RLTasksby ulam.ai
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Mathematics5Math-Hard-5

5Math-Hard-5

Five mathematical system-identification environments with an extreme information bottleneck: two priced measurements must resolve a calibrated posterior over 1,024 hidden systems. From renormalization and p-adic dynamics to noncommutative geometry, spin glasses, and information geometry, obvious low-order invariants are identical and sealed transfer matters as much as identification.

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 an extreme information bottleneck: two priced measurements must resolve a calibrated posterior over 1,024 hidden systems. From renormalization and p-adic dynamics to noncommutative geometry, spin glasses, and information geometry, obvious low-order invariants are identical and sealed transfer matters as much as identification.

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
RenormalizationCartographerWilsonian flows and operator mixingDistinguish universality structure beyond a shared fixed point, Jacobian, and critical spectrum.
PAdicTelescopep-adic dynamics and Hensel liftingProbe precision, residue, iterate, and character choices to recover behavior aliased at low precision.
SpectralTripleProbeFinite noncommutative geometryRecover an ordered representation frame although Dirac spectra, heat traces, and spectral actions agree.
SpinGlassGaugeTAP and spin-glass gauge geometryMove beyond zero-field linearization using fields, cavity effects, response statistics, and stability directions.
AmariHolonomyHigher-order information geometryUse higher divergences, curvature, and holonomy beyond identical Fisher and third-order local tensors.
03 Why it is interesting

What the supplied evaluation reveals.

Across 240 expert control episodes, even the strongest myopic exact-Bayes policy passed 0/60 despite 0.7465 mean reward, 0.9020 experiment design, and 0.9041 held-out prediction. Five oracle-selected fixtures pass, establishing reachability while preserving the extreme two-measurement bottleneck. The package passed 51/51 tests and a 20-case, 1,024-candidate generation audit.

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 reward0.2868

12 reported runs.

Result artifactIncluded

ulam_score_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
cab9c4af16f0959d34ca4ec8746d9fd201a7a75bf5a743a850f6499e526cd824
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-5

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