Exact named statement
forall k l d s D ab ac x p wb wc tb tc w0 f h y q t E bb bc z v xb xc ub uc v0 g j o r. ~D=0 ->
~E=0 ->
NatSqrt2ExpSample(k,d,s,D,ab,ac,x,p,wb,wc,tb,tc,w0,f,h,y) ->
NatSqrt2ExpSample(k+S l,q,t,E,bb,bc,z,v,xb,xc,ub,uc,v0,g,j,o) ->
Pow(2,k+2,r) ->
(~d=0) /\ ((~p=0) /\ ((~r=0) /\ ((~w0=0) /\ ((~v0=0) /\ ((Le((p*r)*(w0*o),(p*r)*(v0*y)+((9*3)*r+2*p)*(w0*v0))) /\ (Le(d*(v0*y),d*(w0*o)+9*(w0*v0))))))))Complete certificate and independent checks
273 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: 073e1e33119841ca820f40504b4be88839cec838afc45b6028bda6807fa464dd
Bundle SHA-256: b30e8f3596e922ae6f3391b2bab3b75574459487def0a796d30dba6d283933df
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.
AP004 · AP006 · AP007 · AP008 · CV009 · CV032 · CV062 · CV068 · CV086 · CV087 · CV088 · CV089 · CV090 · CV092 · CV093 · CV094 · CV095 · CV096 · CV097 · CV098 · CV100 · SQ002 · SQ005 · SQ006 · SQ007 · SQ008 · SQ009 · SQ010
Scope
actual supplied samples at k and k plus positive increment have scale free two sided finite errors with positive output and cutoff denominators without input monotonicity or analytic limit claims
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.