Exact named statement
∀ x. ∀ y. ¬x = y → ∃ z. x + S z = y ∨ y + S z = xNo displayed named abbreviation.
Complete certificate and independent checks
3 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: f0598e325456d7992079c20535c5d15740fb9f4a35c1a2619d5983c7ac9ac64b
Bundle SHA-256: e614473e462f9589988e7526d85de6427c03caca9edc9fc8ca5285514d1b1cc5
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
universal natural gap not full campaign
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.