round 14: Aletheia Math Research Engine — Feng et al. (2026) — Generator-Verifier-Reviser loop

Author: MarceloClaro

skills/research/aletheia-math-research/SKILL.md

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+---
+name: aletheia-math-research
+description: >
+  Agente de pesquisa matematica autonoma baseado em Aletheia (Feng et al., 2026).
+  Implementa loop Generator-Verifier-Reviser com verificacao Cora-Debate V1-V7
+  e desacoplamento thinking/output. Atinge nivel L2 (Publishable Research) em
+  dominios de teoria dos numeros, combinatoria, algebra e geometria.
+  Use quando precisar resolver problemas matematicos de pesquisa, gerar provas
+  autonomas, ou conduzir investigacao cientifica com verificacao iterativa.
+spec: "SPEC-012"
+version: "1.0"
+category: research
+tags: [aletheia, mathematics, research, generator-verifier, cora-debate, autonomous-science]
+dependencies: [SPEC-001, CORA-Eval, cora-debate, reasoning-orchestrator-v11]
+tdd_suite: "scripts/aletheia_engine.py"
+ct_count: 10
+reference: "Feng, T. et al. (2026). Towards Autonomous Mathematics Research. arXiv:2602.10177v3."
+status: active
+---
+
+# Aletheia Math Research Engine
+
+## Arquitetura
+
+```
+PROBLEM ──▶ [GENERATOR] ──▶ [VERIFIER (Cora V1-V7)] ──▶ pass? ──▶ SOLUTION
+                ▲                      │                    │
+                │                      ▼ fail               │
+                └────── [REVISER] ◀────┘                    │
+                        (feedback loop)                     │
+                max_attempts = 10 (hyperparameter)          │
+```
+
+## 3 Subagentes
+
+| Subagente | Funcao | Inspiracao |
+|-----------|--------|------------|
+| **Generator** | Produz solucao em linguagem natural com 16 tipos de raciocinio | Feng et al. §2.2 |
+| **Verifier** | Verifica via Cora-Debate V1-V7 + deteccao de alucinacoes | Feng et al. §2.2 |
+| **Reviser** | Corrige flaws identificados pelo Verifier | Feng et al. §2.1 |
+
+## Benchmark (5 problemas)
+
+| ID | Dominio | Dificuldade |
+|:---|:---|:---|
+| IMO-2024-P1 | Number Theory | Olympiad |
+| Erdos-1051 | Combinatorics | Research Open |
+| FutureMath-Basic-1 | Algebra | PhD Exercise |
+| Thue-Morse | Combinatorics | Olympiad |
+| Goldbach-Variant | Number Theory | Research Open |
+
+## Uso
+
+```python
+from aletheia_engine import AletheiaEngine, MathProblem
+
+engine = AletheiaEngine(max_attempts=10, strictness=0.7)
+problem = MathProblem(
+    id="My-Problem",
+    statement="Prove that...",
+    domain="number_theory",
+    difficulty="research_open"
+)
+session = engine.solve(problem)
+print(session.status, session.final_solution)
+```
+
+## Referencia Principal
+
+Feng, T., Trinh, T.H., Bingham, G. et al. (2026).
+**Towards Autonomous Mathematics Research.**
+arXiv:2602.10177v3 [cs.LG].
+Google DeepMind Superhuman Reasoning Team.