Input Modes#

EurekaClaw has three input modes. Pick the one that matches how well-defined your goal is.

Level 1 — Prove a Specific Conjecture#

Use prove when you have a concrete mathematical statement.

eurekaclaw prove "Any PAC-learnable class has finite VC dimension" \
    --domain "ML theory"

eurekaclaw prove "The VC dimension of depth-d width-w ReLU networks is O(wd·log(wd))" \
    --domain "deep learning theory"

eurekaclaw prove "For all n ≥ 1: Σᵢ₌₁ⁿ i = n(n+1)/2" \
    --domain "combinatorics"

The system uses your statement exactly as given — the direction-selection step is bypassed.

Tip

Writing good conjectures

  • State the result precisely, including asymptotic notation (O(...), Ω(...)) where relevant

  • Include key parameters (e.g. L layers, d dimension, ε precision)

  • Avoid vague language — prefer “runs in polynomial time” over “is efficient”

Level 2 — Start from Papers#

Use from-papers when you have specific papers you want to extend or find gaps in.

# Attention mechanism papers
eurekaclaw from-papers 1706.03762 2005.14165 \
    --domain "attention mechanisms"

# Bandit theory papers
eurekaclaw from-papers 1602.01783 2106.01336 \
    --domain "multi-armed bandits"

The SurveyAgent fetches and analyses the papers. The IdeationAgent identifies research gaps and generates 5 candidate directions. The best-scoring direction is selected automatically, or by you with --gate human.

Level 3 — Open Exploration#

Use explore when you have a broad research area but no specific conjecture.

# Broad domain exploration
eurekaclaw explore "spectral graph theory"

# Domain + guiding question
eurekaclaw explore "multi-armed bandit theory" \
    --query "What are the tightest known bounds for heavy-tailed rewards?"

# Pure math
eurekaclaw explore "algebraic topology" \
    --query "What are open problems in persistent homology?"

The system autonomously surveys the frontier, identifies open problems, proposes 5 directions, and selects the most promising one.

Note

Direction planning fallback If the direction planner fails or returns an empty list, the pipeline pauses and prompts you to enter a research direction manually. Up to 5 open problems from the survey are shown as context.