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Mathematics5Math-Hard-3

5Math-Hard-3

Five advanced mathematical inverse problems compressed into an extreme two-measurement challenge. Across microlocal analysis, Hamiltonian geometry, polynomial certificates, braid topology, and oscillatory microstructure, agents distinguish 256 hidden models from noisy observations; exact seed invariants provide no shortcut, so success requires complementary design, calibrated inference, and sealed transfer.

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

A real, versioned RL environment.

Five advanced mathematical inverse problems compressed into an extreme two-measurement challenge. Across microlocal analysis, Hamiltonian geometry, polynomial certificates, braid topology, and oscillatory microstructure, agents distinguish 256 hidden models from noisy observations; exact seed invariants provide no shortcut, so success requires complementary design, calibrated inference, and sealed transfer.

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
MicrolocalLensMicrolocal analysis and Fourier-integral operatorsChoose complementary phase-space measurements to reveal subprincipal behavior invisible in the shared calibration jet.
NoetherCurrentHamiltonian dynamics and symplectic geometryDiagnose nonlinear symmetry breaking from trajectories and currents beyond a shared equilibrium and linearization.
SOSWitnessMoment problems and sum-of-squares certificatesSeparate high-degree positive-measure structure with complementary moment or certificate probes.
KnotSurgeryBraid groups and knot invariantsIdentify ordered noncommuting braid modifications using parameter-dependent representation probes.
YoungMeasureCipherYoung measures and oscillatory microstructureRecover laminate orientation from nonlinear averages when barycentric and energy summaries erase it.
03 Why it is interesting

What the supplied evaluation reveals.

A pair-planned exact-Bayes policy averaged 0.7749 and passed 11/60 fresh expert episodes, outperforming the same-seed greedy control on reward, identification, prediction, and pass rate. KnotSurgery identified all 12 systems and passed nine; SOSWitness predicted sealed statistics extremely well while remaining uncertain about the exact latent phase. The contrast distinguishes predictive mixtures from mechanism recovery. The release reports 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

Reported result from the evaluation artifact supplied with this package.

Evaluated system / policyGPT-5.6 Pro-assisted evaluation

As identified by the supplied artifact.

Pass rate10.6%

12 reported runs.

Result artifactIncluded

notes.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
6cd6f3bfc14d71e60b12bf9dc1cf00d11995361a2e5fbd794a6271fc04064b11
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-3

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