Exact named statement
forall n. exists r d lb lc x q wb wc ab ac h f t z u. (Pow(2,n,r)) /\ ((~r=0) /\ ((~d=0) /\ ((NatAtanhPrefix(d,lb,lc,S(S(18*r)))) /\ ((NatHornerValue(lb,lc,3,S(S(18*r)),x)) /\ ((Pow(3,S(S(18*r)),q)) /\ ((~q=0) /\ ((~(d*q)=0) /\ ((Le(3*x,d*q)) /\ ((~h=0) /\ ((NatExpWeightTable(2*(d*q),(S(S(S(18*r))))+(S(S(18*r))),wb,wc)) /\ ((NatPowerWeightedPrefix(3*x,wb,wc,ab,ac,S((S(S(S(18*r))))+(S(S(18*r)))))) /\ ((BetaAt(wb,wc,0,h)) /\ ((BetaAt(ab,ac,0,h)) /\ ((Factorial((S(S(S(18*r))))+(S(S(18*r))),f)) /\ ((Pow(2*(d*q),(S(S(S(18*r))))+(S(S(18*r))),t)) /\ ((h=f*t) /\ ((Sum(ab,ac,S((S(S(S(18*r))))+(S(S(18*r)))),z)) /\ ((NatScaledExpRecurrence(2*(d*q),3*x,ab,ac,(S(S(S(18*r))))+(S(S(18*r))))) /\ ((Sum(ab,ac,S(S(S(18*r))),u)) /\ ((Le(r*(u*u),(r*2)*(h*h)+3*(h*h))) /\ (Le((r*2)*(h*h),r*(u*u)+(h*h)))))))))))))))))))))))PD0001 — Le · PD0013 — BetaAt · PD0015 — Sum · ND0423 — NatExpWeightTable · PD0020 — Pow · PD0023 — Factorial · ND0437 — NatHornerValue · ND0425 — NatAtanhPrefix · ND0442 — NatPowerWeightedPrefix · ND0443 — NatScaledExpRecurrence
Complete certificate and independent checks
535 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: b66c87c593359c085b44249ad7621de4058ef1ab24fbba8de8d70e15ef26af40
Bundle SHA-256: bcfc3286e107e3bdd1183f92793abd07c53a65c28f685c9f8f147cde6b08dc08
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.
AP032 · AP033 · AP034 · AP037 · AP038 · AP040 · AP041 · AP042 · AP043 · AP044 · AP045 · AP046 · CV001 · CV002 · CV004 · CV008 · CV009 · CV011 · CV012 · CV019 · CV020 · CV021 · CV022 · CV024 · CV025 · CV027 · CV028 · CV029 · CV030 · CV031 · CV032 · CV033 · CV037 · CV038 · CV039 · CV043 · CV044 · CV046 · CV047 · CV048 · CV049 · CV056 · CV057 · CV058 · CV059 · CV060 · CV061 · CV062 · CV063 · CV064 · CV065 · CV068 · CV069 · CV070 · CV072 · CV073 · CV075 · CV077 · CV078 · CV079 · CV081 · CV082 · CV083 · CV084 · CV086 · CV087 · CV088 · CV094 · CV095 · CV096 · CV097 · CV098 · CV100
Scope
construct the actual atanh horner half logarithm exponential and prove its short sum square has upper error three over two to n and lower error one over two to n with positive normalization without identifying an infinite exponential or sqrt two
None of these finite arithmetic statements closes an IR campaign parent. The analytic identification, interpolation and final positive irrationality certificate remain open.