RLTasksby ulam.ai
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Mathematics5Math-6

5Math-6

Five research-tier mathematical investigations built around hidden systems with deceptively identical public invariants. Across cellular sheaves, non-normal dynamics, algebraic geometry, quantum channels, and tensor orbits, agents must spend a severe measurement budget, distinguish competing mechanisms, calibrate their posterior, and generalize beyond chosen probes.

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

A real, versioned RL environment.

Five research-tier mathematical investigations built around hidden systems with deceptively identical public invariants. Across cellular sheaves, non-normal dynamics, algebraic geometry, quantum channels, and tensor orbits, agents must spend a severe measurement budget, distinguish competing mechanisms, calibrate their posterior, and generalize beyond chosen probes.

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
SheafGaugeCellular sheaves, holonomy, graph diffusionChoose signed, energetic, cycle, and spectral probes that cut across overlapping aliases in a sheaf-valued system.
KoopmanMirageNon-normal operators, resolvents, pseudospectraDiagnose dynamics with shared eigenvalues using finite-time, transient, resolvent, and Hankel measurements.
IdealNavigatorFinite-field algebraic geometryInfer a hidden polynomial transformation from two compressed algebraic probes, then transfer it to unseen polynomials.
QuantumProcessLensQuantum channels and compressed tomographySeparate ordered coherent and stochastic effects through phase-sensitive, nonlinear measurements under incomplete tomography.
TensorOrbitTensor invariant theory and group actionsRecover orbit coordinates when standard norms and spectra are invariant, using contractions that retain sign and order.
03 Why it is interesting

What the supplied evaluation reveals.

A public-prompt Bayesian controller earned 0.8213 mean reward across 40 expert episodes but only 17 strict passes. Held-out prediction averaged 0.9326 while correct identification reached 62.5%, revealing the intended gap between locally good experiments and sufficiently concentrated inference. The package's exact-likelihood reference itself passed only 67/200 expert cases; the release records 61/61 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 reward0.8213

8 reported runs.

Result artifactIncluded

ulam_rlvr_score_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
84977548ec9ebf5bc456419d633b0502c195963a5dea0b9ba6418c82f71fefdf
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-6

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