ModelSpec is an analysis of alternatives for AI models: it decides which models fit a job from your requirements, sourced benchmarks and real cost, and shows its work.

Maths and proofs

Find a text model with the strongest evidence on mathematical problems and proofs.

Worked example as of 2026-09-23, from the public data image.

Strongest maths evidence, cost no object.

Requirements

model.class = text-generator: The answer must be generated as mathematical text or a proof.

Preferences

maths: Rank only by the maths capability estimate.

Applied template spec

spec_version

where

model.class = text-generator

optimize

weights

maths: 1.0

Worked answer

Decision status: partial.

Tied on the evidence

openai/gpt-6-astra
openai/gpt-6-sol

probability bands: a model joins the leader when P(its score >= the leader's) >= 0.25 under the score posteriors; a weighted capability with an 80% interval wider than 2.8 is not enough evidence

Tie-breakers describe members of the tie. They do not establish a winner.

Cheapest tie-breaker: openai/gpt-6-sol
Most independently measured tie-breaker: openai/gpt-6-astra

This is a partial answer. Unknown facts or missing objective evidence can leave eligible candidates unranked.

probability bands: a model joins the leader when P(its score >= the leader's) >= 0.25 under the score posteriors; a weighted capability with an 80% interval wider than 2.8 is not enough evidence

Score and score interval use the objective's dimensionless normalised units. Cost per task is for the engine-selected offering and the applied spec's task size. When task size is omitted, the engine uses its documented default. P(best) is the engine probability. Unavailable means the engine did not return a value. Thin evidence is undetermined and is not a recommendation.

Best band

Model	Score	Score interval	P(best)	Cost per task, USD	Capability estimates and intervals
`openai/gpt-6-astra`	1.0	[0.747794, 1.252206]	0.2489	0.6	maths: 1.561674136; interval [0.843459177, 2.279889095]; benchmarks 5; direct benchmarks 2
`openai/gpt-6-sol`	0.836582	[0.496071, 1.177094]	0.1208	0.12	maths: 1.096304173; interval [0.126618298, 2.065990048]; benchmarks 2; direct benchmarks 1

Rest band

Model	Score	Score interval	P(best)	Cost per task, USD	Capability estimates and intervals
`openai/gpt-5-4`	0.776654	[0.523558, 1.02975]	0.041	0.16	maths: 0.925643173; interval [0.204892258, 1.646394088]; benchmarks 5; direct benchmarks 2
`openai/gpt-5-6-sol`	0.773894	[0.431217, 1.11657]	0.0819	0.24	maths: 0.917782921; interval [-0.058069444, 1.893635285]; benchmarks 3; direct benchmarks 1
`anthropic/claude-fable-5`	0.74706	[0.397852, 1.096269]	0.0714	0.6	maths: 0.841368906; interval [-0.153084238, 1.83582205]; benchmarks 3; direct benchmarks 1
`anthropic/claude-opus-5`	0.711502	[0.372092, 1.050913]	0.052	0.3	maths: 0.740109404; interval [-0.226442817, 1.706661626]; benchmarks 3; direct benchmarks 1
`google/gemma-4-31b-it`	0.710848	[0.354875, 1.066821]	0.0587	Unavailable	maths: 0.738245786; interval [-0.275470144, 1.751961715]; benchmarks 2; direct benchmarks 1
`anthropic/claude-opus-5-5`	0.657078	[0.331425, 0.982731]	0.0302	0.24	maths: 0.585121901; interval [-0.3422515, 1.512495301]; benchmarks 5; direct benchmarks 2
`google/gemma-4-26b-a4b-it`	0.648495	[0.292522, 1.004467]	0.0378	Unavailable	maths: 0.560680002; interval [-0.453035927, 1.574395932]; benchmarks 2; direct benchmarks 1
`anthropic/claude-fable-5-1`	0.576136	[0.335907, 0.816366]	0.0033	0.6	maths: 0.354621934; interval [-0.329488136, 1.038732003]; benchmarks 6; direct benchmarks 2
`google/gemini-3-1-pro-preview`	0.489414	[0.236318, 0.742511]	0.0014	0.128	maths: 0.10766147; interval [-0.613089445, 0.828412385]; benchmarks 5; direct benchmarks 2
`google/gemini-3-7-flash`	0.445149	[0.110308, 0.77999]	0.005	0.045	maths: -0.018394566; interval [-0.971933015, 0.935143883]; benchmarks 3; direct benchmarks 1
`moonshot/kimi-k3`	0.440324	[0.183718, 0.69693]	0.0008	Unavailable	maths: -0.032135085; interval [-0.762881535, 0.698611364]; benchmarks 4; direct benchmarks 2
`anthropic/claude-opus-4-6`	0.420098	[0.167002, 0.673194]	0.0005	0.3	maths: -0.089733789; interval [-0.810484704, 0.631017127]; benchmarks 5; direct benchmarks 2
`zhipu/glm-5-3`	0.396513	[0.064064, 0.728962]	0.0029	0.0736	maths: -0.156897477; interval [-1.103624192, 0.789829238]; benchmarks 3; direct benchmarks 1
`anthropic/claude-opus-4-7`	0.386849	[0.133669, 0.640028]	0.0003	0.3	maths: -0.184419351; interval [-0.905407051, 0.536568349]; benchmarks 5; direct benchmarks 2
`meta/muse-spark-1-3`	0.328301	[0.002412, 0.65419]	0.0012	0.067	maths: -0.351147097; interval [-1.279192008, 0.576897813]; benchmarks 3; direct benchmarks 1
`google/gemini-3-8-flash`	0.29095	[0.045129, 0.536771]	0.0	0.045	maths: -0.457512924; interval [-1.157546025, 0.242520177]; benchmarks 5; direct benchmarks 2
`xai/grok-4-7`	0.257137	[-0.083374, 0.597648]	0.0007	0.104	maths: -0.553802871; interval [-1.523488746, 0.415883004]; benchmarks 2; direct benchmarks 1
`google/gemini-3-5-flash`	0.25661	[-0.003379, 0.516598]	0.0	0.096	maths: -0.555304745; interval [-1.295683765, 0.185074274]; benchmarks 4; direct benchmarks 2
`moonshot/kimi-k2-6`	0.256027	[-0.003962, 0.516016]	0.0	Unavailable	maths: -0.556964019; interval [-1.297343038, 0.183415001]; benchmarks 4; direct benchmarks 2
`google/gemma-4-e4b-it`	0.221605	[-0.151979, 0.595189]	0.0011	Unavailable	maths: -0.654988816; interval [-1.718857134, 0.408879502]; benchmarks 1; direct benchmarks 1
`deepseek/deepseek-v4-pro`	0.19322	[-0.066137, 0.452576]	0.0	0.06864	maths: -0.735823404; interval [-1.474402989, 0.00275618]; benchmarks 4; direct benchmarks 2
`deepseek/deepseek-flash`	0.19176	[-0.148752, 0.532271]	0.0003	0.0168	maths: -0.739981184; interval [-1.709667059, 0.22970469]; benchmarks 4; direct benchmarks 1
`google/gemma-4-e2b-it`	0.179237	[-0.194347, 0.552821]	0.0007	Unavailable	maths: -0.775641911; interval [-1.839510228, 0.288226407]; benchmarks 1; direct benchmarks 1
`zhipu/glm-5-2`	0.071531	[-0.187644, 0.330707]	0.0	0.0736	maths: -1.082359497; interval [-1.820422979, -0.344296015]; benchmarks 4; direct benchmarks 2

Thin evidence: undetermined

Model	Score	Score interval	P(best)	Cost per task, USD	Capability estimates and intervals
`meta/muse-spark-1-1`	0.4768	[-0.225798, 1.179397]	0.1021	0.067	maths: 0.07173741; interval [-1.929073517, 2.072548336]; benchmarks 1; direct benchmarks 0
`deepseek/deepseek-v3-1`	0.410067	[-0.185733, 1.005866]	0.0511	Unavailable	maths: -0.118300498; interval [-1.814980752, 1.578379755]; benchmarks 2; direct benchmarks 0
`anthropic/claude-sonnet-5-5`	0.353488	[-0.346493, 1.053469]	0.0662	0.12	maths: -0.279421228; interval [-2.27278183, 1.713939374]; benchmarks 1; direct benchmarks 0
`google/gemini-2-5-flash`	0.222734	[-0.302595, 0.748062]	0.0113	0.022	maths: -0.651775501; interval [-2.147773284, 0.844222281]; benchmarks 3; direct benchmarks 0
`microsoft/phi-4`	0.0	[-0.5958, 0.5958]	0.0062	Unavailable	maths: -1.286061682; interval [-2.982741936, 0.410618572]; benchmarks 2; direct benchmarks 0

Unknown requirements

Some candidates may qualify. Missing facts:

maths

Engine warnings

cite_only_not_machine_verified
not_separable

Omitted result rows: models 20; offerings 23. The bands above include all ranked models.

Decision dec_388a0da2b93b9cbf4ad18d04 on public snapshot snap_745a6b4354bbc69a.

What this template teaches

Use one Must to select the right model class and one Prefer to state what best means.

The live board uses current data. Its answer can change as evidence changes.

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