SN001 — signed norm

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) → m = 2 · k → x = y ∧ z = n

No displayed named abbreviation.

Fully expanded target AST

Complete certificate and independent checks

206 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: c948aa0e7350e5c51c464721215573a489b0921c9d1a3263c9c5181f20164941
Bundle SHA-256: 5685db9bdbe1ceb79e29a25dff767c519ccf424705a1e395dad5fcb3b01911de

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.

IR016

Scope

signed norm zero core not IR032

None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.