Exact named statement
forall k d s D ab ac x p wb wc tb tc w0 f h y. ~D=0 ->
NatSqrt2ExpSample(k,d,s,D,ab,ac,x,p,wb,wc,tb,tc,w0,f,h,y) ->
(~w0=0) /\ ((~((D*p)*s)=0) /\ ((Le(((3*x)*d),((D*p)*s))) /\ ((NatScaledExpRecurrence(((D*p)*s),((3*x)*d),tb,tc,(k+2))) /\ (forall j t f0 p0 q. Le(j,(k+2)) ->
BetaAt(tb,tc,j,t) ->
Factorial(j,f0) ->
Pow(((D*p)*s),j,p0) ->
Pow(((3*x)*d),j,q) ->
(t*f0)*p0=w0*q))))PD0013 — BetaAt · PD0020 — Pow · PD0001 — Le · PD0023 — Factorial · ND0443 — NatScaledExpRecurrence · ND0448 — NatSqrt2ExpSample
Complete certificate and independent checks
152 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: 2579d5bd54a8bf1f91831ce86386ca747605c6022da544548553dc22186cb198
Bundle SHA-256: 07e3c3a0d8f95c3c80461832be66d79d54ccd6da2c213b6995af7c451fc22669
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
every supplied finite exponential sample with positive coefficient scale has nonzero input and output denominators input at most one exact same table recurrence and all index factorial normalization no replacement computation
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.