Exact named statement
forall k d s D ab ac x p wb wc tb tc w0 f h y. ((Factorial(S(2*k),D)) /\ ((~D=0) /\ ((NatSqrt2ExpSample(k,d,s,D,ab,ac,x,p,wb,wc,tb,tc,w0,f,h,y)) /\ (~w0=0)))) \/ ~((Factorial(S(2*k),D)) /\ ((~D=0) /\ ((NatSqrt2ExpSample(k,d,s,D,ab,ac,x,p,wb,wc,tb,tc,w0,f,h,y)) /\ (~w0=0))))Complete certificate and independent checks
174 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: 0bfc201f0143e0b3fb6e1b1b1a23ea925cf898cbfb266cbfb272ce264b3275cd
Bundle SHA-256: 8a300a0f1234e476a3ad2e12a5d7bea7320b757d76fb8138689c7b2eff25a6ce
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
constructively decide the entire supplied prescribed factorial sample and positive scale output denominator by sequentially checking every actual computation field without assuming correctness accuracy or canonical record construction
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.