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Mathematics5Math-11

5Math-11

Thirty exact-mathematics environments spanning algebraic geometry, homological algebra, representation theory, arithmetic forms, and real algebraic geometry. Agents build connected chains of verified artifacts rather than isolated answers: accepted work unlocks later steps, revisions invalidate dependencies, and exact certificate gates test transfer across semantically distinct constructions.

MathematicsAdaptive reasoningRLVR
Version3.0.0
Environments30
RewardScalar · 0–1
DeliveryPrivate ZIP
01 Task contract

A real, versioned RL environment.

Thirty exact-mathematics environments spanning algebraic geometry, homological algebra, representation theory, arithmetic forms, and real algebraic geometry. Agents build connected chains of verified artifacts rather than isolated answers: accepted work unlocks later steps, revisions invalidate dependencies, and exact certificate gates test transfer across semantically distinct constructions.

Agent objective

  • Interact with the supplied stateful environment.
  • Produce verifier-checkable actions or artifacts.
  • Maximise scalar reward under the package contract.

Evaluation

  • 30 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
Algebraic Geometry Workbench · 6 regimesIdeals, elimination, saturation, implicitizationBuild canonical bases and exact witnesses through connected elimination and saturation chains, including held-out composed constructions.
Filtered & Homological Algebra · 6 regimesSpectral sequences, cones, torsion, extensionsMaintain exact chain, filtration, kernel, image, Smith, and extension artifacts whose dependencies must remain consistent after revisions.
Symmetric-Group Representations · 6 regimesBranching, Kronecker products, Schur functorsConstruct restriction, induction, tensor, square, and cubic decompositions with character and dimension consistency checks.
Arithmetic Forms & Lattices · 6 regimesQuadratic forms, local-global methods, p-adicsDistinguish rational and integral equivalence, certify obstructions, and compose exact local and global witnesses.
Real Algebraic Certificates · 6 regimesSOS, Positivstellensatz, Gram reconstructionMove from optimum candidates to exact positivity identities, sparse Gram factorizations, and degree-selected certificates.
03 Why it is interesting

What the supplied evaluation reveals.

A GPT-5.6-Pro-authored, source-informed program completed 90 episodes across all 30 regimes and four semantic splits, achieving 45/90 exact successes and 0.5463 mean reward. It solved both algebraic-geometry and homological-algebra families completely, but reached only 3/18 in arithmetic forms and 0/18 in real algebraic certificates. The contrast exposes tractable regions and genuine post-training frontiers within one exact artifact-building interface. Independent audits found 94/94 isolated tests passing.

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

Source-informed, tool-assisted agent evaluation across 30 semantic regimes; mean training reward 0.546285.

Evaluated system / policyGPT-5.6 Pro

As identified by the supplied artifact.

Exact success rate50.0%

90 reported runs.

Result artifactIncluded

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 3.0.0
  • 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
386ec17c68fa092ca4a1d31733dc38065d03e5f4ce1e1971733af004dffe17c6
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-11

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