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theory-assumption-extractor

theory-assumption-extractor

github.com/jurgendnProductivity1153 installsUpdated 6w ago
Repository

About theory-assumption-extractor

A theory-analysis skill for researchers checking what a theorem or empirical conclusion depends on. It surfaces explicit and hidden assumptions, traces where they enter an argument, classifies their role, and considers what changes when they are weakened or removed.

Key features

  1. 01States the target claim precisely
  2. 02Separates explicit and hidden assumptions
  3. 03Traces assumptions to proof or empirical steps
  4. 04Classifies assumptions by necessity and strength
  5. 05Explains what breaks when assumptions are removed
  6. 06Suggests plausible weaker alternatives

Use cases

  1. 01Auditing assumptions behind a theorem
  2. 02Checking premises hidden in a cited result
  3. 03Assessing whether an experiment relies on distributional assumptions
  4. 04Finding possible relaxations of a model's conditions

Install

Copy the command and run it in a terminal.

$npx skills add https://github.com/jurgendn/agent-skills --skill theory-assumption-extractor

After installing, type/theory-assumption-extractorin Claude Code to confirm it loaded.

Details

From the project README

Assumption Extractor

Make hidden premises visible before trusting the conclusion.

A strong result often depends on assumptions that are:

  • implicit;
  • buried in notation;
  • hidden inside a theorem citation;
  • or introduced indirectly through the proof technique.

The goal is not merely to list assumptions.
The goal is to determine:

  • which assumptions are structurally necessary;
  • which are artifacts of the proof;
  • and what fails if they are removed.

Procedure

1. State the Target Claim

Write the conclusion precisely.

Bad:

The method converges.

Better:

The estimator converges almost surely to the true parameter
under increasing sample size.

The claim should specify:

  • variables;
  • regime;
  • convergence notion;
  • probabilistic qualifier;
  • comparison target.

2. Extract Explicit Assumptions

List assumptions stated directly in the theorem, model, or experiment.

Example:

Explicit assumptions:
- graph is connected;
- loss function is convex;
- samples are IID;
- Markov chain is reversible.

Separate:

  • mathematical assumptions;
  • statistical assumptions;
  • computational assumptions;
  • data-generation assumptions.

3. Search for Hidden Assumptions

Inspect every proof step, approximation, and empirical claim.

Common hidden assumptions include:

Regularity Assumptions
  • smoothness;
  • Lipschitz continuity;
  • differentiability;
  • bounded gradients.
Structural Assumptions
  • convexity;
  • sparsity;
  • low rank;
  • separability;
  • stationarity.
Probabilistic Assumptions
  • independence;
  • exchangeability;
  • concentration;
  • sub-Gaussian tails;
  • ergodicity.
Identifiability Assumptions
  • uniqueness of optimum;
  • invertibility;
  • sufficient excitation;
  • non-degenerate covariance.
Asymptotic Assumptions
  • large-sample regime;
  • vanishing noise;
  • fixed dimension;
  • infinite-time horizon.
Empirical Assumptions
  • train/test distributions match;
  • benchmark labels are reliable;
  • preprocessing does not leak information.

4. Identify Where Each Assumption Enters

Do not merely list assumptions.
State where the argument actually uses them.

Example:

Convexity is required when applying Jensen's inequality
during the convergence proof.

Independence is used only in the concentration step.

This separates:

  • logically necessary assumptions;
  • proof-specific assumptions.

5. Classify Assumptions

For each assumption, label it as:

Essential

Removing it invalidates the claim itself.

Example:

Connectivity is essential for global mixing.
Proof Convenience

Used to simplify analysis but may not be fundamentally required.

Example:

Bounded degree simplifies concentration bounds
but may not be strictly necessary.
Likely Overkill

Stronger than needed.

Example:

Global Lipschitz continuity may only be needed locally.

6. Test Assumption Removal

Ask:

What breaks if this assumption is removed?

Be specific.

Bad:

The proof becomes harder.

Better:

Without reversibility, the spectral decomposition step fails
because orthogonal eigenbasis arguments no longer apply.

7. Suggest Weaker Alternatives

Where possible, replace strong assumptions with weaker ones.

Examples:

Strong AssumptionPossible Relaxation
IID samplesMixing process
Global convexityLocal convexity
Bounded supportFinite variance
Exact sparsityApproximate sparsity
Deterministic graphRandom graph ensemble

Do not claim the weaker version works unless the proof pathway is plausible.

Rules

  • Distinguish logical necessity from proof convenience.
  • Hidden assumptions inside cited theorems still count.
  • If removing an assumption breaks the argument, state exactly where.
  • Avoid treating asymptotic assumptions as automatically realistic.
  • Separate:
    • mathematically sufficient;
    • empirically plausible;
    • computationally feasible.
  • Do not confuse “common in literature” with “necessary.”

Output Format

# Target Claim

...

# Explicit Assumptions

- ...

# Hidden Assumptions

| Assumption | Where It Enters | Essential or Convenient | What Breaks Without It |
|---|---|---|---|
| ... | ... | ... | ... |

# Likely Over-Strong Assumptions

- ...

# Possible Weaker Alternatives

| Original Assumption | Possible Relaxation |
|---|---|
| ... | ... |

# Main Structural Dependency

State the single assumption the argument depends on most heavily.

# Risk Assessment

Which assumptions are:
- mathematically fragile;
- empirically unrealistic;
- difficult to verify in practice.

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