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Mathematics5Math-8

5Math-8

A five-environment supercompact mathematics benchmark with thousands of candidate systems, identical starting evidence, and only two noisy measurements before submission. It spans Hodge-theoretic period maps, higher algebra, information geometry, nonlinear convex PDEs, and graph-cover spectra, rewarding complementary experiment planning and calibrated transfer to sealed probes.

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

A real, versioned RL environment.

A five-environment supercompact mathematics benchmark with thousands of candidate systems, identical starting evidence, and only two noisy measurements before submission. It spans Hodge-theoretic period maps, higher algebra, information geometry, nonlinear convex PDEs, and graph-cover spectra, rewarding complementary experiment planning and calibrated transfer to sealed probes.

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
PeriodMapCipherHodge structures and period mapsChoose complementary continuation-sensitive probes when all candidates share the complete low-order local expansion.
MasseyProductXRayA-infinity algebras and higher homotopyInfer hidden higher operations through multilinear and basis-transformed measurements while ordinary cohomology agrees.
RateDistortionAtlasRate-distortion theory and information geometryProbe complementary temperature regimes to distinguish semantic distortions with shared high-temperature invariants.
MongeAmpereOracleMonge–Ampère geometry and convex analysisSelect off-anchor measurements revealing high-order convex structure hidden by identical local derivatives.
IharaCoverXRayGraph coverings and Ihara zeta geometryRecover covering geometry from walk and marked-fiber evidence when quotients and local neighborhoods are shared.
03 Why it is interesting

What the supplied evaluation reveals.

A frozen exact-likelihood policy achieved 0.7073 mean reward and 8/20 correct identifications but no expert passes. Its closest episode reached 0.9897 reward and cleared every gate except posterior concentration, showing how severe the two-measurement, 8,192-hypothesis bottleneck is even with strong experiment design. Package checks covered 101 files, five self-tests, and 51 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.

Mean reward0.7073

20 reported runs.

Result artifactIncluded

REPORT.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
3982d7669968ade2d1eac76143785522cbaf074bf3d1ab8d2688c6451071c591
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-8

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