Exact named statement
forall r x y k a b. ~k=0 ->
Le(k,x+y) ->
Le(r*(x*x),r*(y*y)+a*(k*k)) ->
Le(r*(y*y),r*(x*x)+b*(k*k)) ->
Le(r*x,r*y+a*k) /\ Le(r*y,r*x+b*k)Complete certificate and independent checks
31 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: f1e75bcb47244d65e8f878a65bf2a5d7d7328ac4d6b03d2211b360a44946610c
Bundle SHA-256: a69169cdb3b811afc5b43e104aae815589b7f6c60381eb67edd17d5543986487
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
convert two supplied natural square errors to linear errors by decidable order actual additive gaps difference of squares and positive scale cancellation without an analytic square root assumption
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.