HA + independent Lean evidence · Research, not Alpha admission

QN001 — quadratic nonzero

Full irrationality (IR072/G121) remains open. Stable: 432. Alpha v35: 4,318. This checkpoint changes neither catalogue.

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.

Fully expanded target AST

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.

IR016 · SI001 · SN001 · SN003

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.