RLTasksby ulam.ai
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Mathematics5Math-9

5Math-9

A five-environment research suite where advanced mathematics becomes a sequence of consequential decisions. Agents navigate higher coherence, Stokes geometry, singular learning, generalized symmetry, and mean-field games while managing noisy evidence, nuisance variables, scarce resources, and irreversible interventions; success requires calibrated beliefs and sealed prediction, not merely naming the right concept.

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

A real, versioned RL environment.

A five-environment research suite where advanced mathematics becomes a sequence of consequential decisions. Agents navigate higher coherence, Stokes geometry, singular learning, generalized symmetry, and mean-field games while managing noisy evidence, nuisance variables, scarce resources, and irreversible interventions; success requires calibrated beliefs and sealed prediction, not merely naming the right concept.

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
HigherCoherenceLabWeak 2-categories and higher coherenceReconstruct interacting coherence evidence while deciding when localization and strictification claims are justified.
RiemannHilbertStokesLabIrregular singularities and Stokes geometryChoose contour coordinates and deformations while avoiding irreversible crossings that destroy later diagnostics.
SingularLearningGeometryLabSingular statistics and resolution geometrySelect a chart, separate non-identifiability from singularity, and judge whether symmetry breaking clarifies or biases inference.
GeneralizedSymmetryAnomalyLabHigher symmetries, anomalies, topological phasesAllocate manifold and defect probes before irreversible gauging or condensation and certify the anomaly mechanism.
MeanFieldMasterEquationLabMean-field games and master equationsCoordinate finite-population and measure-space probes, adaptive controls, and principled identification or abstention.
03 Why it is interesting

What the supplied evaluation reveals.

The supplied ten-episode run averaged 0.6627 with no formal passes, despite mean terminal-decision and path scores near 0.80. One episode predicted sealed behavior perfectly but failed confidence and path gates; another had near-perfect posterior and decision scores but poor prediction. These traces show why identification, forecasting, and sequential intervention are independently necessary. The release reports 132/132 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 reward0.6700

5 reported runs.

Result artifactIncluded

ulam_my_scores_and_log.zip:ulam_my_scores_summary.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
f3683756e9f51ce96c396c4fb699e42835faaf06d4d705a9e1779b891776c051
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-9

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