RLTasksby ulam.ai
Sign inAll tasks
Mathematics5Math-10

5Math-10

A five-environment mathematics benchmark for extreme adaptive identification: each expert episode hides one system among 32,768 candidates and permits only two noisy measurements. Its worlds range from thermodynamic dynamics and cluster wall crossing to entropy solutions, planar algebras, and non-Shannon information geometry, demanding complementary experiment planning, sharp posterior inference, and sealed transfer.

MathematicsAdaptive reasoningRLVR
Version1.0.0
Environments5
RewardScalar · 0–1
DeliveryPrivate ZIP
01 Task contract

A real, versioned RL environment.

A five-environment mathematics benchmark for extreme adaptive identification: each expert episode hides one system among 32,768 candidates and permits only two noisy measurements. Its worlds range from thermodynamic dynamics and cluster wall crossing to entropy solutions, planar algebras, and non-Shannon information geometry, demanding complementary experiment planning, sharp posterior inference, and sealed transfer.

Agent objective

  • Interact with the supplied stateful environment.
  • Produce verifier-checkable actions or artifacts.
  • Maximise scalar reward under the package contract.

Evaluation

  • 5 verifier-backed environments.
  • Reported reward range 0–1.
  • Package-specific public and private checks.

Delivery boundary

  • Private object stored in Cloudflare R2.
  • Authenticated entitlement required.
  • Short-lived signed URL per download.
02 What you will work on

Distinct environments, one demanding research contract.

Enough detail to understand the intellectual terrain; generated instances, hidden mechanisms, and solution paths remain inside the private package.

EnvironmentMathematical or technical frontierAdaptive research problem
RuelleCocycleCipherThermodynamic formalism and transfer operatorsChoose long-orbit and twisted-transfer measurements beyond common short-cylinder statistics.
ClusterScatteringOracleCluster varieties and wall crossingProbe distinct path sectors to recover noncommuting wall geometry hidden beyond low-order tropical expansion.
ShockEntropyLabyrinthConservation laws and entropy solutionsCombine shock, entropy, rarefaction, and viscous evidence to infer off-anchor flux structure.
PlanarAlgebraTangleProbeSubfactor planar algebras and tensor networksSelect phase-sensitive closed-tangle measurements despite identical modulus data and exact unitarity.
EntropyConeXRayEntropy cones and non-Shannon inequalitiesDetect high-order dependence through complementary inequalities when all lower-order marginals are uniform.
03 Why it is interesting

What the supplied evaluation reveals.

A direct five-episode expert run selected high-quality probes—0.9710 mean action quality and 0.9487 experiment-design score—yet achieved 0.5007 mean reward, no exact identifications, and no passes. This is a useful extreme frontier: good local measurements are insufficient to resolve a 15-bit posterior in two calls. The audit also documents prompt-likelihood limitations rather than hiding them; the release passed 32/32 tests.

We publish aggregate behavior and task structure, while withholding generated instances, hidden labels, exact successful probes, private checks, and solution trajectories.

04 Supplied evaluation

Observed evaluation result.

Shown with its provenance and limitations; it is not a performance guarantee.

i
Methodology matters

Reported result from the evaluation artifact supplied with this package.

Evaluated system / policyGPT-5.6 Pro-assisted evaluation

As identified by the supplied artifact.

Mean reward0.5007

5 reported runs.

Result artifactIncluded

direct_selftest_audit_bundle.zip:direct_selftest_report.md

Public result record

Machine-readable provenance and the exact displayed metric are available in results.json.

Open result JSON
05 Private delivery

The package stays off the public website.

The paid ZIP will live in a private R2 bucket. Vercel authorizes the buyer and issues a 2–5 minute object URL; R2 serves the bytes directly.

Included with purchase

  • Exact package version 1.0.0
  • Environment and task contracts
  • Verifier or scoring interface
  • Supplied reference/evaluation artifacts
  • Purchase record and licence v1.1
delivery flow
Authenticated buyer + entitlement check
+ private R2 object + 2–5 minute signed URL
= direct, auditable download

Package SHA-256
717aad4d87e90b78767192cad6d21504dd78b1a67677472490fcde00fe99eae4
06 Licence v1.1

Commercial use, without exclusivity.

One purchase licenses this identified item to one legal organisation for worldwide, perpetual commercial model training, evaluation, research and development. Redistribution and resale of the package are not permitted.

Read the full licenceYotta Content LTD · business customers only
5Math-10

Ready to add this environment?

Back to marketplace
Stripe checkout

Business purchase confirmation

Sign in or create an account, then complete secure Stripe Checkout. Access is granted only by the verified payment webhook.