RLTasksby ulam.ai
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Mathematics5Math-Hard-10

5Math-Hard-10

A five-environment frontier suite with 16,384 hidden hypotheses and only two compressed measurements. It spans automorphic forms, Morse continuation, symplectic phase retrieval, scattering amplitudes, and convex integral geometry. Every signal sits beyond an exact invariant quotient, forcing complementary experiments, enormous-posterior reasoning, and confident transfer to disjoint sealed mathematics.

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

A real, versioned RL environment.

A five-environment frontier suite with 16,384 hidden hypotheses and only two compressed measurements. It spans automorphic forms, Morse continuation, symplectic phase retrieval, scattering amplitudes, and convex integral geometry. Every signal sits beyond an exact invariant quotient, forcing complementary experiments, enormous-posterior reasoning, and confident transfer to disjoint sealed mathematics.

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
HeckeEigenpacketCipherAutomorphic forms and Hecke analysisChoose arithmetic probes with complementary phase and Fourier nullspaces beyond a shared low-coefficient panel.
MorseContinuationProbeMorse/Floer continuationInfer global flow and continuation structure although every critical point has identical local data.
MetaplecticPauliProbeSymplectic tomography and phase retrievalRecover relative phase geometry when every candidate shares the same position-basis probabilities.
AmplitudeResidueCipherScattering amplitudes and positive geometryDiagnose off-shell contact structure despite identical poles, residues, factorization, and soft limits.
ConvexValuationXRayMixed volumes and integral geometryIdentify an ordered rotation through marked measurements beyond all shared rotation-invariant geometry.
03 Why it is interesting

What the supplied evaluation reveals.

A non-oracle exact-Bayes control averaged 0.6461 over 20 fresh expert cases and passed none, despite 0.8869 experiment design. It identified only four systems and assigned the truth 11.65% mean probability. All five oracle-assisted reachability fixtures replayed and the release passed 32/32 tests, so the result characterizes the severe 16,384-way two-probe bottleneck rather than an unreachable verifier.

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 reward0.6827

20 reported runs.

Result artifactIncluded

ulam_rlvr_greedy_scores_200_203.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
41bea6bc8db562c9a1e57a23c15e77439f92ea70279e1ce42fd6cae518dc2cce
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-10

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