Exact named statement
∀ x. ∀ y. ∀ z. ∀ n. ∀ m. ∀ k. ∀ i. ∀ j. ∀ u. ∀ v. ∀ w. ∀ x0. u + (x · k + y · m + 2 · (z · j + n · i)) = x · m + y · k + 2 · (z · i + n · j) + v → w + (x · j + y · i + (z · k + n · m)) = x · i + y · j + (z · m + n · k) + x0 → ¬(x = y ∧ z = n) → ¬(m = k ∧ i = j) → ¬(u = v ∧ w = x0)No displayed named abbreviation.
Complete certificate and independent checks
221 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: f4d0bc4f03497b4b9d2b601380b0958486e631f8a2c5f4d0b647b43662f18ca9
Bundle SHA-256: faeb2544f48735855f80ba183dc596190cc4d788f804ed57af793bd6a7b89aa3
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
quadratic integer binary nonzero not finite IR046
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.