Exact named statement
∀ x. ∀ y. ∀ z. ∀ n. ∀ m. ∀ k. x · x + y · y = m + (x · y + y · x) → z · z + n · n = k + (z · n + n · z) → ¬(x = y ∧ z = n) → ∃ i. m + S i = 2 · k ∨ 2 · k + S i = mNo displayed named abbreviation.
Complete certificate and independent checks
210 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: 7a0c83cccc0c50cb487d5dda5fc177677b4aeb7758ac7179e2f46023dcccd4c5
Bundle SHA-256: 3b4257b6bd12ed44eb2de6342652a69480045fc09fe63dd62b9d94d0eabb2dc6
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
signed norm integer gap not full IR032
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.