Brainstorm

The recurring ideation step. Reads the current research state and proposes new or refined ideas for investigation. This skill is lightweight and fast — it generates ideas, not experiments.

Usage

Invoke this skill by name; pass an optional context hint as a quoted string. On slash-command hosts, prefix with / (e.g. /brainstorm "<hint>").

# Generate ideas based on current state
brainstorm

# With a hint about what direction to explore
brainstorm "explore liveness under partial synchrony"

Relationship to Other Skills

• /formalize-problem handles initial formalization: pinning down trust assumptions, the core question, definitional hygiene, and the first set of hypotheses. It runs once.
• /brainstorm handles recurring ideation: generating additional ideas as the investigation progresses. It runs many times.
• /investigate handles execution: deep-diving into specific ideas. It does not generate new hypotheses.

Inputs

Always read before starting:

• reaper-workspace/notes/problem-statement.md — model assumptions and property definitions
• reaper-workspace/notes/ideas.md — the current ideas and their resolution status
• reaper-workspace/notes/current-understanding.md — the "branch tip" of accumulated knowledge
• reaper-workspace/notes/results.md — what's been tried and what happened. If the file is long (20+ rows), read the batch summaries at the end instead of every individual row. Look for patterns in failures across batches, not individual cycle details.

Lazy-load only when needed (skip these unless you're stuck or exploring a specific direction):

• reaper-workspace/notes/paper-summary.md — the source paper (if provided)
• reaper-workspace/notes/literature.md — known prior work
• reaper-workspace/notes/clarified-goal.md — refined research goal and scope
• reaper-workspace/papers/ — downloaded PDFs and per-paper notes
• The optional context hint from the argument

Process

1. Assess Current State

Read all inputs and build a picture of:

• Resolved ideas: Which hypotheses have been confirmed, refuted, or are no longer worth pursuing?
• Unresolved ideas: Which are still open? Are any stuck (multiple inconclusive cycles)?
• Patterns in failures: Do discarded cycles cluster around a common obstacle? A pattern in dead ends is itself informative.
• Emerging themes: Have "keep" results revealed a direction that wasn't anticipated in the original formalization?

2. Generate New Ideas

Apply these techniques systematically. Not all will produce ideas every time — use the ones that fit the current state.

Gap-Finding (Qian: Fill in the Blank)

Map the dimensions of existing work and find unexplored combinations. Consult ../reaper/references/model.md for the domain-appropriate gap-finding matrix dimensions. Which cells in this matrix are empty? Those are candidate hypotheses.

Problem Inversion (Hamming)

For each stuck or failed hypothesis, invert it:

• Can't prove it? Try to disprove it.
• Can't find a counterexample? Ask what minimal assumption would make the proof work.
• Can't achieve a property? Ask what weaker property is achievable, or what stronger model is needed.

What seems like a blockage often becomes the key insight.

Qian's Patterns

• Start small then generalize: What's the simplest case (n=2, 1 round, crash-only)? Can you solve it there first, then lift?
• Build a hammer: Can a technique from a previous cycle apply here in a different way? Look at "keep" results for reusable proof strategies.
• Expansion: Take a confirmed result and ask what happens when you relax one assumption.

Follow the Evidence

What do the "keep" results imply that hasn't been stated as a hypothesis yet? If you proved safety holds under X, does that suggest liveness might fail under X? If you found a gap in the proof, does the same gap appear in related protocols?

Negative Result Escalation

If a hypothesis has trended toward refutation over 3+ cycles (counterexample attempts partially succeed, proof attempts consistently fail at the same point):

• Propose a new hypothesis that proves the negative: "Protocol X cannot achieve property Y under model Z because..."
• Propose a "minimal fix" hypothesis: "What is the weakest additional assumption that restores property Y?"

3. Screen Against Known Impossibilities

For each candidate idea, check whether it contradicts a known impossibility or lower bound. Consult ../reaper/references/impossibility-results.md for the domain-relevant impossibility results and lower bounds.

If a candidate contradicts a known impossibility:

1. Flag it explicitly with a warning
2. Reformulate: "Under what additional assumptions does this become possible?" or "What weaker property can be achieved?"
3. Do NOT leave it as a hypothesis for investigate to waste cycles on

4. Prioritize (Hamming: Importance Filter)

Not all ideas are equally worth investigating. Rank by consequence — ask: "If we resolved this idea, who would care and why?" Consult ../reaper/references/model.md for domain-specific examples of how to rank by importance.

5. Write Output

Update reaper-workspace/notes/ideas.md:

• New ideas: Add under a clearly marked section.
• Existing ideas: If an idea should be deprioritized, marked as subsumed, or have its statement refined based on new understanding, edit it inline rather than leaving stale entries.

New ideas use this format:

## Ideas — Brainstorm Round N

### H<next>: [Short descriptive title]
- **Statement**: [Precise, falsifiable claim — specific enough that a reader could disagree]
- **Success condition**: [What evidence would confirm this?]
- **Failure condition**: [What evidence would refute this?]
- **Priority**: High / Medium / Low
- **Rationale**: [Why this priority? What's the consequence of resolving it?]
- **Source**: [What prompted this idea — a pattern in failures, a gap in the matrix, an inversion of H<x>, etc.]

Where N is one more than the highest existing brainstorm round (or 1 if none exist). Use hypothesis numbers that continue from the highest existing H number.

Constraints:

• At most 3-5 new ideas per round — focus beats breadth
• Every idea must be atomic — investigable in a single cycle. Split compound ideas (e.g., "prove safety AND liveness") into separate hypotheses
• Every idea must be falsifiable — a reader could disagree with it
• Every idea must have explicit success and failure conditions
• Do not duplicate existing unresolved ideas — check ideas.md first
• If the context hint from the argument suggests a direction, weight it heavily but don't ignore other promising directions

6. Report

After writing, briefly summarize to the orchestrator:

• How many new ideas were added
• What the highest-priority new idea is and why
• Whether any existing ideas should be deprioritized or marked as subsumed

Quality Criteria

• Every new idea is falsifiable with explicit success/failure conditions
• Ideas are screened against known impossibilities before being added
• Priorities are justified by consequence, not convenience
• No duplication of existing unresolved ideas
• The source/motivation for each idea is documented
• At most 3-5 ideas per round — if you have more, merge or drop the low-priority ones
• The brainstorm round is fast — no experiments, no proof attempts, no literature searches within this skill
• If problem-statement.md or ideas.md is missing, return an error to the orchestrator