ProofAtlas

Lean evidence record

Napoleon’s Theorem — Algebraic Core: Lean evidence

This technical record binds the exact theorem statement to its commit-pinned Lean source, checker results, assumptions, and publication-review status.

Read theorem page
Lean buildpassed
Unfinished proof stepsNone
Publication reviewsAccepted

Exact formal proposition

Hypotheses and conclusion

This is the meaningful proposition proved by the checked wrapper declaration. It is extracted from the same commit-pinned Lean source.

noncomputable def NapoleonTheoremStatement : Prop :=
  ∀ ω a b c : ℂ,
    IsSixtyDegreeRotationParameter ω →
      let ab := orientedEquilateralApex ω a b
      let bc := orientedEquilateralApex ω b c
      let ca := orientedEquilateralApex ω c a
      let cab := centroid a b ab
      let cbc := centroid b c bc
      let cca := centroid c a ca
      IsEquilateralBy (1 - ω) cab cbc cca
Definitions used in this proposition

IsSixtyDegreeRotationParameter

def IsSixtyDegreeRotationParameter (ω : ℂ) : Prop :=
  ω ^ 2 - ω + 1 = 0

orientedEquilateralApex

def orientedEquilateralApex (ω a b : ℂ) : ℂ :=
  a + ω * (b - a)

centroid

noncomputable def centroid (a b c : ℂ) : ℂ :=
  (a + b + c) / 3

IsEquilateralBy

def IsEquilateralBy (ω x y z : ℂ) : Prop :=
  z - x = ω * (y - x)
Lean wrapper declaration

The checked endpoint names the expanded proposition above. Both come from the same commit-pinned source.

theorem napoleonTheorem : NapoleonTheoremStatement
Open main Lean file

Line counts exclude blank lines; comments and documentation count. The total is the commit-pinned first-party Lean import closure; Mathlib and other third-party dependencies are excluded.

Technical evidence record

Source identity, checker results, and assumptions

Main Lean declaration
napoleonTheorem
Source commit
4ce4e5b03e56

Mechanical evidence

Lean verification

These fields support the exact Lean declaration, not a broader informal claim.

Artifact ID
artifact.known-napoleon-theorem.algebraic-core.v002
Accepted-result title
Accepted Result: Napoleon Theorem Algebraic Core
Accepted-result status
Accepted formalization of a known theorem
Accepted-result boundary
This target records the algebraic complex-plane Napoleon core with an abstract parameter omega satisfying omega^2 - omega + 1 = 0. Non-claim: This is not reviewed public external-triangle diagram wording. Non-claim: This does not instantiate exp(pi i / 3). Non-claim: This accepted-result record does not establish novelty and does not by itself authorize public export or deployment.
Declarations covered by recorded evidence
AtlasKnownTheorems.NapoleonTheorem.napoleonTheorem
AtlasKnownTheorems.NapoleonTheorem.NapoleonTheoremStatement
AtlasKnownTheorems.NapoleonTheorem.napoleon_centroid_relation
AtlasKnownTheorems.NapoleonTheorem.napoleonTheorem_statement
Lean build
passed
Recorded build time
2.4 s one machine-dependent evidence run, not a benchmark
Evidence collected
· clean-source provenance recorded
Unfinished proof check
passed
Lean toolchain
leanprover/lean4:v4.29.1
Recorded source commit
4ce4e5b03e563bdd063533b37a9c60ca3cfee707
Source SHA-256
sha256:3a4a917dec8fbd0c2e502245ca841423fbfd9556bfdb5945f8a0a7618d0d6326
Statement alignment
accepted

Lean foundations

Standard foundations used by the proof

Lean reports the logical foundations below through Mathlib. They are standard proof-system foundations, not conjectural mathematical assumptions about this theorem. The recorded closure stays within the approved classical_mathlib_standard profile, with no unexpected axiom or unfinished-proof placeholder.

  • Classical.choice
  • Quot.sound
  • propext

Files and machine-readable evidence

Reproduce or inspect the recorded check

Use the complete first-party source bundle for reconstruction, or inspect the exact main file and checker evidence separately. Mathlib and other third-party dependencies are identified but not rebundled.

Complete checked Lean source · 1 Lean file · 1 evidence record · Download ZIPBrowse counted source onlineDownload main Lean fileDownload checker evidence (JSON)Download Apache-2.0 license

Review results

Publication reviews accepted

All four required publication-review gates are accepted for the reviewed presentation of this exact theorem. The review results are separate from the Lean build and do not broaden the formal statement.

Read the publication-review details