Exact named statement
1 = 1 ∧ (1 = 1 · 1 ∧ 2 · 1 = 2 · 1 · 1) ∧ (2 · S (2 · 1) = S (2 · 1) · (2 · 1) ∧ (2 · (2 · (2 · S (2 · 1))) = 2 · (2 · 1) · (2 · S (2 · 1)) ∧ 2 · (2 · (2 · S (2 · S (2 · S (2 · 1))))) = S (2 · (2 · 1)) · (2 · (2 · (2 · S (2 · 1))))))No displayed named abbreviation.
Complete certificate and independent checks
39 actual local proof nodes. Each node carries its complete ordinary HA proof body.
Full canonical proof bundle · Original HA receipt · Independent Lean receipt
Target SHA-256: 4a60e8f9088cac962514a8c81c382ce8c690d2c0342b7ef74876dd40d8a15002
Bundle SHA-256: 9cac06c9d494e86d88aa7dff44e2fed35a5ef33f387f292aefa9c207a9f3bb57
Checked statement containment
These exact targets occur inside this certificate. These links summarize containment, not direct dependency arrows; the downloadable bundle records every private lemma and ordered edge.
Scope
complete exact subconjunction child
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.