Alphabeta Math
ExampleConstruction: AI-adaptedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-08-30
How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Stirling's approximation for 10!

Example

Using Stirling's leading term at z=11 gives

10!=Γ(11)≈2π 1121/2e−11≈3.60×106,

while the exact value is 3,628,800.

Facts & Assumptions

Given: Stirling's asymptotic and the factorial values of Gamma.

[L1]

Γ(n+1)=n! for integers n≥0 (Gamma at the positive integers).

[L2]

Stirling's formula for Gamma is Γ(z)∼2π zz−1/2e−z on the positive real axis as part of the sectorial asymptotic (Stirling's formula for Gamma).

Verification

technique · direct
1.1

By [L1], 10!=Γ(11).

L1given
2.1

Applying [L2] at z=11 gives the displayed leading-term approximation. The comparison with the exact factorial from step 1.1 shows the scale and the size of the first neglected correction.

step 1.1L2algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources