Reasoning you can check

Is n² + n even for every integer n?
n² + n = n(n + 1)
n, n + 1 consecutive
One of them is even
01
Decompose
Breaks a question into claims small enough to check one at a time.
- Factorisation holds✓ proof checked
- Consecutive integers alternate parity✓ proof checked
- Product with an even factor is even✓ proof checked
02
Check
Verifies each claim with code, a proof assistant, a search or a second model.
0.97confidence · above threshold
03
Score
Gives every step a calibrated confidence, so people know where to look first.
⚑ 0.62 · pattern, not proofSmall cases look like squares
Reviewer
04
Review
Sends the steps it is least sure of to a person before anything counts.
claim · n² + n = n(n + 1)
check · lean · passed
score · 0.97
review · approved by reviewer
Trace saved · trace_4f2a
05
Record
Keeps the whole trace: every claim, check and decision, ready to audit.

Try Lemma

Pick an example or ask your own question. Flagged steps open to show why.

Recorded trace

What is the sum of the first 100 odd numbers?

For developers

One engine.
Every step on record.

Every Lemma answer comes back as a trace: each claim, the check behind it, its confidence, and what went to a person. There is no public API yet; these are sample traces.

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{
  "id": "odd",
  "question": "What is the sum of the first 100 odd numbers?",
  "steps": [
    {
      "kind": "claim",
      "text": "The first 100 odd numbers are 1, 3, 5, …, 199.",
      "confidence": 0.99,
      "status": "verified"
    },
    {
      "kind": "claim",
      "text": "Small cases look like perfect squares: 1, 4, 9, 16.",
      "confidence": 0.62,
      "status": "flagged",
      "flag": "Pattern, not proof",
      "why": "A few matching cases suggest a pattern but do not prove it, so Lemma proves the general case by induction before this step counts."
    },
    {
      "kind": "check",
      "text": "Proving 1 + 3 + … + (2n − 1) = n² by induction",
      "result": "Proof checked"
    },
    {
      "kind": "claim",
      "text": "Base case holds. Adding 2n + 1 to n² gives (n + 1)², so it holds for every n.",
      "confidence": 0.99,
      "status": "verified"
    }
  ],
  "answer": {
    "text": "100² = 10,000",
    "confidence": 0.99
  },
  "source": "recorded"
}