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. ~D=0 ->
~E=0 ->
NatSqrt2ExpSample(k,d,s,D,ab,ac,x,p,wb,wc,tb,tc,w0,f,h,y) ->
NatSqrt2ExpSample(k+l,q,t,E,bb,bc,z,v,xb,xc,ub,uc,v0,g,j,o) ->
(~d=0) /\ ((~w0=0) /\ ((~v0=0) /\ ((Le(d*(w0*o),d*(v0*y)+((9*3)+2)*(w0*v0))) /\ (Le(d*(v0*y),d*(w0*o)+((9*3)+2)*(w0*v0))))))Complete certificate and independent checks
297 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: 2ea71d464e47c52e625a986dcb55ac5c92ff24daf2fd7b95c71d36d58aad8634
Bundle SHA-256: e02a1654a4fa32bfa0c52da1c745d22083dc69a1eaf362ee3950df341d422a73
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.
AP003 · AP004 · AP005 · AP006 · AP007 · AP008 · AP009 · AP010 · AP011 · AP012 · CV009 · CV032 · CV062 · CV068 · CV086 · CV087 · CV088 · CV089 · CV090 · CV092 · CV093 · CV094 · CV095 · CV096 · CV097 · CV098 · CV100 · SQ001 · SQ002 · SQ003 · SQ004 · SQ005 · SQ006 · SQ007 · SQ008 · SQ009 · SQ010
Scope
actual supplied samples have positive output denominators and uniform two sided dyadic error for every precision increment including zero by constructive case split and exact value independence
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.