Exact named statement
∀ x. ∀ y. ∀ z. ∀ n. ∀ m. ∀ k. ∀ i. ∀ j. ∀ u. ∀ v. ∀ w. ∀ x0. ∀ x1. ∀ x2. ¬m = 0 ∧ (¬v = 0 ∧ x · v + i · m = y · v + k · m) → ¬m = 0 ∧ (¬v = 0 ∧ z · v + u · m = n · v + j · m) → x · x + y · y = w + (x · y + y · x) → z · z + n · n = x0 + (z · n + n · z) → k · k + i · i = x1 + (k · i + i · k) → j · j + u · u = x2 + (j · u + u · j) → ¬m · m = 0 ∧ (¬v · v = 0 ∧ w · (v · v) + 2 · x2 · (m · m) = 2 · x0 · (v · v) + x1 · (m · m))No displayed named abbreviation.
Complete certificate and independent checks
29 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: db34efff2aecd8c2f5afdb13cad631533c9dd9cbe2de2a878318cd31ac2290da
Bundle SHA-256: 795cd64495f9ab37dc7b12add368225567bbb63bcca6e1f698ffbd08db431667
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
rational norm representative transport not full IR031
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.