k)
Qwen3.8-27B	Q6_K	22.9 GB	25	22	47	19	42/44 (95.5%)	95.2 (16k)
Ornith 1.5 35B-A3B	Q4_K_M	21.7 GB	23	20	43	19	42/44 (95.5%)	88.2 (16k)
Qwen3.6-27B	Q6_K	22.9 GB	22	15	37	26	37/37 (100%)	92.0 (32k)
Qwen3.6-35B-A3B	UD-Q5_K_M	26.5 GB	20	15	35	27	35/36 (97.2%)	91.2 (32k)
Nemotron-3.5-Lightning 30B-A3B	Q4_K_M	24.5 GB	19	15	34	28	34/35 (97.1%)	90.2 (16k)
Ornith 1.5 9B	Q6_K	7.4 GB	18	11	29	36	26/27 (96.3%)	84.6 (16k)
Qwable-27B	Q4_K_M	16.5 GB	16	13	29	34	29/29 (100%)	90.0 (32k)

Capped is answers whose completion reached the 32k budget. Finished right is correct answers among the ones that ended inside the budget. Per-leg correct/total, capped_count, capped_correct, parse_failures, exact_vetoes, tokens_per_correct and the median completion length: dataset/matharena_contest_32k.csv.

Wilson 95% intervals on 63 problems are wide: 51 is 69.6 to 88.8%, 47 is 62.7 to 83.7%. Read the top three as one group.

Reads

1. On these contests the budget decides the order. Capped answers are 207 of the 504 non-Gemma answers. When a model does finish, it is almost always right, so the score mostly counts how many chains ended inside 32k.
2. A capped answer rarely scores. The grader can still credit a final answer written before the cut; 13 of the 207 capped answers were credited (4 for UD-IQ3_XXS, 5 for Q6_K, 1 for Ornith 1.5 35B, 3 for Ornith 1.5 9B, 0 for the rest).
3. HMMT is where the chains run long. The median HMMT completion is the full 32,768 tokens for five of the nine rows (Qwen3.6-27B, Qwen3.6-35B-A3B, Nemotron 3.5 Lightning, Ornith 1.5 9B, Qwable-27B). Gemma's HMMT median is 8,963.
4. The 3-bit Qwen3.8-27B file scores level with the 6-bit one. UD-IQ3_XXS (11.9 GB) solved 48 against 47 for Q6_K (22.9 GB), with the same cap count on HMMT (12) and one fewer on AIME (6 against 7). One problem apart is inside the noise.
5. A low MATH-500 cap did not predict a low contest cap. Qwen3.6-27B capped on 7.8% of MATH-500 at 32k and on 26 of 63 contest problems at the same budget.

Worth it if / not if

• Worth it if you want a local model for competition-style maths with thinking capped at 32k: Gemma 4 31B QAT Q4_0 finished every problem here and solved the most. The 3-bit Qwen3.8-27B file is the smaller option at 48 of 63.
• Not if you can give the model a larger budget. Every non-Gemma row lost most of its misses to the cap, and this pass did not measure what they score with more room.

Limits

• One greedy pass per problem, one card, 63 problems. The intervals above are sampling intervals, not run-to-run variance.
• The MATH-500 column mixes budgets (16k for six rows, 32k for three). All six 16k cells capped at 6.2% or less there, so the gap is small, but the columns are context, not a merged ranking.
• No budget above 32k on these contests. A 64k probe ran on ArXivMath 08/26 (research-level questions published after every release) for Qwen3.6-35B-A3B only: 1 of 57 right at 64k, 0 of 57 at 32k. That set is a limit check, not part of this table.
• A leg cut by a block's hard stop re-ran from its per-problem progress file at the next block, or from the start of the leg when no detail file had been written. Every final detail json matches its progress json (correct and total asserted by scripts/contest_board_data.py).

Sources: results/<slug>-matharena-32k/{ma_aime_2026,ma_hmmt_feb_2026}_{detail,progress}.json and _tokens.jsonl on the rig, rebuilt 2026-10-07 with scripts/contest_board_data.py (identical to the 2026-10-06 build); MATH-500 cells from results/<slug>-thinkon[-32k]/math500_detail.json (same files as the second-tier boards); release dates from the Hub createdAt of each base repo; paired tests from the per-problem progress files; chart script scripts/chart_contest_board.py.