HA + independent Lean evidence · Research, not Alpha admission

QH001 — quadratic height

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

Exact named statement

forall ap an bp bn cp cn dp dn rp rn sp sn a b c. IQuadCanonicalProduct(ap,an,bp,bn,cp,cn,dp,dn,rp,rn,sp,sn) ->
  IQuadHeight(ap,an,bp,bn,a) ->
  IQuadHeight(cp,cn,dp,dn,b) ->
  IQuadHeight(rp,rn,sp,sn,c) ->
  exists gap. gap+c=a*b

ND0394 — IQuadCanonicalProduct · ND0395 — IQuadHeight

Fully expanded target AST

Complete certificate and independent checks

13 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: b9459095385fa95c3e8d4d7ff638db6464c2053389c1921031dabfe88560f7e6
Bundle SHA-256: d23dff4f88d369f48781cbe4293f474c6c16308a5679661b6cdd5295eb4c88ba

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

canonical integer quadratic binary height not finite or real IR046

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