{"id":"d051cc33-de88-400c-9efb-6ea13fa4100b","shortId":"t6BgMV","kind":"skill","title":"brainstorm","tagline":"Generate, prioritize, and refine research ideas based on current investigation state. Use when the pipeline needs new or better hypotheses — after formalization, between investigation batches, or when all current ideas are resolved.","description":"# Brainstorm\n\nThe 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.\n\n## Usage\n\nInvoke this skill by name; pass an optional context hint as a quoted string. On slash-command hosts, prefix with `/` (e.g. `/brainstorm \"<hint>\"`).\n\n```\n# Generate ideas based on current state\nbrainstorm\n\n# With a hint about what direction to explore\nbrainstorm \"explore liveness under partial synchrony\"\n```\n\n## Relationship to Other Skills\n\n- **`/formalize-problem`** handles *initial* formalization: pinning down trust assumptions, the core question, definitional hygiene, and the first set of hypotheses. It runs once.\n- **`/brainstorm`** handles *recurring* ideation: generating additional ideas as the investigation progresses. It runs many times.\n- **`/investigate`** handles *execution*: deep-diving into specific ideas. It does not generate new hypotheses.\n\n## Inputs\n\n**Always read** before starting:\n- `reaper-workspace/notes/problem-statement.md` — model assumptions and property definitions\n- `reaper-workspace/notes/ideas.md` — the current ideas and their resolution status\n- `reaper-workspace/notes/current-understanding.md` — the \"branch tip\" of accumulated knowledge\n- `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.\n\n**Lazy-load only when needed** (skip these unless you're stuck or exploring a specific direction):\n- `reaper-workspace/notes/paper-summary.md` — the source paper (if provided)\n- `reaper-workspace/notes/literature.md` — known prior work\n- `reaper-workspace/notes/clarified-goal.md` — refined research goal and scope\n- `reaper-workspace/papers/` — downloaded PDFs and per-paper notes\n- The optional context hint from the argument\n\n\n## Process\n\n### 1. Assess Current State\n\nRead all inputs and build a picture of:\n- **Resolved ideas**: Which hypotheses have been confirmed, refuted, or are no longer worth pursuing?\n- **Unresolved ideas**: Which are still open? Are any stuck (multiple inconclusive cycles)?\n- **Patterns in failures**: Do discarded cycles cluster around a common obstacle? A pattern in dead ends is itself informative.\n- **Emerging themes**: Have \"keep\" results revealed a direction that wasn't anticipated in the original formalization?\n\n### 2. Generate New Ideas\n\nApply these techniques systematically. Not all will produce ideas every time — use the ones that fit the current state.\n\n#### Gap-Finding (Qian: Fill in the Blank)\n\nMap 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.\n\n#### Problem Inversion (Hamming)\n\nFor each stuck or failed hypothesis, invert it:\n- Can't prove it? Try to disprove it.\n- Can't find a counterexample? Ask what minimal assumption would make the proof work.\n- Can't achieve a property? Ask what weaker property is achievable, or what stronger model is needed.\n\nWhat seems like a blockage often becomes the key insight.\n\n#### Qian's Patterns\n\n- **Start small then generalize**: What's the simplest case (n=2, 1 round, crash-only)? Can you solve it there first, then lift?\n- **Build a hammer**: Can a technique from a previous cycle apply here in a different way? Look at \"keep\" results for reusable proof strategies.\n- **Expansion**: Take a confirmed result and ask what happens when you relax one assumption.\n\n#### Follow the Evidence\n\nWhat 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?\n\n#### Negative Result Escalation\n\nIf a hypothesis has trended toward refutation over 3+ cycles (counterexample attempts partially succeed, proof attempts consistently fail at the same point):\n- Propose a new hypothesis that *proves* the negative: \"Protocol X cannot achieve property Y under model Z because...\"\n- Propose a \"minimal fix\" hypothesis: \"What is the weakest additional assumption that restores property Y?\"\n\n### 3. Screen Against Known Impossibilities\n\nFor 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.\n\nIf a candidate contradicts a known impossibility:\n1. Flag it explicitly with a warning\n2. Reformulate: \"Under what additional assumptions does this become possible?\" or \"What weaker property can be achieved?\"\n3. Do NOT leave it as a hypothesis for investigate to waste cycles on\n\n### 4. Prioritize (Hamming: Importance Filter)\n\nNot 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.\n\n### 5. Write Output\n\nUpdate `reaper-workspace/notes/ideas.md`:\n- **New ideas**: Add under a clearly marked section.\n- **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.\n\nNew ideas use this format:\n\n```markdown\n## Ideas — Brainstorm Round N\n\n### H<next>: [Short descriptive title]\n- **Statement**: [Precise, falsifiable claim — specific enough that a reader could disagree]\n- **Success condition**: [What evidence would confirm this?]\n- **Failure condition**: [What evidence would refute this?]\n- **Priority**: High / Medium / Low\n- **Rationale**: [Why this priority? What's the consequence of resolving it?]\n- **Source**: [What prompted this idea — a pattern in failures, a gap in the matrix, an inversion of H<x>, etc.]\n```\n\nWhere 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.\n\n**Constraints**:\n- At most 3-5 new ideas per round — focus beats breadth\n- Every idea must be **atomic** — investigable in a single cycle. Split compound ideas (e.g., \"prove safety AND liveness\") into separate hypotheses\n- Every idea must be **falsifiable** — a reader could disagree with it\n- Every idea must have **explicit** success and failure conditions\n- Do not duplicate existing unresolved ideas — check `ideas.md` first\n- If the context hint from the argument suggests a direction, weight it heavily but don't ignore other promising directions\n\n### 6. Report\n\nAfter writing, briefly summarize to the orchestrator:\n- How many new ideas were added\n- What the highest-priority new idea is and why\n- Whether any existing ideas should be deprioritized or marked as subsumed\n\n## Quality Criteria\n\n- Every new idea is falsifiable with explicit success/failure conditions\n- Ideas are screened against known impossibilities before being added\n- Priorities are justified by consequence, not convenience\n- No duplication of existing unresolved ideas\n- The source/motivation for each idea is documented\n- At most 3-5 ideas per round — if you have more, merge or drop the low-priority ones\n- The brainstorm round is fast — no experiments, no proof attempts, no literature searches within this skill\n- If `problem-statement.md` or `ideas.md` is missing, return an error to the 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