RLTasksby ulam.ai
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Mathematics5Math-Hard-2

5Math-Hard-2

Five advanced mathematics environments built around adaptive inference from deliberately non-identifying evidence. Across arithmetic representations, optimal stopping, free probability, oriented matroids, and filtered homological algebra, agents face 128 shuffled hypotheses and at most two noisy measurements, rewarding complementary probes, calibrated uncertainty, and transfer to unseen conditions.

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

A real, versioned RL environment.

Five advanced mathematics environments built around adaptive inference from deliberately non-identifying evidence. Across arithmetic representations, optimal stopping, free probability, oriented matroids, and filtered homological algebra, agents face 128 shuffled hypotheses and at most two noisy measurements, rewarding complementary probes, calibrated uncertainty, and transfer to unseen conditions.

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
FrobeniusCipherFinite representations and Frobenius actionsSelect primes and noncommutative readouts whose activation patterns jointly reveal hidden arithmetic twists.
SnellEnvelopeOptimal stopping and Bellman free boundariesCombine value and policy-boundary evidence when similar values conceal different stop/continue mechanisms.
FreeMomentProbeFree probability and mixed operator momentsRecover relative eigenbases through mixed words although every marginal spectrum and pure moment agrees.
ChirotopeCipherOriented matroids and Plücker geometryChoose sign-sensitive geometric measurements when Gram magnitudes and the underlying unoriented matroid reveal nothing.
SpectralSequenceXRayFiltered complexes and extension dataPair filtration-sensitive probes with analytic operators while all associated-graded and homological invariants agree.
03 Why it is interesting

What the supplied evaluation reveals.

A task-adaptive exact-Bayesian policy averaged 0.7881 on 60 fresh expert episodes, identifying 33 systems and passing 19. A one-hot submission raised formal passes to 29 but reduced mean reward when confidently wrong, exposing a useful calibration-versus-commitment tradeoff. FrobeniusCipher passed 10/12 while two families passed none under calibrated submission. The package passed 47/47 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

The report identifies this as a source-informed or executable-policy result, not a clean black-box benchmark.

Evaluated system / policyGPT-5.6 Pro-assisted evaluation

As identified by the supplied artifact.

Mean reward0.7342

60 reported runs.

Result artifactIncluded

ulam_rlvr_scores.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
f4a0845fddb6827ca1063ad29a58c61aa241e9beeee2b3edadebce8c26fe4d37
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-2

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