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Mathematics5Math-Hard-7

5Math-Hard-7

Five measurable-tier mathematics environments spanning Bridgeland wall crossing, KAM resonance, random-matrix edges, theta characteristics, and proof-net dynamics. Agents receive invariant starting evidence and only two noisy measurements, then must choose complementary probes that expose hidden geometry while maintaining calibrated uncertainty and predicting disjoint sealed functionals.

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

A real, versioned RL environment.

Five measurable-tier mathematics environments spanning Bridgeland wall crossing, KAM resonance, random-matrix edges, theta characteristics, and proof-net dynamics. Agents receive invariant starting evidence and only two noisy measurements, then must choose complementary probes that expose hidden geometry while maintaining calibrated uncertainty and predicting disjoint sealed functionals.

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
BridgelandWallCipherDerived categories and stability conditionsSelect wall- and phase-sensitive probes to recover hidden stability geometry under exact categorical invariants.
KAMResonanceAtlasKAM theory and resonant normal formsCombine resonance, splitting, and transport evidence across complementary dynamical regimes.
RandomMatrixEdgeOracleRandom matrices and edge asymptoticsDistinguish latent edge mechanisms through bulk, tail, deformation, and finite-size measurements.
ThetaCharacteristicXRayTheta functions and abelian varietiesUse phase- and characteristic-sensitive analytic identities beyond shared coarse geometric summaries.
ProofNetGoIProbeLinear logic and Geometry of InteractionProbe execution and path geometry to separate proof structures that share ordinary correctness summaries.
03 Why it is interesting

What the supplied evaluation reveals.

The packaged 80-episode control sweep found no strict passes. Its strongest exact-likelihood greedy policy still achieved 0.7336 mean reward, 0.9297 experiment design, and 0.9115 held-out prediction, but only 30% identification. This is useful evidence of an intentionally unsaturated frontier: locally excellent two-probe plans leave substantial posterior ambiguity. The scores are controls, not external model results.

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 reward0.2443

20 reported runs.

Result artifactIncluded

ulam_fresh_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
041b2324813be053d9fe0c6fcdbc71c26f7c74144862191d5a3a421510b66df0
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-7

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