Mathematics5Math-5

5Math-5

Name: 5Math-5
SKU: 5Math-5
Price: 250.00 USD
Availability: PreOrder

Five research mathematics environments built around exact nuisance equivalences: familiar summaries are identical across candidate systems, so agents must discover which advanced invariant actually carries information. The suite spans cellular sheaves, Schrödinger bridges, inverse operators, algebraic varieties, and random-matrix spectra with strict budgets and sealed generalization.

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
SheafHolonomy	Cellular sheaves and connection geometry	Combine invariant and anchored probes to determine hidden cycle geometry when local edge spectra are exact decoys.
SchrodingerBridge	Entropic transport and reciprocal processes	Select coupling, potential, barycentric, and bridge measurements across scales to recover geometry hidden by matching marginals.
OperatorTomography	Inverse PDEs and spectral geometry	Infer eigenspace alignment with forces, sensors, and boundaries although every candidate shares the full eigenvalue spectrum.
VarietyChow	Computational algebraic geometry	Use mixed algebraic probes to uncover coordinate relationships hidden by identical degree, Hilbert, marginal, and single-coordinate data.
FreeSpectrum	Free probability and random-matrix theory	Combine analytic transforms, edge measurements, and perturbation response to distinguish laws matched on mass and low moments.

03 Why it is interesting

What the supplied evaluation reveals.

The public-contract evaluation reached 0.7206 mean reward and 24/40 passes, solving all evaluated SheafHolonomy, OperatorTomography, and VarietyChow episodes but none in two other families. The report openly traces that split to missing public likelihood parameters, while an evaluator-side control passed 40/40. This makes the package unusually transparent about public-agent identifiability versus simulator solvability. Validation passed 77/77 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.

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 reward0.9958

40 reported runs.

Result artifactIncluded

ulam_rlvr_score_report.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
4846fa16b7cd86e882bb06c9f6801f0e48330df760aa815f70f246754d76c9a0

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-5

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5Math-5

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.

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5Math-3

Ready to add this environment?