Exact named statement
forall k d s D ab ac x p. ~D=0 ->
NatSqrt2LogArgument(k,d,s,D,ab,ac,x,p) ->
(~d=0) /\ ((~s=0) /\ ((~p=0) /\ ((~(D*p)=0) /\ ((~((D*p)*s)=0) /\ ((~(2*((D*p)*d))=0) /\ ((Le(((3*x)*d),((D*p)*s))) /\ ((Le(((3*x)*s),(2*((D*p)*d)))) /\ ((Le(((D*p)*s)*((3*x)*s),(2*((D*p)*d))*((3*x)*d))) /\ (Le(d*((2*((D*p)*d))*((3*x)*d)),d*(((D*p)*s)*((3*x)*s))+2*(((D*p)*s)*(2*((D*p)*d)))))))))))))Complete certificate and independent checks
69 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: 244e83e9bb6930441b55dd6bc755802920abede937100ccbd61c180210112cf3
Bundle SHA-256: d8a884f082830521daf08ad2866919f91894adbf5dcff76af374cdc6049f2ec5
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
compare supplied original log root quotient with half root argument proving both denominators positive unit interval bounds and explicit two over d square residual without an exact finite or analytic identity
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.