Mathematics5Math-Hard-1

5Math-Hard-1

Name: 5Math-Hard-1
SKU: 5Math-Hard-1
Price: 1000.00 USD
Availability: PreOrder

Five apex mathematics environments where 64 candidate mechanisms share exactly non-identifying seed evidence and agents get at most three costly probes. The suite spans rough paths, weighted automata, lattice geometry, replicator dynamics, and inverse conductivity, demanding noncommutative reasoning, complementary measurements, calibrated posteriors, and transfer to sealed probes.

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
RoughPathOracle	Rough paths and noncommuting flows	Combine endpoint and operator-level probes to recover higher Lie interactions hidden by identical first-level calibration.
AutomatonHankel	Weighted automata and rational series	Choose complementary word, Hankel, reversal, and continuation probes to expose hidden transition couplings.
VoronoiCipher	Lattices, Voronoi cells, nearest-vector geometry	Sample complementary hard and soft cell-boundary behavior when covolume and origin quantization agree.
ReplicatorResonance	Game theory and replicator dynamics	Use signed global trajectories across horizons to recover hidden strategic orientation beyond shared equilibrium spectra.
CalderónSketch	Inverse conductivity and graph Laplacians	Combine signed and quadratic boundary responses across sectors to infer conductivity fields after harmonic elimination.

03 Why it is interesting

What the supplied evaluation reveals.

A public exact-likelihood complementarity planner was tested on 60 fresh expert episodes. It averaged 0.7781 and passed 21/60, versus 11/60 for the bundled greedy control. VoronoiCipher passed 12/12 while RoughPathOracle and ReplicatorResonance passed none, demonstrating distinct noncommutative and geometric bottlenecks rather than reskinned tasks. Package integrity included 47/47 tests and 107 verified checksums.

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.

Pass rate18.3%

60 reported runs.

Result artifactIncluded

ulam_self_score_bundle.zip:SELF_SCORE_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
c3b54c253e4813f538077ddf5f5a05311c2f65c82d9a33accfe586db14ca8910

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-1

Ready to add this environment?

Back to marketplace

5Math-Hard-1

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?