RLTasksby ulam.ai
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Mathematics5Math-Hard-6

5Math-Hard-6

Five mathematical system-identification environments with 2,048 hypotheses and only two noisy measurements. From hyperbolic geometry and graph limits to inverse scattering, conformal bootstrap, and mean-field games, every candidate shares substantial exact invariants, so success depends on a complementary probe pair and a sharply calibrated posterior that transfers to sealed functionals.

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

A real, versioned RL environment.

Five mathematical system-identification environments with 2,048 hypotheses and only two noisy measurements. From hyperbolic geometry and graph limits to inverse scattering, conformal bootstrap, and mean-field games, every candidate shares substantial exact invariants, so success depends on a complementary probe pair and a sharply calibrated posterior that transfers to sealed functionals.

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
TeichmullerEchoMarked hyperbolic and Teichmüller geometrySelect marked functionals probing complementary deformations hidden by identical individual lengths and traces.
GraphonGaugeGraph limits and compact operatorsRecover a hidden spectral frame through marked statistics beyond shared spectra and unmarked cycle densities.
SolitonScatteringCipherToda inverse scatteringInfer norming and collision structure behind a fixed spectrum using complementary times and spectral locations.
BootstrapFunctionalXRayConformal bootstrapProbe off-anchor crossing behavior beyond a complete shared low-order crossing jet.
MeanFieldMasterProbeNonlinear mean-field gamesCoordinate path, equilibrium-residual, and curvature measurements to reveal mechanisms absent from linearization.
03 Why it is interesting

What the supplied evaluation reveals.

A two-stage exact-likelihood planner averaged 0.7619 over 25 fresh expert episodes and passed three with its calibrated posterior. More aggressive confidence-gated and one-hot submissions raised pass counts but reduced average reward, exposing the cost of false certainty. The planner beat the same-seed greedy control by 6.2 reward points. These are simulator-control scores, not a raw model rollout; the release passed 51/51 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 reward0.7619

See the source methodology.

Result artifactIncluded

mahlo_passplanner_fresh_results.json

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
e6d0f7d125514ce4ee996bd844187c2eb6fd60a38919745767574bf12621d2a3
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-Hard-6

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