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Mathematics5Math-4

5Math-4

Five adaptive mathematics environments spanning tensor decomposition, topological invariants, kernel geometry, coding theory, and nonlinear dynamics. Each hides meaningful structure behind deliberately non-identifying summaries, forcing agents to choose complementary probes, manage experimental cost, and make calibrated predictions on sealed cases.

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

A real, versioned RL environment.

Five adaptive mathematics environments spanning tensor decomposition, topological invariants, kernel geometry, coding theory, and nonlinear dynamics. Each hides meaningful structure behind deliberately non-identifying summaries, forcing agents to choose complementary probes, manage experimental cost, and make calibrated predictions on sealed cases.

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
TensorCircuitTensor decomposition and multilinear sensingAlign complementary contractions and operator views to recover sparse tensor structure hidden by shared null and crossed-factor responses.
TopologyLensTopological data analysis and Hodge geometryUse anchored cohomological probes to recover labeled attachment geometry that global Betti and heat summaries cannot identify.
KernelForgeKernel methods, Gaussian processes, operator learningProbe away from a shared seed point to reveal differences in spectra, uncertainty, leverage, and learning-flow behavior.
DecoderLabCoding theory and probabilistic decodingConstruct ambiguous multi-bit errors that expose learned decoder bias while clean and single-bit behavior remains identical.
KoopmanLabNonlinear dynamics, Koopman operators, controlMove off a shared fixed point and choose states, controls, observables, and horizons that enter the nonlinear regime.
03 Why it is interesting

What the supplied evaluation reveals.

In a blind public-interface evaluation, GPT-5.6 Pro passed all ten hard and expert episodes with 0.9285 mean reward using an average of 3.3 queries. No-query and inert controls passed none, while the release passed 71/71 tests and all ten fixture replays. The result demonstrates that targeted mathematical probes work, without making the tasks a one-step lookup.

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

As identified by the supplied artifact.

Mean reward0.9395

5 reported runs.

Result artifactIncluded

5Math-4_results.zip:scores_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
c00f23b4726c2149a65ba7964dbeb6f7d7787562284631c4485503d51684fdb6
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-4

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