OMEGA - Open Mathematics Exploration by Generative Agents

English: a standalone, registry-first research environment for bounded AI-assisted investigation of open mathematical problems.

Русский: автономная исследовательская среда с реестром задач и ограниченным контуром исполнения для ИИ-поддержки исследований открытых математических проблем.

Start Here / Быстрый Вход

English

• Abstract
• Verified Snapshot (2026-04-21)
• What Is In The Repo Now
• Boundaries and Non-Claims
• Reproducible Quick Start
• Documentation Map

Русский

• Краткая аннотация
• Проверенный срез на 2026-04-21
• Что сейчас есть в репозитории
• Границы проекта
• Быстрый старт
• Карта документации

---

Abstract

OMEGA is not a single-problem demo and not a generic "AI for math" wrapper. It is a structured research-software repository built around five operational commitments:

1. Registry first: track targets in machine-readable form before execution.
2. Triage first: prioritize by practical AI amenability, not only by prestige.
3. Bounded execution: run explicit, restartable stages with audit-friendly state.
4. Evidence-bearing artifacts: tie claims to ledgers, manifests, checksums, and machine-readable reports.
5. Honest scope: separate what is implemented, what is experimental, and what is still only a scaffold.

OMEGA borrows ideas from external research-agent and proving ecosystems, but it executes on local contracts, local scripts, and local evidence surfaces.

Documentation Design Note (April 2026)

This README is an entrypoint and router.

• It tells you what the repository can already do.
• It points to the protocol and evidence surfaces that carry the details.
• It avoids turning the root README into a dump of every internal document.

Verified Snapshot (2026-04-21)

Surface	Verified state	Source
Release version	0.6.0	pyproject.toml
Python support	3.12, 3.13	pyproject.toml
Registry size	252 problems	registry/index.yaml
Triage coverage	73 / 252 (29.0%)	registry/index.yaml
Domain files	14	registry/index.yaml
Collection files	6	registry/index.yaml
Tier distribution	T1 28, T2 22, T3 10, T4 5, T5 8, untriaged 179	registry/index.yaml
Latest local full test run	241 passed in 27.74s	python -m pytest -q (2026-04-21)
Runtime baseline report	APPROVED	reports/omega_runtime_evidence_report_v1.json
Execution maturity report	WARNING on the audited host: Lean/Lake and z3 absent, SAT fallback still works	reports/omega_execution_maturity_report_v1.json
FT scaffold gate	APPROVED	reports/omega_ft_scaffold_gate_report_v1.json
Docs closure rail	8 passed, 0 warnings, 0 failures	agent:preflight:docs

What Is In The Repo Now

Core research runtime

• Schema-validated registry and generated index under registry.
• Deterministic per-problem workflow controller, including stricter transition validation and machine-readable YAML or JSON output through omega-workflow.
• Experiment lifecycle, evidence bundle generation, and global experiment index surfaces through omega-runner, omega-verify-evidence, and omega-generate-experiment-index.
• Query surfaces for per-run ledgers and the global experiment index through omega-query.

Execution and orchestration surfaces

• Lean, SAT/SMT, and CAS adapters through omega-lean, omega-solve, and omega-cas.
• Machine-readable runtime capability probing for Lean/Lake and solver backends.
• Model routing and multi-stage orchestration through omega-model-router and omega-orchestrate.
• Orchestrator result envelopes that now preserve failed stage metadata and prompt-packet file references.

Literature and novelty surfaces

• Programmatic literature lookup, title matching, and search through omega-literature.
• Deterministic novelty-collision packet generation through omega-literature novelty-packet.
• Local literature evidence surfaces under input_files/literature.md, input_files/literature_graph.md, and input_files/citation_evidence.md.

Synthetic reasoning packet lane

• A bounded synthetic reasoning contract in protocol/synthetic-reasoning-packets.md.
• Problem-local taxonomy and evaluation packet templates under templates/synthetic-reasoning-taxonomy.md and templates/synthetic-evaluation-packet.md.
• Ledger support for prompt-packet, synthetic-taxonomy, and evaluation-packet artifacts.

Runtime evidence and export surfaces

• Runtime baseline export through omega-export-runtime-baseline.
• Lean or solver execution maturity export through omega-export-execution-maturity.
• FT scaffold gate export through omega-export-ft-scaffold-gate.
• Machine-readable reports under reports.

FT scaffold (OMG-201)

• A bounded train/eval/serve smoke scaffold under llm.
• Deterministic dataset manifest and split policy for the smoke lane.
• Local smoke entrypoints for training, evaluation, and serving.
• An explicit non-claim boundary: this scaffold proves readiness prerequisites, not theorem-quality model performance or production serving.

Boundaries and Non-Claims

OMEGA does not currently claim:

1. End-to-end autonomous publication with acceptance-grade review guarantees.
2. Full theorem-level correctness closure without human or formal verification gates.
3. Complete literature coverage for every registry entry.
4. A synthetic reasoning lane that by itself proves novelty, correctness, or proof closure.
5. A fine-tuning stack that already delivers production inference or benchmark-leading theorem capability.
6. A host-independent Lean or SMT toolchain guarantee; execution maturity reports are environment-relative.

These are scope controls, not omitted disclaimers.

Flagship Tracks (Run-Ready Surfaces)

Problem	Current executable surface	Primary scripts
Erdős-Straus	covering analysis, parametric decomposition	phase1_covering.py, phase2_parametric.py
Kobon triangles	arrangement search	phase1_pseudoline_enum.py
Thomson problem	multistart optimization, basin hopping, numerical certification scaffold	phase1_multistart.py, phase2_basin_hopping.py, phase3_certify.py

Planned later phases remain in each workspace planning/attack_plan.md; only the surfaces above are treated as run-ready.

Reproducible Quick Start

1) Install

python -m pip install -e .[all]

2) Validate registry and release metadata

omega-validate-registry
omega-verify-version-sync

3) Scaffold and triage a workspace

omega-scaffold-problem erdos-straus --title "Erdos-Straus Conjecture"
omega-workflow triage erdos-straus
omega-workflow status erdos-straus --format json

4) Build a novelty-collision packet before plan or publication work

omega-literature novelty-packet "erdos-straus conjecture unit fractions" --problem-id erdos-straus --max-items 10

5) Dry-run orchestration before live calls

omega-orchestrate run erdos-straus --stage plan --dry-run

6) Export runtime evidence

omega-export-runtime-baseline
omega-export-execution-maturity

7) Run the FT scaffold gate when you need the bounded smoke lane

omega-export-ft-scaffold-gate

8) Optional full local verification

python -m pytest -q

Documentation Map

Explanation surfaces

• README.md
• PROTOCOL.md
• llm/README.md
• research/OMEGA_DEVELOPMENT_ROADMAP_2026_04_05.md

How-to surfaces

• protocol/operator-runbook.md
• protocol/lean-bootstrap.md
• protocol/verification-pipeline.md

Reference surfaces

• protocol/orchestrator-contract.md
• protocol/prover-result-contract.md
• protocol/experiment-ledger-spec.md
• protocol/evidence-governance.md
• protocol/literature-adapter.md
• protocol/synthetic-reasoning-packets.md

Evidence and audit surfaces

• docs/reports/EXTRACTION_REPORT.md
• reports/omega_runtime_evidence_report_v1.json
• reports/omega_execution_maturity_report_v1.json
• reports/omega_ft_scaffold_gate_report_v1.json

Repository Topology

math/
├── README.md
├── PROTOCOL.md
├── protocol/
├── research/
├── docs/
├── registry/
├── scripts/
├── tests/
├── templates/
├── llm/
├── reports/
├── agents/
└── .github/

Governance, Help, and Contribution

• License: LICENSE
• Citation metadata: CITATION.cff
• Contribution guide: CONTRIBUTING.md
• Code of conduct: CODE_OF_CONDUCT.md
• Security policy: SECURITY.md
• Maintainer surface: MicroPhoenix open-source community
• Issue tracker: https://github.com/KonkovDV/OMEGA-MATH/issues

Citation

If you use OMEGA in research or derived tooling, cite via CITATION.cff.

---

Краткая аннотация

OMEGA - это не витрина на одну задачу и не общая обёртка "ИИ для математики". Это исследовательский репозиторий, в котором работа идёт по явному контуру:

1. сначала реестр задач,
2. затем triage по практической доступности,
3. затем ограниченное исполнение по стадиям,
4. затем пакет свидетельств, отчёты и формулировка результата.

Репозиторий сознательно разделяет то, что уже исполняется локально, то, что пока является bounded scaffold, и то, что ещё не должно звучать как закрытая научная претензия.

Проверенный срез на 2026-04-21

Показатель	Значение
Версия	0.6.0
Поддерживаемый Python	3.12, 3.13
Задач в реестре	252
Триажировано	73 / 252 (29.0%)
Последний полный локальный тестовый прогон	241 passed in 27.74s
Runtime baseline report	APPROVED
Execution maturity report	WARNING: на проверенной машине не найден Lean/Lake и z3, SAT fallback работает
FT scaffold gate	APPROVED
Статус docs closure rail	8 passed, 0 warnings, 0 failures

Что сейчас есть в репозитории

Базовый исследовательский runtime

• машиночитаемый реестр с валидацией схем;
• контроллер рабочего процесса по стадиям с более строгой валидацией переходов и выводом в YAML или JSON;
• раннер экспериментов, evidence bundle и глобальный experiment index;
• query surfaces для ledger и experiment index через omega-query.

Исполнительные и orchestration surfaces

• адаптеры Lean, SAT/SMT и CAS;
• capability probing для Lean/Lake и solver backends;
• маршрутизация моделей и стадийная оркестрация;
• более информативные orchestrator envelopes: сохраняются failed stage metadata и prompt-packet file references.

Literature и novelty lane

• omega-literature теперь покрывает lookup, search, match-title и novelty-packet;
• novelty packet строится детерминированно и даёт collision-risk labels для предварительной проверки новизны;
• локальные surfaces для литературы и citation evidence остаются обязательными при реальных novelty claims.

Synthetic reasoning packet lane

• появился локальный контракт для synthetic reasoning work;
• есть problem-local шаблоны taxonomy и evaluation packet;
• ledger умеет хранить prompt-packet, synthetic-taxonomy и evaluation-packet.

Runtime evidence и FT scaffold

• omega-export-runtime-baseline собирает общий runtime evidence report;
• omega-export-execution-maturity фиксирует состояние Lean и solver toolchains на текущем хосте;
• omega-export-ft-scaffold-gate проверяет bounded FT scaffold в llm/;
• под llm/ лежит локальный smoke train/eval/serve scaffold с явными non-claims.

Границы проекта

Сейчас OMEGA не заявляет:

1. полностью автономную публикацию с гарантиями уровня рецензируемого журнала;
2. закрытие теоремных утверждений без человека или формального верификатора;
3. полный литераторный граф по всем записям реестра;
4. что synthetic reasoning lane сам по себе доказывает новизну, корректность или proof closure;
5. что FT scaffold уже означает production inference или theorem-level model capability;
6. что Lean или SMT toolchain гарантированно доступны на любой машине без отдельной локальной настройки.

Быстрый старт

python -m pip install -e .[all]
omega-validate-registry
omega-verify-version-sync
omega-scaffold-problem erdos-straus --title "Erdos-Straus Conjecture"
omega-workflow triage erdos-straus
omega-workflow status erdos-straus --format json
omega-literature novelty-packet "erdos-straus conjecture unit fractions" --problem-id erdos-straus --max-items 10
omega-orchestrate run erdos-straus --stage plan --dry-run
omega-export-runtime-baseline
omega-export-execution-maturity
omega-export-ft-scaffold-gate
python -m pytest -q

Карта документации

• Полный протокол: PROTOCOL.md
• Операторский запуск: protocol/operator-runbook.md
• Literature adapter contract: protocol/literature-adapter.md
• Synthetic reasoning packet contract: protocol/synthetic-reasoning-packets.md
• Контракт оркестратора: protocol/orchestrator-contract.md
• Контракт результата доказательства: protocol/prover-result-contract.md
• Политика свидетельств: protocol/evidence-governance.md
• FT scaffold note: llm/README.md
• Extraction report: docs/reports/EXTRACTION_REPORT.md
• Machine-readable reports: reports

Лицензия и цитирование

• Лицензия проекта: LICENSE
• Правила цитирования: CITATION.cff