CPRR Methodology
Conjecture-Proof-Refutation-Refinement
Table of Contents
1. Introduction
CPRR (Conjecture-Proof-Refutation-Refinement) is a research methodology that treats hypotheses as artifacts with explicit lifecycle management, evidence tracking, and refutation gates.
10. Example Workflow
- Conjecture: "Algorithm X has O(n log n) complexity"
- Evidence: Benchmark data, theoretical analysis
- Refutation attempt: Edge case with O(n²) behavior
- Refinement: "Algorithm X has O(n log n) for sorted input"
- New conjecture: Refined hypothesis
- Proof: Formal verification or exhaustive testing
11. Applications
- Research hypothesis management
- Experimental software development
- Formal methods integration
- Multi-agent coordination
- Knowledge base maintenance
12. Multi-Agent Team Patterns
Fetched the three primary sources directly. Du et al. 2023 (arXiv:2305.14325) uses symmetric, unnamed debate agents ("Agent 1", "Agent 2"...) with no per-agent role differentiation at all -- "Proposer/Challenger/Judge/Arbiter" is not in the paper, so the Debate row is removed. Chan et al. 2023 (arXiv:2308.07201), Appendix A, names five interchangeable debater personas (General Public, Critic, News Author, Psychologist, Scientist) -- not "Prosecutor/Defender/Judge/Recorder". Hong et al. 2023 (arXiv:2308.00352) names five roles (Product Manager, Architect, Project Manager, Engineer, QA Engineer) -- not the four-role "Architect/Engineer/QA/PM" shown, and "PM" was ambiguous between two of the paper's actual distinct roles. Table corrected to each paper's own role names, in the paper's own listed order, first four of five shown. CrewAI, CAMEL, AutoGen, and DeerFlow rows were not re-checked against primary sources this pass and remain attributed, not verified.
A four-role pattern appears in several of these frameworks. Checked against primary sources, the fit is partial: Du et al.'s debate agents are symmetric and unnamed, and ChatEval and MetaGPT each define five roles.
| Framework | Role 1 | Role 2 | Role 3 | Role 4 | Year |
|---|---|---|---|---|---|
| CPRR | Conjecture | Proof | Refinement | Refutation | 2026 |
| ChatEval (Chan et al.) | General Public | Critic | News Author | Psychologist | 2023 |
| MetaGPT (Hong et al.) | Product Manager | Architect | Project Manager | Engineer | 2023 |
| CrewAI | Researcher | Writer | Reviewer | Editor | 2024 |
| CAMEL | Instructor | Assistant | Critic | User | 2023 |
| AutoGen | Planner | Coder | Executor | Critic | 2023 |
| DeerFlow | Coordinator | Researcher | Coder | Reporter | 2025 |
ChatEval's fifth role is Scientist; MetaGPT's fifth is QA Engineer.
- Architect / Planner – decides what to build
- Builder / Coder – writes the implementation
- Reviewer / Critic – finds problems
- Evaluator / Judge – accepts or rejects
CPRR differs from the others in two ways: the refutation gate can update the spec (the contract is mutable), and the evidence is persisted in git notes rather than ephemeral agent memory.
12.1. Dot-product decomposition
site/research/bots/compliance-spec.org now defines R1 through R14 (14 requirements) -- R14 (Content-Signal) was added after this note's 2026-05-18 date, so "13 requirements" is stale; site/research/bots/orchestrator-pattern.org lists exactly 10 named language implementations (python, go, rust, java, guile, typescript, ruby, swift, clojure, elisp), confirming the 10-language count.
When a spec has N requirements and M implementations (e.g. the compliance harness: 14 requirements × 10 languages), the work is the dot product of two dimensions. The orchestrator parallelizes across languages (columns) but serializes across requirements (rows) because the gate pipeline order is normative.
12.2. Persistence strategies
| Strategy | Framework | Survives compaction? |
|---|---|---|
| Ephemeral memory | AutoGen, CrewAI | No |
| JSON files | MetaGPT | Yes (manual) |
| Database | DeerFlow | Yes |
| git commits | CPRR (proof) | Yes |
| git notes | CPRR (refutation) | Yes |
beads (bd) |
Walsh workflow | Yes |
| aq gossip | Walsh workflow | Advisory only |
| PreCompact hook | Claude Code | Yes |
12.3. Related
- Bot Compliance Orchestrator Pattern – the Walsh-Research 10-language harness
- Agent Memory Systems – how agents persist state across sessions
- REPL-Driven Flight Tracking – the methodology applied to data exploration
- Du et al. Improving Factuality and Reasoning via Debate. arXiv:2305.14325 (2023).
- Chan et al. ChatEval: Towards Better LLM-based Evaluators. arXiv:2308.07201 (2023).
13. Resources
- Lakatos, "Proofs and Refutations" (1976)
- Popper, "The Logic of Scientific Discovery" (1959)
- Du et al., "Improving Factuality and Reasoning in Language Models through Multiagent Debate" (2023)
- Hong et al., "MetaGPT: Meta Programming for Multi-Agent Collaborative Framework" (2023)