Mathematics5Math-Hard-8

5Math-Hard-8

Name: 5Math-Hard-8
SKU: 5Math-Hard-8
Price: 1000.00 USD
Availability: PreOrder

Five independent frontier mathematics environments spanning derived deformation theory, knot concordance, renormalization flows, proof complexity, and ergodic joinings. Agents jointly infer scientific structure and apparatus nuisance variables while navigating branch-dependent probes, scarce resources, irreversible transformations, destructive decoys, calibrated terminal decisions, and sealed predictions.

MathematicsAdaptive reasoningRLVR

Version1.0.0

Environments5

RewardScalar · 0–1

DeliveryPrivate ZIP

01 Task contract

A real, versioned RL environment.

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.

Environment	Mathematical or technical frontier	Adaptive research problem
DerivedDeformationLab	Derived deformation and obstruction theory	Route tangent, obstruction, higher-operation, gauge, and miniversal evidence while managing irreversible base changes.
KnotConcordanceLab	Floer/Khovanov concordance and surgery	Coordinate coefficients, satellites, covers, mutation, and surgery while consuming distinct topological resources.
RenormalizationFlowLab	Nonlinear PDE blow-up and dynamic rescaling	Infer scaling and measurement clock jointly through profile, modulation, spectrum, virial, and defect diagnostics.
ProofComplexityLab	Proof lower bounds and restrictions	Preserve valid width, degree, rank, communication, and pseudoexpectation routes through irreversible transformations.
ErgodicJoiningLab	Ergodic systems and joinings	Distinguish intrinsic structure from recoding and induction before choosing identification, a bounded set, or abstention.

03 Why it is interesting

What the supplied evaluation reveals.

On ten hard/expert calibration episodes, a bounded continuation-aware exact-likelihood control passed five, while static planning passed one and myopic planning none. The package's task narratives explain why: branch choices change which later measurements remain legal, and attractive decoys can destroy the fine diagnostic route. These are evaluator controls rather than model scores, but they provide direct evidence that observation-contingent planning matters.

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.

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 reward0.7711

40 reported runs.

Result artifactIncluded

rl_env_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
a48e7822099a0b491fbd3f0cacf2fc018e77c238fdfe90b79246377dbe17e171

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-8

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5Math-Hard-8

A real, versioned RL environment.

Agent objective

Evaluation

Delivery boundary

Distinct environments, one demanding research contract.

What the supplied evaluation reveals.

Observed evaluation result.

Public result record

The package stays off the public website.

Included with purchase

Commercial use, without exclusivity.

Related RL environments.

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5Math-2

5Math-3

Ready to add this environment?