Skill: Matrix Combinatorial Creativity

Before First Use

Read .claude/skills/combinatorial-creativity/examples.md to calibrate expected output quality.

Purpose

Generate non-trivial, testable ideas by decomposing existing examples into comparable dimensions, identifying missing values, and recombining patterns.

Core principle:

Proven patterns + new values + explicit validation = useful creative possibilities.

Hard rule: Do not brainstorm freely. Every idea must be traceable to a matrix, a pattern, and a novelty mechanism. No matrix → no ideas.

When to Use

Apply this skill when the user asks for:

• new ideas, hypotheses, research directions
• startup concepts or product features
• experimental designs or strategic options
• "what are we missing?" analysis
• "generate N variants" requests
• novel combinations from existing examples

If the user asks a direct factual question → do not use this skill.

Domain Detection (Step 0 — before everything else)

Before running the algorithm, detect the domain:

State the detected mode before Step 1. If Predictive Gate fires → apply it before Step 5 (before generating ideas).

Algorithm

Step 1 — Define the Category

Identify the object being generated.

Examples:

• scientific hypothesis
• bioinformatics workflow
• product feature
• startup thesis
• research experiment
• strategy
• diagnostic method
• AI agent workflow

If ambiguous → choose the safest useful interpretation and state it briefly.

Step 2 — Select Existing Examples

Choose or ask for 4–7 existing examples. Examples become matrix rows.

If examples are provided by the user → use them. If missing → infer reasonable examples and mark as assumptions:

Assumption: I will use the following existing examples as matrix rows: ...

Do not generate ideas until examples exist.

Step 3 — Define Comparable Dimensions

Create 3–7 matrix columns. Each column must represent a comparable dimension, not a decorative label.

Good columns:

• data type, mechanism, validation method
• unit of analysis, model class
• monetization model, evidence level
• scalability, falsifiability
• minimal experiment, confounders

Bad columns (forbidden):

• "coolness", "vibe", "innovative", "hardcore"
• arbitrary adjectives without a scale
• tone: noir / absurd / strict / wild

If a column contains incomparable labels → normalize into a scale or relation:

Bad:  Tone: noir / absurd / strict
Good: Tone realism: low / medium / high

Measurability Validator (apply before building matrix):

Check each column against the novelty mechanism it will support:

Rule: If you plan to generate an [Interpolation] or [Extrapolation] idea from a column → that column MUST have a numeric or ordinal scale. Categorical column + [Interpolation] claim = logical contradiction → reject and reframe.

Bad:  Core Mechanism: "Radio stabilization" / "Anderson localization"  → cannot interpolate
Good: Degree of determinism: 0=fully stochastic, 100=fully deterministic  → interpolatable

Always add a Data Availability column to the matrix:

Data Availability: 0 = data does not exist / 100 = already in hand

Ideas where Data Availability = 0 across all validation steps → classify as DEFER, not TEST_NOW.

Step 4 — Build the Matrix

Always output a markdown table before generating ideas.

Standard minimum:

Scientific hypothesis mode — required columns: | Example | Core mechanism | Degree of determinism (0–100) | Data source | Validation method | Data Availability (0–100) | Falsifiability | Major confounder |

Startup / Product mode — required columns: | Example | User pain | Data/input | Value mechanism | Monetization | Distribution | Defensibility | Data Availability (0–100) |

Step 5 — Identify Gaps

After the matrix, analyze each column using three novelty mechanisms:

Interpolation — a missing value between existing known values Extrapolation — a value beyond the current range Recombination — a new combination of existing values across rows

Output format:

## Gap Analysis
- Dimension A:
  - Existing range: [X → Y]
  - Missing intermediate values: [Z]
  - Possible extreme values: [W]
- Dimension B:
  - Existing range: [...]
  - Missing combinations: [...]

Step 5.5 — Prior Art Gate (Scientific mode only)

Apply before generating ideas when domain = scientific. This is a mandatory blocking step — Step 6 cannot start until Step 5.5 output is present.

For each candidate idea from gap analysis, run a prior art check:

Search protocol (in order):

1. If WebSearch is available → execute a real arXiv / Google Scholar search before writing output. Tag result: [PRIOR ART: SEARCHED]
2. If WebSearch is NOT available → use training knowledge, but mark explicitly: [PRIOR ART: FROM TRAINING DATA — not verified by real search] Do NOT simulate search confidence. [UNKNOWN] > false [INFERRED].

Prior Art Check per idea:
- Mechanism name → search arXiv / Google Scholar
- Year of first appearance: [UNKNOWN if not found]
- If mechanism pre-dates 2015 → Novelty score capped at 1/2
- If mechanism is well-established (textbook) → Novelty score capped at 0/2
- Keywords to search: ["mechanism name" + "key domain terms"]

Novelty Deflation Rule:

• Pre-2015 mechanism known in literature → Novelty ≤ 1 (not 2) → tag: [KNOWN]
• Textbook result (e.g., Anderson 1958, Hurst 1951) → Novelty = 0 → tag: [CLASSIC]
• Genuinely unexplored combination → Novelty = 2 ✅ → tag: [NOVEL]

If prior art is UNKNOWN: mark [PRIOR ART: NOT CHECKED] explicitly. Do NOT assume novelty without evidence. [UNKNOWN] > false [INFERRED].

Required output format (must appear before Step 6):

## 5.5 Prior Art Check
- Idea 1: [mechanism X] → first described [year/UNKNOWN] → [NOVEL/KNOWN/CLASSIC] → Novelty cap: [N/2]
  arXiv query: ["mechanism keywords"]
- Idea 2: [mechanism Y] → [PRIOR ART: NOT CHECKED] → Novelty = UNKNOWN
  arXiv query: ["mechanism keywords"]

If this block is absent → Step 6 output is incomplete. Do not skip.

Step 6 — Generate New Variants

Generate 3–5 ideas (unless user requested a different number).

Each idea must include:

• [Interpolation], [Extrapolation], or [Recombination] label in the idea heading — not in a footnote, not in a summary. Missing label = incomplete step.
• short name
• core idea
• matrix origin (which cells it combines)
• why it is non-obvious
• validation path
• score 0–10

Label enforcement rule:

### Idea 1 — [Recombination] Clinical Trial Fraud Early-Warning   ← label MUST be here

Not acceptable:

### Idea 1 — Clinical Trial Fraud Early-Warning   ← label missing → step incomplete

Do not output ideas that cannot be traced back to the matrix.

Column–mechanism consistency check (before writing each idea):

• If label = [Interpolation] → confirm the source column has a numeric/ordinal scale
• If label = [Recombination] → confirm ≥2 different matrix rows contributed
• If label = [Extrapolation] → confirm the value is beyond the observed range, not just a different category

Scoring Rubric (0–10, all ideas)

Score interpretation:

• 9–10 → unusually strong; worth prioritizing
• 7–8 → promising; worth testing
• 5–6 → interesting but needs refinement
• 3–4 → weak or too speculative
• 0–2 → discard

Scientific note: Score 9–10 = candidate for minimal experiment. Do NOT submit or publish based on matrix score alone — requires real data validation.

Novelty Deflation Guard (automatic):

• Mechanism known pre-2015 in literature → Novelty score capped at 1/2
• Textbook/classic result → Novelty score capped at 0/2
• Combined score above 8 with Novelty=0 → impossible; cap total at 8

Scientific Hypothesis Mode

When generating scientific hypotheses, add these fields to every idea:

### Hypothesis
### Mechanism
### Prediction
### Falsifiability
This hypothesis would be weakened or rejected if...
### Required Data
### Minimal Experiment
### Main Confounders
### Score: X/10

Rules:

• A hypothesis without falsifiability is not acceptable → reject it
• A hypothesis without a minimal experiment is incomplete
• If evidence is insufficient → say INSUFFICIENT_DATA, not POSSIBLE
• Prefer small validation loops over grand speculative claims
• High score ≠ evidence; score is plausibility, not confirmation

High-Risk Research Mode

For uncertain or high-stakes research, classify each idea:

Do not overstate confidence. INSUFFICIENT_DATA > false POSSIBLE.

Predictive / Time-Series Gate

Apply only if the idea involves: prediction, markets, time series, bubbles, crashes, early-warning signals, or regime shifts.

Do not apply to bioinformatics, product features, or conceptual tasks.

Check whether the idea can be evaluated using at least 3 of these independently:

• LPPLS / DS-LPPLS
• HMM / regime detection
• Hurst exponent
• MFDFA
• Early-warning signals (variance, autocorrelation)
• Out-of-sample validation

Signal rule:

< 3 independent signals available → classify as INSUFFICIENT_DATA
≥ 3 signals available → proceed with score

Output Format

## 0. Domain Detected: [mode]

## 1. Category

## 2. Existing Examples + Assumptions

## 3. Matrix
| Example | ... |

## 4. Pattern Analysis

## 5. Gap Analysis

## 5.5 Prior Art Check (scientific mode)
- Idea 1: [mechanism] → [year/UNKNOWN] → Novelty cap: [N]
- ...

## 6. Generated Ideas (TEST_NOW + REFINE_FIRST only)

**DEFER and DISCARD ideas are moved to Appendix — not shown here.**

### Idea 1 — [Interpolation / Recombination / Extrapolation]
- Core idea:
- Matrix origin: [row X col A] × [row Y col B]
- Why non-obvious:
- Prior art: [checked / NOT CHECKED]
- Validation:
- Main risk:
- Score: X/10 (Novelty: N/2 after deflation check)
- Status: TEST_NOW or REFINE_FIRST only

## 7. Recommendation
→ Strongest idea and why.
→ Prior art check needed before coding? [YES/NO]

## 8. Next Test (3-day horizon)
→ Concrete action to validate the top idea.
→ arXiv search query to verify novelty: ["mechanism keywords"]

## Appendix: Filtered Ideas
### DEFER ideas (too costly/speculative now)
[listed briefly, no full breakdown]

### DISCARD ideas (weak/redundant)
[listed briefly with one-line reason]

Quality Rules

Never:

• generate ideas without a matrix
• use vague dimensions without normalization
• present decorative creativity as strategic insight
• claim scientific validity without a validation path
• confuse plausibility with evidence
• apply Predictive Gate to non-prediction tasks
• produce more ideas when fewer stronger ideas are better
• use a categorical column as source for [Interpolation] or [Extrapolation]
• skip Step 5.5 Prior Art block — its absence makes Step 6 output incomplete
• write an idea heading without [Interpolation] / [Extrapolation] / [Recombination] label
• classify an idea as TEST_NOW when Data Availability = 0

Always:

• make assumptions explicit
• separate facts from hypotheses
• prefer falsifiable ideas
• include a score with rubric breakdown
• include a next test
• identify confounders for scientific work
• recommend the strongest option and explain why

Gotchas

• Matrix = mandatory. If user resists → explain why free brainstorming produces decorative output
• "User Context" does not belong here — keep in CLAUDE.md per project
• Score 9–10 on a matrix ≠ evidence. Score is plausibility assessment only
• Predictive Gate fires on domain keywords, not user intent — verify before applying