Mathematics5Math-Hard-9

5Math-Hard-9

Name: 5Math-Hard-9
SKU: 5Math-Hard-9
Price: 1000.00 USD
Availability: PreOrder

Five deep-frontier mathematical investigations across polyhedral homotopy, symplectic capacities, graphon stability, microlocal propagation, and motivic regulators. Each environment has a distinct scientific state machine: agents must route observation-dependent diagnostics, manage nuisance variables and irreversible choices, preserve future options, and satisfy separate posterior, prediction, decision, and path-quality gates.

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
PolyhedralHomotopyLab	Sparse polynomial systems and continuation	Choose mixed-cell, path, endgame, and certification operations while preserving viable continuation branches.
SymplecticCapacityLab	Symplectic embeddings and capacities	Coordinate capacity obstructions, embeddings, and normalization evidence under limited geometric interventions.
GraphonStabilityLab	Graph limits and extremal stability	Distinguish structural graphon explanations through adaptive densities, perturbations, and stability tests.
MicrolocalPropagationLab	Wavefront propagation and PDE diagnostics	Route phase-space observations and interventions to recover hidden propagation mechanisms and nuisance structure.
MotivicRegulatorLab	Motivic cohomology and regulator evidence	Assemble compatible arithmetic and period evidence while retaining paths to sealed regulator predictions.

03 Why it is interesting

What the supplied evaluation reveals.

A recomputed 40-episode calibration exactly matched the packaged records and passed 132/132 tests. The strongest continuation-aware control averaged 0.6817 and passed only one of ten hard/expert cases. One non-passing episode scored 0.9614 but failed the path-quality gate, showing that excellent belief and prediction cannot excuse a wasteful or scientifically invalid investigation path.

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 reward0.9716

10 reported runs.

Result artifactIncluded

Ulam_RLVR_run_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
4085aeecb8f39c3603580764027ca0f660306596cb1e872ed4ab48bb58eeed5e

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-9

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5Math-Hard-9

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.

5Math-1

5Math-2

5Math-3

Ready to add this environment?